Nested structure role in the mechanical response of spicule inspired fibers

Euplectella aspergillummarine sponge spicules are renowned for their remarkable strength and toughness. These spicules exhibit a unique concentric layering structure, which contributes to their exceptional mechanical resistance. In this study, finite element method simulations were used to comprehensively investigate the effect of nested cylindrical structures on the mechanical properties of spicules. This investigation leveraged scanning electron microscopy images to guide the computational modeling of the microstructure and the results were validated by three-point bending tests of 3D-printed spicule-inspired structures. The numerical analyses showed that the nested structure of spicules induces stress and strain jumps on the layer interfaces, reducing the load on critical zones of the fiber and increasing its toughness. It was found that this effect shows a tapering enhancement as the number of layers increases, which combines with a threshold related to the 3D-printing manufacturability to suggest a compromise for optimal performance. A comprehensive evaluation of the mechanical properties of these fibers can assist in developing a new generation of bioinspired structures with practical real-world applications.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Effects of different contact angles during forefoot running on the stresses of the foot bones: a finite element simulation study

Introduction: The purpose of this study was to compare the changes in foot at different sole-ground contact angles during forefoot running. This study tried to help forefoot runners better control and improve their technical movements by comparing different sole-ground contact angles. Methods: A male participant of Chinese ethnicity was enlisted for the present study, with a recorded age of 25 years, a height of 183 cm, and a body weight of 80 kg. This study focused on forefoot strike patterns through FE analysis. Results: It can be seen that the peak von Mises stress of M1-5 (Metatarsal) of a (Contact angle: 9.54) is greater than that of b (Contact angle: 7.58) and c (Contact angle: 5.62) in the three cases. On the contrary, the peak von Mises stress of MC (Medial Cuneiform), IC (Intermediate Cuneiform), LC (Lateral Cuneiform), C (Cuboid), N (Navicular), T (Tarsal) in three different cases is opposite, and the peak von Mises stress of c is greater than that of a and b. The peak von Mises stress of b is between a and c. Conclusion: This study found that a reduced sole-ground contact angle may reduce metatarsal stress fractures. Further, a small sole-ground contact angle may not increase ankle joint injury risk during forefoot running. Hence, given the specialized nature of the running shoes designed for forefoot runners, it is plausible that this study may offer novel insights to guide their athletic pursuits.

Cartilage thickness mismatches in patellar osteochondral allograft transplants affect local cartilage stresses

Osteochondral allograft implantation is a form of cartilage transplant in which a cylindrical graft of cartilage and subchondral bone from a donor is implanted into a patient's prepared articular defect site. No standard exists for matching the cartilage thickness of the donor and recipient. The goal of this study was to use finite element (FE) analysis to identify the effect of cartilage thickness mismatches between donor and recipient cartilage on cartilage stresses in patellar transplants. Two types of FE models were used: patient-specific 3D models and simplified 2D models. 3D models highlighted which geometric features produced high-stress regions in the patellar cartilage and provided ranges for the parameter sweeps that were conducted with 2D models. 2D models revealed that larger thickness mismatches, thicker recipient cartilage, and a donor-to-recipient cartilage thickness ratio (DRCR) < 1 led to higher stresses at the interface between the donor and recipient cartilage. A surface angle between the donor-recipient cartilage interface and cartilage surface normal near the graft boundary increased stresses when DRCR > 1, with the largest increase observed for an angle of 15°. A surface angle decreased stresses when DRCR < 1. Clinical Significance: This study highlights a potential mechanism to explain the high rates of failure of patellar OCAs. Additionally, the relationship between geometric features and stresses explored in this study led to a hypothetical scoring system that indicates which transplanted patellar grafts may have a higher risk of failure.

