Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Biomechanics of the Human Osteochondral Unit: A Systematic Review

The damping system ensured by the osteochondral (OC) unit is essential to deploy the forces generated within load-bearing joints during locomotion, allowing furthermore low-friction sliding motion between bone segments. The OC unit is a multi-layer structure including articular cartilage, as well as subchondral and trabecular bone. The interplay between the OC tissues is essential in maintaining the joint functionality; altered loading patterns can trigger biological processes that could lead to degenerative joint diseases like osteoarthritis. Currently, no effective treatments are available to avoid degeneration beyond tissues' recovery capabilities. A thorough comprehension on the mechanical behaviour of the OC unit is essential to (i) soundly elucidate its overall response to intra-articular loads for developing diagnostic tools capable of detecting non-physiological strain levels, (ii) properly evaluate the efficacy of innovative treatments in restoring physiological strain levels, and (iii) optimize regenerative medicine approaches as potential and less-invasive alternatives to arthroplasty when irreversible damage has occurred. Therefore, the leading aim of this review was to provide an overview of the state-of-the-art-up to 2022-about the mechanical behaviour of the OC unit. A systematic search is performed, according to PRISMA standards, by focusing on studies that experimentally assess the human lower-limb joints' OC tissues. A multi-criteria decision-making method is proposed to quantitatively evaluate eligible studies, in order to highlight only the insights retrieved through sound and robust approaches. This review revealed that studies on human lower limbs are focusing on the knee and articular cartilage, while hip and trabecular bone studies are declining, and the ankle and subchondral bone are poorly investigated. Compression and indentation are the most common experimental techniques studying the mechanical behaviour of the OC tissues, with indentation also being able to provide information at the micro- and nanoscales. While a certain comparability among studies was highlighted, none of the identified testing protocols are currently recognised as standard for any of the OC tissues. The fibril-network-reinforced poro-viscoelastic constitutive model has become common for describing the response of the articular cartilage, while the models describing the mechanical behaviour of mineralised tissues are usually simpler (i.e., linear elastic, elasto-plastic). Most advanced studies have tested and modelled multiple tissues of the same OC unit but have done so individually rather than through integrated approaches. Therefore, efforts should be made in simultaneously evaluating the comprehensive response of the OC unit to intra-articular loads and the interplay between the OC tissues. In this regard, a multidisciplinary approach combining complementary techniques, e.g., full-field imaging, mechanical testing, and computational approaches, should be implemented and validated. Furthermore, the next challenge entails transferring this assessment to a non-invasive approach, allowing its application in vivo, in order to increase its diagnostic and prognostic potential.

Prediction of moisture content for a single maize kernel based on viscoelastic properties

BACKGROUND

The rapid and accurate detection of moisture content is important to ensure maize quality. However, existing technologies for rapidly detecting moisture content often suffer from the use of costly equipment, stringent environmental requirements, or limited accuracy. This study proposes a simple and effective method for detecting the moisture content of single maize kernels based on viscoelastic properties.

RESULTS

Two types of viscoelastic experiments were conducted involving three different parameters: relaxation tests (initial loads: 60, 80, 100 N) and frequency-sweep tests (frequencies: 0.6, 0.8, 1 Hz). These experiments generated corresponding force-time graphs and viscoelastic parameters were extracted based on the four-element Maxwell model. Then, viscoelastic parameters and data of force-time graphs were employed as input variables to explore the relationships with moisture content separately. The impact of different preprocessing methods and feature time variables on model accuracy was explored based on force-time graphs. The results indicate that models utilizing the force-time data were more accurate than those utilizing viscoelastic parameters. The best model was established by partial least squares regression based on S-G smoothing data from relaxation tests conducted with initial force of 100 N. The correlation coefficient and the root mean square error of the calibration set were 0.954 and 0.021, respectively. The corresponding values of the prediction set were 0.905 and 0.029, respectively.

CONCLUSIONS

This study confirms the potential for accurate and fast detection of moisture content in single maize kernels using viscoelastic properties, which provides a novel approach for the detection of various components in cereals. © 2024 Society of Chemical Industry.

Research on the Hot Deformation Process of A100 Steel Based on High-Temperature Rheological Behavior and Microstructure

To obtain the optimal hot deformation process, the rheological and dynamic recrystallization behaviors of A100 steel were researched through isothermal compression tests. Firstly, a Hensel-Spittel constitutive model was established based on the stress-strain curves. Secondly, dynamic recrystallization percentage and grain size models were established to identify the necessary conditions for complete dynamic recrystallization. Finally, microstructural analysis was employed to validate the accuracy of the recrystallization model. The results indicate that the flow stress is highly sensitive to both the strain rate and the temperature, and the HS model demonstrates a high predictive accuracy, with a correlation coefficient of 0.9914. There exists a contradictory relationship between decreasing the average grain size and increasing the recrystallization percentage. The higher the percentage of dynamic recrystallization, the larger the average grain size tends to be. This situation should be avoided when devising the actual processing procedures. The optimal hot working processes for achieving complete dynamic recrystallization and a smaller average grain size are as follows: a strain equal to or greater than 0.6, a temperature between 1193 and 1353 K, and a strain rate between 0.1 and 1 s-1.

Developing a New Constitutive Model of High Damping Rubber by Combining GRU and Attention Mechanism

High damping rubber (HDR) bearings are extensively used in seismic design for bridges due to their remarkable energy dissipation capabilities, which is critical during earthquakes. A thorough assessment of crucial factors such as temperature, rate, experienced maximum amplitude, and the Mullins effect of HDR on the mechanics-based constitutive model of HDR is lacking. To address this issue, we propose a deep learning approach that integrates the Gate Recurrent Unit (GRU) and attention mechanism to identify time series characteristics from compression-shear test data of HDR specimens. It is shown that the combination of GRU and attention mechanism enables accurate prediction of the mechanical behavior of HDR specimens. Compared to the sole use of GRU, this suggested method significantly reduces model complexity and computation time while maintaining good prediction performance. Therefore, it offers a new approach to constructing the HDR constitutive model. Finally, the HDR constitutive model was used to analyze the impact of experienced maximum amplitudes and cycles on following processes. It was observed that maximum amplitudes directly influence the stress-strain relationship of HDR during subsequent processes. Consequently, a solid foundation is laid for evaluating the responses of HDR bearings under earthquakes.

Calculation of and Key Influencing Factors Analysis on Equivalent Resilient Modulus of a Submerged Subgrade

To calculate and analyze the equivalent resilient modulus of a submerged subgrade, a constitutive model considering the effect of saturation and matrix suction was introduced using ABAQUS's user-defined material (UMAT)subroutine. The pavement response under falling weight deflectometer (FWD) load was simulated at various water levels based on the derived distribution of the resilient modulus within the subgrade. The equivalent resilient modulus of the subgrade was then calculated using the equivalent iteration and weighted average methods. Based on this, the influence of the material and structural parameters of the subgrade was analyzed. The results indicate that the effect of water level rise on the tensile strain at the bottom of the asphalt layer and the compressive strain at the top of the subgrade is obvious, and its trend is similar to an exponential change. The equivalent resilient modulus of the subgrade basically decreases linearly with the rise in the water level, and there is high consistency between the equivalent iteration and weighted average methods. The saturated permeability coefficient and subgrade height have the most significant effect on the resilient modulus of the subgrade, which should be emphasized in the design of submerged subgrades, and the suggested values of the resilient modulus of the subgrade should be proposed according to the relevant construction conditions.