FEM Simulation of AlSi10Mg Artifact for Additive Manufacturing Process Calibration with Industrial-Computed Tomography Validation

Dimensional accuracy of selective laser melting (SLM) parts is one of manufacturers' major concerns. The additive manufacturing (AM) process is characterized by high-temperature gradients, consolidation, and thermal expansion, which induce residual stress on the part. These stresses are released by separating the part from the baseplate, leading to plastic deformation. Thermo-mechanical finite elements (FE) simulation can be adopted to determine the effect of process parameters on final geometrical accuracy and minimize non-compliant parts. In this research, a geometry for process parameter calibration is presented. The part has been manufactured and then analyzed with industrial computed tomography (iCT). An FE process simulation has been performed considering material removal during base plate separation, and the computed distortions have been compared with the results of the iCT, revealing good accordance between the final product and its digital twin.

Does a novel bridging collar in endoprosthetic replacement optimise the mechanical environment for osseointegration? A finite element study

Introduction: Limb-salvage surgery using endoprosthetic replacements (EPRs) is frequently used to reconstruct segmental bone defects, but the reconstruction longevity is still a major concern. In EPRs, the stem-collar junction is the most critical region for bone resorption. We hypothesised that an in-lay collar would be more likely to promote bone ongrowth in Proximal Femur Reconstruction (PFR), and we tested this hypothesis through validated Finite Element (FE) analyses simulating the maximum load during walking. Methods: We simulated three different femur reconstruction lengths (proximal, mid-diaphyseal, and distal). For each reconstruction length one in-lay and one traditional on-lay collar model was built and compared. All reconstructions were virtually implanted in a population-average femur. Personalised Finite Element models were built from Computed Tomography for the intact case and for all reconstruction cases, including contact interfaces where appropriate. We compared the mechanical environment in the in-lay and on-lay collar configurations, through metrics of reconstruction safety, osseointegration potential, and risk of long-term bone resorption due to stress-shielding. Results: In all models, differences with respect to intact conditions were localized at the inner bone-implant interface, being more marked in the collar-bone interface. In proximal and mid-diaphyseal reconstructions, the in-lay configuration doubled the area in contact at the bone-collar interface with respect to the on-lay configuration, showed less critical values and trends of contact micromotions, and consistently showed higher (roughly double) volume percentages of predicted bone apposition and reduced (up to one-third) percentages of predicted bone resorption. In the most distal reconstruction, results for the in-lay and on-lay configurations were generally similar and showed overall less favourable maps of the bone remodelling tendency. Discussion: In summary, the models corroborate the hypothesis that an in-lay collar, by realising a more uniform load transfer into the bone with a more physiological pattern, creates an advantageous mechanical environment at the bone-collar interface, compared to an on-lay design. Therefore, it could significantly increase the survivorship of endo-prosthetic replacements.

PIPER adult comfort: an open-source full body human body model for seating comfort assessment and its validation under static loading conditions

Introduction: In this paper we introduce an adult-sized FE full-body HBM for seating comfort assessments and present its validation in different static seating conditions in terms of pressure distribution and contact forces. Methods: We morphed the PIPER Child model into a male adult-sized model with the help of different target sources including his body surface scans, and spinal and pelvic bone surfaces and an open sourced full body skeleton. We also introduced soft tissue sliding under the ischial tuberosities (ITs). The initial model was adapted for seating applications with low modulus soft tissue material property and mesh refinements for buttock regions, etc. We compared the contact forces and pressure-related parameters simulated using the adult HBM with those obtained experimentally from the person whose data was used for the model development. Four seat configurations, with the seat pan angle varying from 0° to 15° and seat-to-back angle fixed at 100°, were tested. Results: The adult HBM could correctly simulate the contact forces on the backrest, seat pan, and foot support with an average error of less than 22.3 N and 15.5 N in the horizontal and vertical directions, which is small considering the body weight (785 N). In terms of contact area, peak, and mean pressure, the simulation matched well with the experiment for the seat pan. With soft tissue sliding, higher soft tissue compression was obtained in agreement with the observations from recent MRI studies. Discussion: The present adult model could be used as a reference using a morphing tool as proposed in PIPER. The model will be published openly online as part of the PIPER open-source project (www.PIPER-project.org) to facilitate its reuse and improvement as well as its specific adaptation for different applications.

Multiscale modeling of the dynamic growth of cancerous tumors under the influence of chemotherapy drugs

A comprehensive model of chemotherapy treatment of cancer can help us to optimize the drug administration/dosage and improve the treatment outcome. In the present study, a multiscale mathematical model of tumor growth during chemotherapy treatment is developed to predict its response to the medication and cancer progression. The modeling is a continuous multiscale simulation consisting of three tissue phases including cancer cells, normal cells, and extracellular matrix. In addition to the drug administration, the impacts of immune cells, programmed cell death, nutrient competition, and glucose concentration are included. The outputs of our mathematical model conform to the published experimental and clinical data, and it can be used in optimizing chemotherapy, and personalized cancer treatment.

A Nodal Immersed Finite Element-Finite Difference Method

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve.

Biomechanical evaluation of custom-made short implants with wing retention applied in severe atrophic maxillary posterior region restoration: A three-dimensional finite element analysis

Severe bone atrophy in the maxillary posterior region poses a big challenge to implant restoration. Digitally designed and customized short implants with wing retention provide a safer and minimally invasive implant restoration scheme in such circumstances. Small titanium wings are integrated with the short implant supporting the prosthesis. Using digital designing and processing technology, the wings fixed by titanium screws can be flexibly designed, providing the main fixation. The design of the wings will influence the stress distribution and implant stability. This study analyzes the position, structure, and spread area of the wings fixture scientifically by means of three-dimensional finite element analysis. The design of the wings is set to linear, triangular, and planar styles. Under the simulated vertical and oblique occlusal forces, the implant displacement and stress between the implant and the bone surface are analyzed at different bone heights of 1 mm, 2 mm, and 3 mm. The finite element results show that the planar form can better disperse the stress. By adjusting the cusp slope to reduce the influence of lateral force, short implants with planar wing fixtures can be used safely even if the residual bone height is only 1 mm. The results of the study provide a scientific basis for the clinical application of this new customized implant.

A Brief Note on Building Augmented Reality Models for Scientific Visualization

Augmented reality (AR) has revolutionized the video game industry by providing interactive, three-dimensional visualization. Interestingly, AR technology has only been sparsely used in scientific visualization. This is, at least in part, due to the significant technical challenges previously associated with creating and accessing such models. To ease access to AR for the scientific community, we introduce a novel visualization pipeline with which they can create and render AR models. We demonstrate our pipeline by means of finite element results, but note that our pipeline is generally applicable to data that may be represented through meshed surfaces. Specifically, we use two open-source software packages, ParaView and Blender. The models are then rendered through the <model-viewer> platform, which we access through Android and iOS smartphones. To demonstrate our pipeline, we build AR models from static and time-series results of finite element simulations discretized with continuum, shell, and beam elements. Moreover, we openly provide python scripts to automate this process. Thus, others may use our framework to create and render AR models for their own research and teaching activities.

Innovative Design of Residual Stress and Strain Distributions for Analyzing the Hydrogen Embrittlement Phenomenon in Metallic Materials

Round-notched samples are commonly used for testing the susceptibility to hydrogen embrittlement (HE) of metallic materials. Hydrogen diffusion is influenced by the stress and strain states generated during testing. This state causes hydrogen-assisted micro-damage leading to failure that is due to HE. In this study, it is assumed that hydrogen diffusion can be controlled by modifying such residual stress and strain fields. Thus, the selection of the notch geometry to be used in the experiments becomes a key task. In this paper, different HE behaviors are analyzed in terms of the stress and strain fields obtained under diverse loading conditions (un-preloaded and preloaded causing residual stress and strains) in different notch geometries (shallow notches and deep notches). To achieve this goal, two uncoupled finite element (FE) simulations were carried out: (i) a simulation by FE of the loading sequences applied in the notched geometries for revealing the stress and strain states and (ii) a simulation of hydrogen diffusion assisted by stress and strain, for estimating the hydrogen distributions. According to results, hydrogen accumulation in shallow notches is heavily localized close to the wire surface, whereas for deep notches, hydrogen is more uniformly distributed. The residual stress and plastic strains generated by the applied preload localize maximum hydrogen concentration at deeper points than un-preloaded cases. As results, four different scenarios are established for estimating "a la carte" the HE susceptibility of pearlitic steels just combining two notch depths and the residual stress and strain caused by a preload.