Effects of C and Al Alloying on Constitutive Model Parameters and Hot Deformation Behavior of Medium-Mn Steels

Single-pass isothermal hot compression tests on four medium-Mn steels with different C and Al contents were conducted using a Gleeble-3500 thermal simulation machine at varying deformation temperatures (900-1150 °C) and strain rates (0.01-5 s-1). Based on friction correction theory, the friction of the test stress-strain data was corrected. On this basis, the Arrhenius constitutive model of experimental steels considering Al content and strain compensation and hot processing maps of different experimental steels at a strain of 0.9 were established. Moreover, the effects of C and Al contents on constitutive model parameters and hot processing performance were analyzed. The results revealed that the increase in C content changed the trend of the thermal deformation activation energy Q with the true strain. The Q value of 2C7Mn3Al increased by about 50 KJ/mol compared with 7Mn3Al at a true strain greater than 0.4. In contrast, increasing the Al content from 0 to 1.14 wt.% decreased the activation energy of thermal deformation in the true strain range of 0.4-0.9. Continuing to increase to 3.30 wt.% increased the Q of 7Mn3Al over 7Mn by about 65 KJ/mol over the full strain range. In comparison, 7Mn1Al exhibited the best hot processing performance under the deformation temperature of 975-1125 °C and strain rate of 0.2-5 s-1. This is due to the addition of C element reduces the δ-ferrite volume fraction, which leads to the precipitation of κ-carbides and causes the formation of microcracks; an increase in Al content from 0 to 1.14 wt.% reduces the austenite stability and improves the hot workability, but a continued increase in the content up to 3.30 wt.% results in the emergence of δ-ferrite in the microstructure, which slows down the austenite DRX and not conducive to the hot processing performance.

Dynamic Mechanical Properties and Modified Johnson-Cook Model Considering Recrystallization Softening for Nickel-Based Powder Metallurgy Superalloys

The material undergoes high temperature and high strain rate deformation process during the cutting process, which may induce the dynamic recrystallization behavior and result in the evolution of dynamic mechanical properties of the material to be machined. In this paper, the modified Johnson-Cook (J-C) model for nickel-based powder metallurgy superalloy considering dynamic recrystallization behavior in high strain rate and temperature is proposed. The dynamic mechanical properties of the material under different strain rates and temperature conditions are obtained by quasi-static compression test and split Hopkinson pressure bar (SHPB) test. The coefficients of the modified J-C model are obtained by the linear regression method. The modified model is verified by comparison with experimental and model prediction results. The results show that the modified J-C model proposed in this paper can accurately describe the mechanical properties of nickel-based powder metallurgy superalloys at high temperatures and high strain rates. This provides help for studying the cutting mechanism and finite element simulation of nickel-based powder metallurgy superalloy.

Effect of internal fractures on mechanical properties and failure of sandstone under multi-physical fields

Under deep mining conditions, rocks are subjected to complex multi-physical fields and can contain numerous pores and fractures. To explore the influence and correlation of these factors on the physical and mechanical properties of fractured rock samples, this study conducted triaxial compression tests on sandstone specimens under various physical conditions using a rock full stress multi-field coupling triaxial tester. Additionally, a random fracture model for multi-field coupling numerical simulation was established. This allowed the study to obtain the mechanical parameters, failure mode, and internal fracture development of rocks under multi-physical field conditions. By analyzing the complete stress-strain curve, mechanical characteristic points, and permeability, a combination of laboratory tests and numerical simulations was used to examine how temperature, seepage, and stress fields affect the development of pores and fractures in rocks. It was found that the temperature field, under conventional geothermal conditions, generates tensile force through thermal expansion and the presence of fluid, thereby promoting fracture development within the rocks. This mechanism is similar to that of seepage. The confining pressure caused by deep geo stress uniformly inhibits the expansion of pores and fissures within the rocks.

Accurate Finite Element Simulations of Dynamic Behaviour: Constitutive Models and Analysis with Deep Learning

Owing to the challenge of capturing the dynamic behaviour of metal experimentally, high-precision numerical simulations have become essential for analysing dynamic characteristics. In this study, calculation accuracy was improved by analysing the impact of constitutive models using the finite element (FE) model, and the deep learning (DL) model was employed for result analysis. The results showed that FE simulations with these models effectively capture the elastic-plastic response, and the ZA model exhibits the highest accuracy, with a 26.0% accuracy improvement compared with other models at 502 m/s for Hugoniot elastic limit (HEL) stress. The different constitutive models offer diverse descriptions of stress during the elastic-plastic response because of temperature effects. Concurrently, the parameters related to the yield strength at quasi-static influence the propagation speed of elastic waves. Calculation show that the yield strength at quasi-static of 6061 Al adheres to y = ax + b for HEL stress. The R-squared (R2) and mean absolute error (MAE) values of the DL model for HEL stress predictions are 0.998 and 0.0062, respectively. This research provides a reference for selecting constitutive models for simulation under the same conditions.

Investigation on Creep Deformation and Age Strengthening Behavior of 304 Stainless Steel under High Stress Levels

The creep deformation behavior and age strengthening behavior of 304 stainless steel under high stress levels were systematically studied by uniaxial creep test, tensile test, XRD diffraction test and transmission electron microscopy. The results show that the total creep strain and the initial creep strain rate increase with the increase in stress level, and the creep strain in the whole aging process is mainly produced in the initial creep stage. The calculated stress exponent shows that the main mechanism of creep deformation of 304 stainless steel at 453 K is dislocation slip. The strength and plasticity of 304 stainless steel after creep aging are improved simultaneously. Microstructural observations indicate an increase in dislocation density and martensite content, as well as austenite and twins, leading to an improvement in strength and plasticity, respectively. In addition, considering the influence of dislocation density on creep behavior, the relative dislocation density increase is introduced into the hyperbolic sine creep model, and a simple mechanism-based creep aging constitutive model is established. The creep strain predicted by the model is in good agreement with the experimental data of 304 stainless steel. The findings can provide theoretical support for the application of creep age forming in 304 stainless steel parts.

Study on the Constitutive Modeling of (2.5 vol%TiB + 2.5 vol%TiC)/TC4 Composites under Hot Compression Conditions

The hot deformation behavior of titanium matrix composites plays a crucial role in determining the performance of the formed components. Therefore, it is significant to establish an accurate constitutive relationship between material deformation parameters and flow stress. In this study, hot compression experiments were conducted on a (2.5 vol%TiB + 2.5 vol%TiC)/TC4. The experiments were performed under temperatures ranging from 1013.15 to 1133.15 K and strain rates ranging from 0.001 to 0.1 s-1. Based on the stress-strain data obtained from the experiment, the constitutive models were established by using the Arrhenius model and the BP neural network algorithm, respectively. Considering the relationship between strain rate, hot working temperature, and flow stress, a comparative analysis was conducted to evaluate the prediction accuracy of two different constitutive models. The research results indicate that the flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4 increases with decreasing temperature and increasing strain rate, and the stress-strain curve shows obvious work hardening and softening behaviors. Both the Arrhenius model and the BP neural network algorithm are effective in predicting the hot compression flow stress of (2.5 vol%TiB + 2.5 vol%TiC)/TC4, but the average relative error and root mean square error of the BP neural network algorithm are smaller and the correlation coefficient is higher, thus possessing higher accuracy and reliability.