A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental Pressure-Correction Method

In this paper, a new decoupling method is proposed to solve a nematic liquid crystal flow with stretching effect. In the finite element discrete framework, the director vector is calculated by introducing a new auxiliary variable w, and the velocity vector and scalar pressure are decoupled by a nonincremental pressure-correction projection method. Then, the energy dissipation law and unconditional energy stability of the resulting system are given. Finally, some numerical examples are given to verify the effects of various parameters on the singularity annihilation, stability and accuracy in space and time.

A PDE-regularized smoothing method for space-time data over manifolds with application to medical data

We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regularizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in practical contexts, by dealing with neuroimaging and hemodynamic data.

On the Crashworthiness Behaviour of Innovative Sandwich Shock Absorbers

Increasing the impact resistance properties of any transport vehicle is a real engineering challenge. This challenge is addressed in this paper by proposing a high-performing structural solution. Hence, the performance, in terms of improvement of the energy absorbing characteristics and the reduction of the peak accelerations, of highly efficient shock absorbers integrated in key locations of a minibus chassis have been assessed by means of numerical crash simulations. The high efficiency of the proposed damping system has been achieved by improving the current design and manufacturing process of the state-of-the-art shock absorbers. Indeed, the proposed passive safety system is composed of additive manufactured, hybrid polymer/composite (Polypropylene/Composite Fibres Reinforced Polymers-PP/CFRP) shock absorbers. The resulting hybrid component combines the high stiffness-to-mass and strength-to-mass ratios characteristic of the composites with the capability of the PP to dissipate energy by plastic deformation. Moreover, thanks to the Additive Manufacturing (AM) technique, low-mass and low-volume highly-efficient shock-absorbing sandwich structures can be designed and manufactured. The use of high-efficiency additively manufactured sandwich shock absorbers has been demonstrated as an effective way to improve the passive safety of passengers, achieving a reduction in the peak of the reaction force and energy absorbed in the safety cage of the chassis' structure, respectively, up to up to 30 kN and 25%.

Thermomechanical Performance Analysis of Novel Cement-Based Building Envelopes with Enhanced Passive Insulation Properties

The design of new insulating envelopes is a direct route towards energy efficient buildings. The combinations of novel materials, such as phase-change (PCM), and advanced manufacturing techniques, such as additive manufacturing, may harness important changes in the designing of building envelopes. In this work we propose a novel methodology for the design of cement-based building envelopes. Namely, we combined the use of a multiscale, multiphysical simulation framework with advanced synthesis techniques, such as the use of phase-change materials and additive manufacturing for the design of concrete envelopes with enhanced insulation properties. At the material scale, microencapsulated PCMs are added to a cementitious matrix to increase heat storage. Next, at the component level, we create novel designs for the blocks, here defined as HEXCEM, by means of additive manufacturing. The material and component design process is strongly supported on heat transfer simulations with the use of the finite element method. Effective thermal properties of the mixes can be obtained and subsequently used in macroscale simulations to account for the effect of the volume fraction of PCMs. From the experimental and numerical tests, we report an increase in the the thermal inertia, which results in thermal comfort indoors.

The risk of rupture and abdominal aortic aneurysm morphology: A computational study

Prediction of rupture and optimal timing for abdominal aortic aneurysm (AAA) surgical intervention remain wanting even after decades of clinical, histological, and numerical research. Although studies estimating rupture from AAA geometrical features from CT imaging showed some promising results, they are still not being used in practice. Patient-specific numerical stress analysis introduced too many assumptions about wall structure for the related rupture potential index (RPI) to be considered reliable. Growth and remodeling (G&R) numerical models eliminate some of these assumptions and thus might have the most potential to calculate mural stresses and RPI and increase our understanding of rupture. To recognize numerical models as trustworthy, it is necessary to validate the computed results with results derived from imaging. Elastin degradation function is one of the main factors that determine idealized aneurysm sac shape. Using a hundred different combinations of variables defining AAA geometry or influences AAA stability (elastin degradation function parameters, collagen mechanics, and initial healthy aortic diameters), we investigated the relationship between AAA morphology and RPI and compared numerical results with clinical findings. Good agreement of numerical results with clinical expectations from the literature gives us confidence in the validity of the numerical model. We show that aneurysm morphology significantly influences the stability of aneurysms. Additionally, we propose new parameters, geometrical rupture potential index (GRPI) and normalized aneurysm length (NAL), that might predict rupture of aneurysms without thrombus better than currently used criteria (i.e., maximum diameter and growth rate). These parameters can be computed quickly, without the tedious processing of CT images.