Analysis of Hot Tensile Fracture and Flow Behaviors of Inconel 625 Superalloy

In this work, Inconel 625 alloy is explored regarding high-temperature tensile deformation and fracture behaviors at a strain rate of 0.005-0.01 s-1 under a deformation temperature ranging from 700-800 °C. The subsequent analysis focuses on the impact of deformation parameters on flow and fracture characteristics. The fractured surface reveals that ductile fracture is dominated by the nucleation, growth, and coalescence of microvoids as the primary failure mechanisms. The elevated deformation temperature and reduced strain rate stimulate the level of dynamically recrystallized (DRX) structures, resulting in intergranular fractures. The Arrhenius model and the particle swarm optimization-artificial neural network (PSO-ANN) model are developed to predict the hot tensile behavior of the superalloy. It indicates that the PSO-ANN model exhibits a correlation coefficient (R) as high as 0.9967, surpassing the corresponding coefficient of 0.9344 for the Arrhenius model. Furthermore, the relative absolute error of 9.13% (Arrhenius) and 1.85% (PSO-ANN model) are recorded. The developed PSO-ANN model accurately characterizes the flow features of the Inconel 625 superalloy with high precision and reliability.

The Significance of Cross-Sectional Shape Accuracy and Non-Linear Elasticity on the Numerical Modelling of Cerebral Veins under Tensile Loading

Traumatic brain injury (TBI) is a serious global health issue, leading to serious disabilities. One type of TBI is acute subdural haematoma (ASDH), which occurs when a bridging vein ruptures. Many numerical models of these structures, mainly based on the finite element method, have been developed. However, most rely on linear elasticity (without validation) and others on simplifications at the geometrical level. An example of the latter is the assumption of a regular cylinder with a constant radius, or the geometry of the vein acquired from medical images. Unfortunately, these do not replicate the real conditions of a mechanical tensile test. In this work, the main goal is to evaluate the influence of the vein's geometry in its mechanical behaviour under tensile loading, simulating the real conditions of experimental tests. The second goal is to implement a hyperelastic model of the bridging veins where it would be possible to observe its non-linear elastic behaviour. The results of the developed finite element models were compared to experimental data available in the literature and other models. It was possible to conclude that the geometry of the vein structure influences the tensile stress-strain curve, which means that flattened specimens should be modelled when validating constitutive models for bridging veins. Additionally, the implementation of hyperelastic material models has been verified, highlighting the potential application of the Marlow and reduced polynomial (of fourth and sixth orders) constitutive models.

A Static Damage Constitutive Model of Concrete Based on Microscopic Damage Mechanism

In this article, a microscopic constitutive model is established that includes friction, plastic, and spring elements and has clear physical meaning. The friction unit reflects the mutual friction between crack surfaces, the plastic unit reflects the development of concrete plasticity, and the fracture of the spring unit reflects the formation and expansion of interior cracks in concrete. In addition, the integration of the random field theory into this model uncovers the physical underpinnings of the relationship between concrete's nonlinearity and randomness. The multi-scale modeling of the concrete static damage constitutive model is then realized once the parameters of the random field are discovered using the macro test results. In order to apply the model's applicability in finite element programs, a subroutine was ultimately constructed. The experimental data and the anticipated values from the numerical simulation are in good agreement, supporting the model's realism.

Finite Bending of Fiber-Reinforced Visco-Hyperelastic Material: Analytical Approach and FEM

This paper presents a new anisotropic visco-hyperelastic constitutive model for finite bending of an incompressible rectangular elastomeric material. The proposed approach is based on the Mooney-Rivlin anisotropic strain energy function and non-linear visco-hyperelastic method. In this study, we aim to examine the mechanical response of a reinforced viscoelastic rectangular bar with a group of fibers under bending. Anisotropic materials are typically composed of one (or more) family of reinforcing fibers embedded within a soft matrix material. This operation may lead to an enhancement in the strength and stiffness of soft materials. In addition, a finite element simulation is carried out to validate the accuracy of the analytical solution. In this research, the well-known stress relaxation test, as well as the multi-step relaxation test, are examined both analytically and numerically. The results obtained from the analytical solution are found to be in good agreement with those from the finite element method. Therefore, it can be deduced that the proposed model is competent in describing the mechanical behavior of fiber-reinforced materials when subjected to finite bending deformations.

A Novel Approach for Optimization of Soft Material Constitutive Model Parameters Based on a Genetic Algorithm and Drucker's Stability Criterion

The growing interest in soft materials to develop flexible devices involves the need to create accurate methodologies to determine parameter values of constitutive models to improve their modeling. In this work, a novel approach for the optimization of constitutive model parameters is presented, which consists of using a genetic algorithm (GA) to obtain a set of solutions from data of uniaxial tensile tests, which are later used to simulate the mechanical test using finite element analysis (FEA) software to find an optimal solution considering Drucker's stability criterion. This approach was applied to the elastomer Ecoflex 00-30 considering the Warner and Yeoh models and Rivlin's phenomenological theory. The correlation between the experimental and the predicted data by the models was determined using the root mean squared error (RMSE), where the found parameter sets provided a close fit to the experimental data with RMSE values of 0.022 (ANSYS) and 0.024 (ABAQUS) for Warner's model, while for Yeoh's model were 0.014 (ANSYS) and 0.012 (ABAQUS). It was found that the best parameter values accurately follow the experimental material behavior using FEA. The proposed GA not only optimizes the material parameters but also has a high reproducibility level with average RMSE values of 0.024 for Warner's model and 0.009 for Yeoh's model, fulfilling Drucker's stability criterion.

A One-Dimensional Dynamic Constitutive Modeling of Ethylene Vinyl Acetate (EVA) Foam

Ethylene vinyl acetate copolymer (EVA) is good for impact protection and energy absorption, and belongs to rate sensitive-dependent materials. This study aimed to investigate the influence of increased strain rate and the presence of entrapped air on the enhancement of foam material strength. The compression deformation behavior of EVA foams containing a microporous structure was extensively investigated over different strain rates of 0.0017/s, 0.033/s, and 0.17/s, where each test was conducted at a constant compression velocity. A one-dimensional dynamic constitutive model was established to describe the large deformation response of EVA to different strain rates. The model included two components, the material action part and the air pressure part. Quasi-static and dynamic compression tests were used to determine the constitutive relations of three parameters, a1, a2, and the leaking rate δ·. The samples with EVA foams at different strain rates were fitted using ORIGIN software, and the constitutive model parameters were obtained. It was found that the ratio of the air leaking rate to the strain rate gradually decreases, causing air within the EVA to be trapped in the cells rather than escaping in a timely manner with increasing strain rates.

Advancements in the Evolution of Engineering Characteristics and Reinforcement Technologies for Subgrade Silt

Technical challenges associated with the treatment of silt subgrades frequently arise in coastal and river delta areas. Given the importance of environmental sustainability, the selection of efficient, cost-effective, and eco-friendly techniques for silt subgrade stabilization is paramount. While recycled polyester fibers primarily sourced from discarded polyester bottles have not yet been systematically employed in silt subgrade reinforcement, their potential is considerable. This paper offers a comprehensive review of the existing literature on the microstructural, physicochemical, and mechanical properties of silt, summarizing prior advancements in silt stabilization methodologies. Building upon this foundation, we introduce a novel approach utilizing recycled polyester fibers for silt subgrade improvement, outlining both its application prospects and challenges, which require further investigation. The findings of this study serve as a robust scientific foundation for the broader adoption and engineering implementation of this technology.

Combined Influences of Water Content and Coarse Grain Content on Shear Strength of Unsaturated Soil Mixture

An interlayer existed between the ballast layer and subgrade in the conventional railway substructure. Considering that the shear strength τ of the interlayer soil was influenced by the changes in the ballast grain content and water content, this aspect was explored in the present study. Monotonic triaxial tests were fulfilled, which considered five coarse grain contents fv and three water contents of fine soil wf. The results showed that the growth in fv contributed to an increment in τ of the soil mixture under both saturation and unsaturation. Conversely, in previous studies, the growth of fv induced an increment in τ under saturation, but a decline in that under unsaturation. This was explained by the competing influences of fv and suction ψ: in previous studies, increasing fv induced a decline in the dry density of the fine soil fraction ρd-f, which contributed to a decline in ψ. When the negative influence of declining ψ outweighed the positive influence of the incrementing fv, the τ of the soil mixture decreased. Meanwhile, modelling of the τ-ψ relationship in the soil mixture with varying fv was performed. This proposed model was examined using the test results from both the present and previous studies, which shows its reasonably good performance.

Construction of Human Periodontal Ligament Constitutive Model Based on Collagen Fiber Content

Periodontal ligament (PDL) is mainly composed of collagen fiber bundles, and the content of collagen fiber is an important factor affecting the mechanical properties of PDL. Based on this, the purpose of this study is to explore the effect of the PDL collagen fiber content on its viscoelastic mechanical behavior. Transverse and longitudinal samples of different regions of PDL were obtained from the human maxilla. The fiber content at different regions of human PDL was quantitatively measured using image processing software, and a new viscoelastic constitutive model was constructed based on the fiber content. The nano-indentation experiment was carried out with a loading rate of 0.5 mN·s-1, a peak load of 3 mN, and a holding time of 200 s, and the model parameters were obtained through the experiment data. The results showed that with the increase of fiber content, the deformation resistance of PDL also increased, and compared with the neck and middle region, the compressive strain in the apical region of PDL was the largest. The range of reduced elastic modulus of human PDL was calculated to be 0.39~5.08 MPa. The results of the experimental data and the viscoelastic constitutive model fit well, indicating that the model can well describe the viscoelastic behavior of human PDL.

Chemical Corrosion-Water-Confining Pressure Coupling Damage Constitutive Model of Rock Based on the SMP Strength Criterion

Aiming at the problem of chemical-mechanics-hydro (C-M-H) action encountered by rocks in underground engineering, chemical damage variables, water damage variables, and force damage variables are introduced to define the degree of degradation of rock materials. Stone is selected as the sample for acid corrosion treatment at pH 3, 4, and 7, and a chemical damage factor is defined that coupled the pH value and duration of exposure. Then based on the spatial mobilized plane (SMP) criterion and the Lemaitre strain equivalence hypothesis, this research develops a constitutive model considering rock chemical corrosion-water-confining pressure damage. The proposed damage constitutive model employs the extremum method to ascertain the two Weibull distribution parameters (m and F0) by theoretical derivation and exhibits satisfactory conformity between the theoretical and experimental curves. The damage constitutive model can be consistent in the stress-strain characteristics of the rock triaxial compression process, which verifies the rationality and reliability of the model parameters. The model effectively represents the mechanical properties and damage characteristics of rocks when subjected to the combined influence of water chemistry and confinement. The presented model contributes to a better understanding of tangible rock-engineered structures subjected to chemical corrosion in underwater environments.

Hot Deformation Behavior of Hastelloy C276 Alloy: Microstructural Variation and Constitutive Models

Isothermal deformation experiments of the Hastelloy C276 alloy were executed using the Gleeble-3500 hot simulator at a temperature range of 1000-1150 °C and a strain rate range of 0.01-10 s-1. Microstructural evolution mechanisms were analyzed via transmission electron microscope (TEM) and electron backscatter diffraction (EBSD). Results reveal that the influences of hot compression parameters on the microstructure variation features and flow behaviors of the Hastelloy C276 alloy were significant. The intense strain hardening (SH) effects caused by the accumulation of substructures were promoted when the strain rates were increased, and true stresses exhibited a notable increasing tendency. However, the apparent DRV effects caused by the annihilation of substructures and the increasingly dynamic recrystallization (DRX) behaviors occurred at high compressed temperature, inducing the reduction in true stresses. In addition, a physical-based (PB) constitutive model and a long short-term memory (LSTM) model optimized using the particle swarm optimization (PSO) algorithm were established to predict the flow behavior of Hastelloy C276 alloy. The smaller average absolute relative error and greater relation coefficient suggest that the LSTM model possesses a higher forecasting accuracy than the PB model.

Constitutive Damage Model of Foamed Lightweight Concrete Using Statistical Damage Theory

Foamed lightweight concrete has been applied in different fields of civil engineering because of its superior properties, but the related research considering internal pore damage is limited. Based on statistical damage theory and considering the uneven distribution of fracture damage and strength between the pores of light concrete, a damage constitutive model of foamed lightweight concrete was established based on the Weibull function. The parameters of the damage model were determined through a triaxial compression test, and the rationality was verified by combining the existing test data. Comparative tests show that the theoretical calculation results of the proposed statistical damage model of foamed light soil are consistent with the general trend of the experimental results, reflecting the value of the peak stress and strain and describing the overall development law of the stress and strain. The best fit was obtained when the confining pressure was 0.3 MPa and the density was 700 kg·m-3. The suggested damage constitutive method is highly applicable, which is of great significance to the microscopic mechanical analysis of foamed light concrete and the structural design in civil engineering.

Analyzing the Energy and Damage Constitutive of Cemented Backfill with Different Water Content under Dynamic Load

The dynamic characteristics of the filling body are the key parameters for designing the filling ratio and evaluating the stability of an underground stope. The different environment (water-bearing state) of the filling body in the underground stope exerts a complex impact on the mechanical behavior of the filling body. Therefore, six groups of cemented filling body specimens with different states were formed and subjected to dynamic uniaxial impact tests. The effects of water content on the mechanical properties, fractal dimension, and deformation damage characteristics of the cemented backfill under dynamic load were analyzed in depth, and a dynamic damage constitutive model that considers water damage and the compaction stage was established. The results indicate the following: (1) Due to the change of the specimen from the dry state to the water saturation state, the dynamic compressive strength of the cemented filling body decreases from 5.03 Mpa to 1.79 Mpa; however, the ductility of the specimen generally increases, and the filling body specimens with different water contents mainly exhibit tensile failure. (2) There is a significant nonlinear relationship between the water content and the fractal dimension Db of the cemented backfill specimen, and the growth rate of the fractal dimension Db tends to slow down with the increase in the water content. (3) From the energy evolution perspective, the water content of the specimen exerts a significant effect on the elastic deformation and failure stage of the stress-strain curve, and the slope of the dissipated energy-strain curve decreases with the increase in water content. (4) Based on the Weibull distribution and damage theory, a statistical damage constitutive model of cemented backfill was established, and it was compared with the experimental curve to verify the rationality of the model. Therefore, the relationship between stress and damage and the strain curves is discussed, and it is inferred that the damage evolution curve of cemented backfill is a typical S-shaped curve that exhibits a stable development-rapid increase-tending to be gentle. This study can provide a theoretical reference for further understanding the dynamic behavior and stability of backfill under different water conditions.

A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification

Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh model is proposed to improve its prediction performance for multiaxial deformation of hyperelastic polymeric materials while retaining the advantages of the original Yeoh model. The modified constitutive model has one more correction term than the original model. The specific form of the correction term is a composite function based on a power function represented by the principal stretches, which is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation. In addition, a parameter identification method based on the cyclic genetic-pattern search algorithm is introduced to accurately obtain the parameters of the constitutive model. By applying the modified model to the experimental datasets of various rubber or rubber-like materials (including natural unfilled or filled rubber, silicone rubber, extremely soft hydrogel and human brain cortex tissue), it is confirmed that the modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. Meanwhile, the advantages of the modified model over most existing models in the literatures are also demonstrated. For example, when characterizing human brain tissue, which is difficult for most existing models in the literature, the modified model has comparable predictive accuracy with the third-order Ogden model, while maintaining convexity in the corresponding deformation domain. Moreover, the effective prediction ability of the modified model for untested equi-biaxial deformation of different materials has also been confirmed using only the data of uniaxial tension and pure shear from various datasets. The effective prediction for the untested equibiaxial deformation makes it more suitable for the practice situation where the equibiaxial deformation of certain polymeric materials is unavailable. Finally, compared with other parameter identification methods, the introduced parameter identification method significantly improves the predicted accuracy of the constitutive models; meanwhile, the uniform convergence of introduced parameter identification method is also better.

A 3D Anisotropic Thermomechanical Model for Thermally Induced Woven-Fabric-Reinforced Shape Memory Polymer Composites

Soft robotic grippers offer great advantages over traditional rigid grippers with respect to grabbing objects with irregular or fragile shapes. Shape memory polymer composites are widely used as actuators and holding elements in soft robotic grippers owing to their finite strain, high specific strength, and high driving force. In this paper, a general 3D anisotropic thermomechanical model for woven fabric-reinforced shape memory polymer composites (SMPCs) is proposed based on Helmholtz free energy decomposition and the second law of thermodynamics. Furthermore, the rule of mixtures is modified to describe the stress distribution in the SMPCs, and stress concentration factors are introduced to account for the shearing interaction between the fabric and matrix and warp yarns and weft yarns. The developed model is implemented with a user material subroutine (UMAT) to simulate the shape memory behaivors of SMPCs. The good consistency between the simulation results and experimental validated the proposed model. Furthermore, a numerical investigation of the effects of yarn orientation on the shape memory behavior of the SMPC soft gripper was also performed.

The Flow Stress Behavior and Physical-Based Constitutive Model for As-Quenched Al-Zn-Mg-Cu Alloy

Although heat-treatable Al-Zn-Mg-Cu alloys are widely used in aerospace industries, distortion and cracks exist due to the residual stress during quenching. Understanding the flow stress behavior and numerically modeling the process is the key to predicting the residual stress. This paper investigated the flow stress behavior of the as-quenched 7050 alloy at strain rates from 0.1 s^-1 to 1 s^-1, temperatures between 423 K and 723 K, and cooling rates from 0.1 K/s to 10 K/s. The experimental results showed that the strain rate, cooling rate, and temperature have effects on the flow stress value, except for the cooling rates at a temperature of 423 K or 723 K. The kinetics model was used to obtain the precipitate features, i.e., precipitate size and volume fraction. Then, a physical constitutive model based on the evolution of immobile dislocation, solutes, and precipitates was developed. The predicted flow stresses showed good agreement with the experimental data. The findings of this work expand the knowledge on the as-quenched flow behavior of Al-Zn-Mg-Cu alloys, improving the prediction accuracy of residual stress by FEM.

Constitutive Model for Grouted Rock Mass by Macro-Meso Damage

Rock fractures have a significant impact on the stability of geotechnical engineering, and grouting is currently the most commonly used reinforcement method to address this issue. To ensure the stability of grouted rock mass, it is necessary to study its deformation law and mechanical properties. In this study, theoretical analyses and laboratory experiments were conducted, and the fracture width, Weibull model and effective bearing area were introduced to improve the applicability and accuracy of the original damage constitutive model. Moreover, the constitutive model of grouted rock mass was derived by combining it with the mixing law of composite materials. The main conclusions are summarized as follows: (1) Based on macroscopic damage tensor theory, the fracture width parameter was introduced, which effectively described the variation law of macroscopic damage with fracture width to improve the accuracy of the original damage constitutive model. (2) The effective bearing area was used to optimize the original Weibull model to match the stress-strain curve of the rock mass with fractures. (3) The grouting-reinforced rock mass was considered to be a composite material, the original equivalent elastic modulus model was improved by combining macroscopic damage with the Reuss model, and the constitutive damage model of the grouted rock mass was deduced.

Bond Performance of CFRP Strands to Grouting Admixture for Prestressed Structure and Development of Their Bond-Slip Constitutive Models

Prestressed concrete structures have witnessed widespread use in building and infrastructure applications during the last two decades due to their high stiffness and strength indices. However, structural failures caused by the corrosion of steel reinforcing bars or strands have proliferated, opening the door for carbon fibre-reinforced polymer (CFRP) strands as an excellent alternative with high corrosion resistance. The bonding interaction between the CFRP strands and concrete is the fundamental parameter in shaping the structural behaviour of CFRP prestressed concrete structures. In this paper, the bonding behaviour between CFRP strands and concrete with grouting admixture is experimentally investigated based on three groups of standard pull-out tests. The bond strength of CFRP strands was systematically studied and compared against steel strands. The untreated CFRP strands exhibited an inefficient bonding strength with the grouting admixture, equivalent to only 5% compared to steel strands of the same diameter. Surface coating with epoxy quartz sand can significantly improve the anchoring efficiency of CFRP strands up to 14 times compared to the untreated strands, which is approximately as efficient as steel strands. Moreover, the bond-slip curves between CFRP strands and concrete were analysed and were found to be different compared to steel strands. Finally, this study proposed bond-slip constitutive models of CFRP strands with better applicability, using an exponentially damped sine function to fit the residual segment of the curve.

Hot Deformation Behavior and Processing Maps of Pure Copper during Isothermal Compression

In this study, pure copper's hot deformation behavior was studied through isothermal compression tests at deformation temperatures of 350~750 °C with strain rates of 0.01~5 s^-1 on a Gleeble-3500 isothermal simulator. Metallographic observation and microhardness measurement were carried out of the hot compressed specimens. By analyzing the true stress-strain curves of pure copper under various deformation conditions during the hot deformation process, the constitutive equation was established based on the strain-compensated Arrhenius model. On the basis of the dynamic material model proposed by Prasad, the hot-processing maps were acquired under different strains. Meanwhile, the effect of deformation temperature and strain rate on the microstructure characteristics was studied by observing the hot-compressed microstructure. The results demonstrate that the flow stress of pure copper has positive strain rate sensitivity and negative temperature correlation. The average hardness value of pure copper has no obvious change trend with the strain rate. The flow stress can be predicted with excellent accuracy via the Arrhenius model based on strain compensation. The suitable deforming process parameters for pure copper were determined to be at a deformation temperature range of 700~750 °C and strain rate range of 0.1~1 s^-1.

A Modified Constitutive Model and Microstructure Characterization for 2195 Al-Li Alloy Hot Extrusion

The quality of extruded profiles depends largely on accurate constitutive models and thermal processing maps. In this study, a modified Arrhenius constitutive model for homogenized 2195 Al-Li alloy with multi-parameter co-compensation was developed and further enhanced the prediction accuracy of flow stresses. Through the processing map and microstructure characterization, the 2195 Al-Li alloy could be deformed optimally at the temperature range of 710~783 K and strain rate of 0.001~0.12 s^-1, preventing the occurrence of local plastic flow and abnormal growth of recrystallized grains. The accuracy of the constitutive model was verified through numerical simulation of 2195 Al-Li alloy extruded profiles with large shaped cross-sections. Dynamic recrystallization occurred at different regions during the practical extrusion process, resulting in slight variations in the microstructure. The differences in microstructure were due to the varying degrees of temperature and stress experienced by the material in different regions.

Utilizing ANN for Predicting the Cauchy Stress and Lateral Stretch of Random Elastomeric Foams under Uniaxial Loading

As a result of their cell structures, elastomeric foams exhibit high compressibility and are frequently used as buffer cushions in energy absorption. Foam pads between two surfaces typically withstand uniaxial loads. In this paper, we considered the effects of porosity and cell size on the mechanical behavior of random elastomeric foams, and proposed a constitutive model based on an artificial neural network (ANN). Uniform cell size distribution was used to represent monodisperse foam. The constitutive relationship between Cauchy stress and the four input variables of axial stretch λ_U, lateral stretch λ_L, porosity φ, and cell size θ was given by con-ANN. The mechanical responses of 500 different foam structures (20% < φ < 60%, 0.1 mm < θ < 0.5 mm) under compression and tension loads (0.4 < λ_U < 3) were simulated, and a dataset containing 100,000 samples was constructed. We also introduced a pre-ANN to predict lateral stretch to address the issue of missing lateral strain data in practical applications. By combining physical experience, we chose appropriate input forms and activation functions to improve ANN's extrapolation capability. The results showed that pre-ANN and con-ANN could provide reasonable predictions for λ_U outside the dataset. We can obtain accurate lateral stretch and axial stress predictions from two ANNs. The porosity affects the stress and λ_L, while the cell size only affects the stress during foam compression.

Relevant Choices Affecting the Fatigue Analysis of Ni-Ti Endovascular Devices

Ni-Ti alloys are widely used for biomedical applications due to their superelastic properties, which are especially convenient for endovascular devices that require minimally invasive insertion and durable effects, such as peripheral/carotid stents and valve frames. After crimping and deployment, stents undergo millions of cyclic loads imposed by heart/neck/leg movements, causing fatigue failure and device fracture that can lead to possibly severe consequences for the patient. Standard regulations require experimental testing for the preclinical assessment of such devices, which can be coupled with numerical modeling to reduce the time and costs of such campaigns and to obtain more information regarding the local state of stress and strain in the device. In this frame, this review aimed to enlighten the relevant choices that can affect the outcome of the fatigue analysis of Ni-Ti devices, both from experimental and numerical perspectives.

Research on the Impact Mechanical Properties of Real-Time High-Temperature Granite and a Coupled Thermal-Mechanical Constitutive Model

Studying the mechanical behavior of rocks under real-time high-temperature conditions is of great significance for the development of energy caverns, nuclear waste disposal projects, and tunneling engineering. In this study, a real-time high-temperature impact compression test was conducted on Sejila Mountain granite to explore the effects of temperature and external load on its mechanical properties. Based on the concepts of damage mechanics and statistics, a coupled thermal-mechanical (T-M) damage constitutive model was established, which considers the temperature effect and uses the double-shear unified strength as the yield criterion. The parameter expressions were clarified, and the accuracy and applicability of the model were verified by experimental data. The research results indicated that high temperatures had an obvious damaging and deteriorating effect on the strength of the granite, while an increase in impact velocity had an enhancing effect on the strength of the granite. The established constitutive model theoretical curve and test curve showed a high degree of agreement, indicating that the coupled T-M model can objectively represent the evolution process of damage in rocks and the physical meaning of its parameters is clear.

Study of Flow Stress Models and Ductile Fracture Criteria for CHN327 Nickel-Based Superalloy

The plastic deformation behavior of a CHN327 nickel-based superalloy under temperatures ranging from 600 °C to 700 °C and strain rates ranging from 0.001 to 0.1 s^-1 was investigated using uniaxial high-temperature tensile tests. The stress-strain curves obtained by the tests showed that the maximum stress decreased as the temperature increased, while it increased as the strain rate increased. Based on the extensive data obtained in the experiment, three constitutive models (Hollomon, Swift, and the modified Voce equation) were employed to predict the constitutive relation. It was found that the modified Voce equation had the highest correlation coefficient and the best prediction accuracy. Thereafter, in order to predict the fracture of CHN327 during high-temperature tensile deformation, five ductile fracture criteria (Freudenthal, C&L, Brozzo, Ayada, and the R&T model), and the modified Voce equation obtained were incorporated into the finite element software (DEFORM). According to the results, except for the C&L and Brozzo models, all of the other ductile fracture criteria (DFCs) were suitable for predicting the damage distribution of the CHN327 alloy in tensile tests. For all of the DFCs considered, the R&T model provided the most accurate predictions, whose mean error was only 8.9%, far less than the values that other models predicted.

Room-Temperature Strengthening, Portevin-Le Chatelier Effect, High-Temperature Tensile Deformation Behavior, and Constitutive Modeling in a Lightweight Mg-Gd-Al-Zn Alloy

To explore room-temperature strengthening and high-temperature ductility, a lightweight novel Mg-1.85Gd-0.64Al-0.62Zn alloy was fabricated by innovative multidirectional forging and a hot-rolling technique. Microstructures and mechanical properties were studied at room and elevated temperatures with an optical microscope, an X-ray diffractometer, and a tensile tester. An ultimate tensile strength of 260 MPa, yield strength of 171 MPa, and elongation of 20.4% were demonstrated at room temperature. The room-temperature strengthening mechanisms were identified by strengthening the model estimation. A type C Portevin-Le Chatelier effect was discovered and elucidated in this alloy. X-ray diffraction analysis revealed that the phase composition is α-Mg solid solution and (Mg, Al)₃Gd, Al₇Zn₃, and Al₂Gd intermetallic compounds. Examination of the microstructure at elevated temperatures revealed that dynamic recrystallization and dynamic grain growth occur. In particular, it was discovered that bimodal microstructures or incomplete dynamic recrystallization microstructures exist in high-temperature deformation. A maximum quasi-superplasticity of 228.4% was demonstrated in this alloy at 673 K and 5.0 × 10^-4 s^-1. Flow stress curves showed that the present alloy exhibits Sotoudeh-Bate curves or a long intermediate strain-hardening stage followed by a strain-softening stage. A modified Zerilli-Armstrong constitutive equation incorporating the number of dislocations was established. The power-law constitutive equation was established to identify the deformation mechanism. Both constitutive models had good predictability. At 673 K and 5.0 × 10^-4 s^-1, the stress exponent was 4, and the average deformation activation energy was 104.42 kJ/mol. The number of dislocations inside a grain was 146. This characteristic evidence confirmed that dislocation motion controlled by pipe diffusion dominates the rate-controlling process under this condition.

Durability Performance Investigation for Engineering Fiber Cementitious Composites (ECC): Review

Engineered Cementitious Composite (ECC) is currently receiving more and more attention due to its excellent tensile strain hardening and multiple cracking properties. However, due to the high material cost of polyvinyl alcohol (PVA) fiber and quartz sand, its widespread promotion and application in the market are limited. Therefore, scholars at home and abroad have conducted many active studies on improving ECC. This paper summarizes the development history and research status of ECC materials, summarizes the current domestic and foreign researchers' improvement methods for ECC materials, and classifies the improvement methods into three categories: the type of fiber variation, the water-binder ratio variation and adding mineral admixtures, the influences of the above three factors on the mechanical properties and durability of ECC, such as compressive and flexural resistance, are described in detail, and the mechanism of action is explained. Furthermore, this paper introduces the most common uniaxial compression and uniaxial tension constitutive models of ECC. They are briefly classified and evaluated, hoping to help readers' numerical simulation analysis. Finally, some suggestions for ECC research, such as the proportion of water binders and the application of composite fibers, require further research.

Mechanical Characterization and Constitutive Modeling of Nano-Stabilized Soil under Uniaxial Compression

The stress-strain constitutive model under uniaxial compression is a basic element and important characterization method for determining physical and mechanical properties in cement-based materials research. In this study, a stress-strain constitutive model under uniaxial compression was established, which was based on a new nano-stabilized soil (NSS) through typical mechanical tests and constitutive relationship research. The results indicate that the unconfined compressive strength (UCS) of the nano-stabilized soil was enhanced with the increase in curing period and nano-stabilizer dosage, and that the strength growth rate reaches the maximum at a 12% dosage in the tested samples. The UCS of NSS under a 12% dosage is about 10~15% higher than that of ordinary stabilized soil (SS) without nano doping, and 25~40% higher compared with grade 42.5 cement-soil. The established constitutive model could accurately describe the linear-elastic and elastic-plastic deformation characteristics of NSS under uniaxial compression, which will be conducive to revealing the curve variation law of the stress-strain process. The research results could provide scientific support for the theoretical innovation and engineering application of green environmental protection materials.

Study on the Mechanical Properties and Energy Absorbing Capability of Polyurethane Microcellular Elastomers under Different Compressive Strain Rates

Polyurethane microcellular elastomers (PUME) are good at impact protection and energy absorption, and belong to rate sensitive- and strain history-dependent materials. In this study, PUME with different densities of 800 kg/m³, 600 kg/m³ and 400 kg/m³ were prepared, then the compressive responses of PUME in the strain rate range of 0.001 s^-1 to 3400 s^-1 were systemically investigated. By studying the energy absorption and efficiency diagram of PUME, the compressive properties of materials with different densities under compressive impact load were described, which showed that PUME with a density of 600 kg/m³ had better performance. A visco-hyperelasticity-air constitutive model was established to describe the large deformation response of PUME at high strain rates. The model included three components: hyperelastic part, viscoelastic part and gas pressure part. Quasi-static and dynamic compression tests were used to determine the constitutive relations of seven parameters. The samples with a density of 600 kg/m³ at different strain rates were fitted by MATLAB software, and the constitutive model parameters were obtained. The comparison between the constitutive equation and the experimental results showed that there was a good consistency. The constitutive model can provide data support for simulation analysis and application of PUME as energy absorbing protective facilities.

Experimental Study of Stress and Deformation of Reclaimed Asphalt Concrete at Different Temperatures

Asphalt concrete has been used as a material for dam core walls because of its impermeability, durability and reliability. Firstly, asphalt is a temperature-sensitive material, and many of its characteristics are related to temperature. Secondly, because of the increasing construction height of the dam, the pressure on the asphalt concrete core wall is also great. Finally, for the purpose of resource utilization, it is necessary to verify whether the reclaimed asphalt concrete can be used in dam construction. Therefore, it is necessary to study the stress and deformation characteristics of recycled asphalt concrete under different temperatures and confining pressures. In this study, three groups of triaxial tests of reclaimed asphalt concrete were carried out for the first time in a new temperature-controlled room. Duncan Zhang's E-v model was used to fit the test results. The results show that the stress-strain curves of reclaimed asphalt concrete show softening characteristics at low temperatures and low confining pressure. It evolves to a hardening type with the increase in temperature and confining pressure. The bulk curve is first contracts but is followed by dilatancy. The dilatancy characteristics become more obvious at low temperatures and low confining pressure. With the increase in temperature and confining pressure, the dilatancy characteristics will weaken. Duncan Zhang's E-v model has a good fitting effect on the stress-strain relationship but a poor fitting effect on the volumetric curve. The research of this paper can better combine the utilization of waste resources with engineering and achieve the aim of resource-saving and waste utilization under the premise of ensuring the safety of the engineering.

Prediction of True Stress at Hot Deformation of High Manganese Steel by Artificial Neural Network Modeling

The development of new lightweight materials is required for the automotive industry to reduce the impact of carbon dioxide emissions on the environment. The lightweight, high-manganese steels are the prospective alloys for this purpose. Hot deformation is one of the stages of the production of steel. Hot deformation behavior is mainly determined by chemical composition and thermomechanical parameters. In the paper, an artificial neural network (ANN) model with high accuracy was constructed to describe the high Mn steel deformation behavior in dependence on the concentration of the alloying elements (C, Mn, Si, and Al), the deformation temperature, the strain rate, and the strain. The approval compression tests of the Fe-28Mn-8Al-1C were made at temperatures of 900-1150 °C and strain rates of 0.1-10 s^-1 with an application of the Gleeble 3800 thermomechanical simulator. The ANN-based model showed high accuracy, and the low average relative error of calculation for both training (5.4%) and verification (7.5%) datasets supports the high accuracy of the built model. The hot deformation effective activation energy values for predicted (401 ± 5 kJ/mol) and experimental data (385 ± 22 kJ/mol) are in satisfactory accordance, which allows applying the model for the hot deformation analysis of the high-Mn steels with different concentrations of the main alloying elements.

Hot Tensile Deformation Behavior and Constitutive Models of GH3230 Superalloy Double-Sheet

In this paper, the hot tensile deformation of a GH3230 superalloy double-sheet was conducted under deformation temperatures ranging from 1123~1273 K and strain rates ranging from 0.001~0.2 s^-1. The flow behavior of the GH3230 superalloy double-sheet was analyzed in detail. The hot tensile deformation process of the GH3230 superalloy double-sheet includes four stages of elastic deformation, strain hardening, steady state and fracture. The true stress decreases with the increasing deformation temperature and decreasing strain rate. The variation of the strain rate sensitivity index and strain hardening index with processing parameters were discussed. The average apparent activation energy for hot tensile deformation is 408.53 ± 46.96 kJ·mol^-1. A combined Johnson-Cook and Hensel-Spittle model considering the couple effect of strain hardening, strain rate hardening and thermal softening was established to describe the hot tensile behavior of the GH3230 alloy double-sheet. Compared to Johnson-Cook model and Hensel-Spittle model, this model has the highest predicting accuracy. The average absolute relative error of true stress between the experimental and the predicted is only 2.35%.

Fracture Closure Empirical Model and Theoretical Damage Model of Rock under Compression

The rock or rock mass in engineering often contains joints, fractures, voids, and other defects, which are the root cause of local or overall failure. In response to most of the current constitutive models that fail to simulate the nonlinear fracture compaction deformation in the whole process of rock failure, especially brittle rocks, a piecewise constitutive model was proposed to represent the global constitutive relation of rocks in this study, which was composed of the fracture compaction empirical model and the damage statistical constitutive model. The fracture empirical compaction model was determined by fitting the expressions of fracture closure curves of various rocks, while the rock damage evolution equation was derived underpinned by the fracture growth. According to the effective stress concept and strain equivalence hypothesis, the rock damage constitutive model was deduced. The model parameters of the fracture compaction empirical model and damage statistical constitutive model were all calculated by the geometrical characteristics of the global axial stress-strain curve to guarantee that the models are continuous and smooth at the curve intersection, which is also simple and ready to program. Finally, the uniaxial compression test data and the triaxial compression test data of different rocks in previous studies were employed to validate the models, and the determination coefficient was used to measure the accuracy. The results showed great consistency between the model curves and test data, especially in the pre-peak stage.

Study on Shear Creep Characteristics of the Discontinuities with Different 3D Morphologies

The rheological phenomenon of rock mass affects the long-term safety of rock mass engineering. In this study, gneiss samples with different 3D morphologies are prepared by splitting tests and are tested through multi-step creep tests. The long-term strength of rock discontinuities is determined by using several methods. The test results show that as the 3D morphological parameter increases, the creep deformation, creep rate, and the duration of failure all decrease. The long-term strength of rock discontinuities is linearly related to the 3D morphological parameter. Based on the principle of damage mechanics for rock mass, a damage variable is introduced in the creep model, and an improved non-linear Burgers model is established. Research results are of great theoretical significance and practical value for the design, construction, and long-term safety of rock mass engineering.

Hot Deformation Behavior of TA1 Prepared by Electron Beam Cold Hearth Melting with a Single Pass

The Gleeble-3800 thermal simulator was used for hot compression simulation to understand the hot deformation performance of TA1 prepared by the single-pass electron beam cold hearth (EB) process. The deformation degree is 50% on a thermal simulator when the temperature range is 700-900 °C, with a strain rate of 0.01-10^-1 s. According to the thermal deformation data, the true stress-strain curve of TA1 was studied. Meanwhile, the constitutive model and processing map were established through the experimental data. These results indicate that the deformation temperature negatively affects strain rate and flow stress. The heat deformation activation energy of EB produced TA1 sample was lower than that of VAR produced TA1 sample in the studied range. The best processing areas of EB-produced TA1 were strain rates of 0.05-0.01 s^-1, within 700-770 °C; or strain rates of 0.01-0.15 s^-1; 840-900 °C. The results of this paper enrich the fundamental knowledge of the thermal deformation behavior of TA1 prepared by EB furnaces.

The Comparation of Arrhenius-Type and Modified Johnson-Cook Constitutive Models at Elevated Temperature for Annealed TA31 Titanium Alloy

Constitutive models play a significant role in understanding the deformation behavior of materials and in optimizing the manufacturing process. In order to improve the reliability of calculation results, the high temperature flow behavior of TA31 titanium alloy obtained from an annealed hot-rolled plate has been investigated by a Gleeble-3500 thermo-mechanical simulator. The isothermal hot compression tests are conducted in the temperature range of 850 to 1050 °C and the strain rate range from 0.001 to 10 s^-1 with a height reduction of 60%. The annealed TA31 shows a dynamic recovery characteristic during thermo-mechanical processing. The experimental data have been used to develop an Arrhenius-type constitutive model and a modified Johnson-Cook model under the consideration of coupling effect on strain, temperature, and strain rate, as well as the strain-softening phenomenon. The material parameters are determined by a global optimization method based on the initial values by means of a regression method. A comparation of the predicted results has been performed based on the modified Johnson-Cook model and those acquired from the Arrhenius-type model. The correlation coefficient and average absolute relative error of the modified Johnson-Cook model are 4.57% and 0.9945, respectively. However, when the optimization method has been applied, they are 15.77% and 0.9620 for the Arrhenius-type model, respectively. These results indicate that the modified Johnson-Cook model is more accurate and efficient in predicting the flow stress of annealed TA31 titanium alloy under a set of model material parameters. Furthermore, the simple mathematical expression of this model is helpful to incorporate it into the finite element software to obtain detailed and valuable information during the thermo-mechanical processing simulation for TA31 in further work.

Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

As a typical viscoelastic material, solid propellants have a large difference in mechanical properties under static and dynamic loading. This variability is manifested in the difference in values of the relaxation modulus and dynamic modulus, which serve as the entry point for studying the dynamic and static mechanical properties of propellants. The relaxation modulus and dynamic modulus have a clear integral relationship in theory, but their consistency in engineering practice has never been verified. In this paper, by introducing the “catch-up factor λ” and “waiting factor γ”, a method for the inter-conversion of the dynamic storage modulus and relaxation modulus of HTPB propellant is established, and the consistency between them is verified. The results show that the time region of the calculated conversion values of the relaxation modulus obtained by this method covers 10−8−104 s, spanning twelve orders of magnitude. Compared to that of the relaxation modulus (10−4−104 s, spanning eight orders of magnitude), an expansion of four orders of magnitude is achieved. This enhances the expression ability of the relaxation modulus on the mechanical properties of the propellant. Furthermore, when the conversion method is applied to the dynamic−static modulus conversion of the other two HTPB propellants, the results show that the correlation coefficient between the calculated and measured conversion values is R2 > 0.933. This proves the applicability of this method to the dynamic−static modulus conversion of other types of HTPB propellants. It was also found that λ and γ have the same universal optimal value for different HTPB propellants. As a bridge for static and dynamic modulus conversion, this method greatly expands the expression ability of the relaxation modulus and dynamic storage modulus on the mechanical properties of the HTPB propellant, which is of great significance in the research into the mechanical properties of the propellant.

Deterioration of Mechanical Properties and the Damage Constitutive Model of Corroded Steel in an Industrial Environment

To investigate the degradation law of the mechanical properties of corroded steel, the standard specimens from machining steel members in service for 9 years in an industrial environment were subjected to tensile tests. The influences of different degrees and types of corrosion on the fracture path, stress-strain curve, and mechanical properties of specimens were discussed. Finally, the damage constitutive model of corroded steel was established based on the damage mechanics theory. The results showed that the failure modes of corroded specimens were related to the degrees and types of corrosion. The fracture morphology of specimens with general corrosion were step-like and the fractures of steel were uneven. However, those with local corrosion were mainly flat-like, and the fracture path was along the cross section where the larger corrosion pits were located. The fracture path of the specimen was related to the interaction of the corroded surface and internal material defects (holes). Meanwhile, with the increase of corrosion degree, the yield platform of stress-strain curve gradually became shorter, or even disappeared, and the ultimate strain and elongation at break decreased, implying that the ductility of steel became worse. Ultimately, the good agreement between the curves of the model and test indicated that the damage model could reflect the damage development process of corroded steel in the tensile process better. Corrosion damage resulted in the decrease in the damage threshold, and the damage variable D decreased by the time fracture occurred and the maximum reduction rate was up to 62.5%.

Quasi-Static Mechanical Properties and Continuum Constitutive Model of the Thyroid Gland

The purpose of this study is to obtain the digital twin parameters of the thyroid gland and to build a constitutional model of the thyroid gland based on continuum mechanics, which will lay the foundation for the establishment of a surgical training system for the thyroid surgery robot and the development of the digital twin of the thyroid gland. First, thyroid parenchyma was obtained from fresh porcine thyroid tissue and subjected to quasi-static unconfined uniaxial compression tests using a biomechanical test platform with two strain rates (0.005 s^-1 and 0.05 s^-1) and two loading orientations (perpendicular to the thyroid surface and parallel to the thyroid surface). Based on this, a tensile thyroid model was established to simulate the stretching process by using the finite element method. The thyroid stretching test was carried out under the same parameters to verify the validity of the hyperelastic constitutive model. The quasi-static mechanical property parameters of the thyroid tissue were obtained by a quasi-static unconstrained uniaxial compression test, and a constitutional model that can describe the quasi-static mechanical properties of thyroid tissue was proposed based on the principle of continuum media mechanics, which is of great value for the establishment of a surgical training system for the head and neck surgery robot and for the development of the thyroid digital twin.