Practical computation of the diffusion MRI signal based on Laplace eigenfunctions: permeable interfaces

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal, called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the tissue geometry and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. In a previous publication, we presented a simulation framework that we implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for biological cells subject to impermeable membrane boundary conditions. In this work, we extend our simulation framework to include geometries that contain permeable cell membranes. We describe the new computational techniques that allowed this generalization and we analyze the effects of the magnitude of the permeability coefficient on the eigendecomposition of the diffusion and Bloch-Torrey operators. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

A homogenized cerebrospinal fluid model for diffuse optical tomography in the neonatal head

Diffuse optical tomography is a non-invasive and non-irradiating medical imaging technique that is particularly suitable for cerebral monitoring of newborns since it can be used at the bedside of the patient. Here, a new model for optical tomography in the neonatal brain is presented that takes into account the presence of arachnoid trabeculae in the cerebrospinal fluid (CSF). It is known that the classical diffusion approximation (DA) for light propagation is at the limit of validity in the CSF layer due to the low values of the absorption and scattering coefficients. The new model is obtained by the DA of the homogenized radiative transfer equation and is rigorously justified. Numerical results in two and three dimensions attest for the improved sensitivity of the new model to the presence of perturbations in the brain layer.

Three-dimensional quantification of circulation using finite-element methods in four-dimensional flow MR data of the thoracic aorta

PURPOSE

Three-dimensional (3D) quantification of circulation using a Finite Elements methodology.

METHODS

We validate our 3D method using an in-silico arch model, for different mesh resolutions, image resolution and noise levels, and we compared this with a currently used 2D method. Finally, we evaluated the application of our methodology in 4D Flow MRI data of ascending aorta of six healthy volunteers, and six bicuspid aortic valve (BAV) patients, three with right and three with left handed flow, at peak systole. The in-vivo data was compared using a Mann-Whitney U-test between volunteers and patients (right and left handed flow).

RESULTS

The robustness of our method throughout different image resolutions and noise levels showed subestimation of circulation less than 45 cm² /s in comparison with the 55cm² /s generated by the current 2D method. The circulation (mean ± SD) of the healthy volunteer group was 13.83 ± 28.78 cm² /s, in BAV patients with right-handed flow 724.37 ± 317.53 cm² /s, and BAV patients with left-handed flow -480.99 ± 387.29 cm² /s. There were significant differences between healthy volunteers and BAV patients groups (P-value < .01), and also between BAV patients with a right-handed or left-handed helical flow and healthy volunteers (P-value < .01).

CONCLUSION

We propose a novel 3D formulation to estimate the circulation in the thoracic aorta, which can be used to assess the differences between normal and diseased hemodynamic from 4D-Flow MRI data. This method also can correctly differentiate between the visually seen right- and left-handed helical flow, which suggests that this approach may have high clinical sensitivity, but requires confirmation in longitudinal studies with a large cohort.

Optimizing the Mechanical Properties of Ultra-High-Performance Fibre-Reinforced Concrete to Increase Its Resistance to Projectile Impact

This study describes an extensive experimental investigation of various mechanical properties of Ultra-High-Performance Fibre-Reinforced Concrete (UHPFRC). The scope is to achieve high strength and ductile behaviour, hence providing optimal resistance to projectile impact. Eight different mixtures were produced and tested, three mixtures of Ultra-High-Performance Concrete (UHPC) and five mixtures of UHPFRC, by changing the amount and length of the steel fibres, the quantity of the superplasticizer, and the water to binder (w/b) ratio. Full stress-strain curves from compression, direct tension, and flexural tests were obtained from one batch of each mixture to examine the influence of the above parameters on the mechanical properties. The Poisson's ratio and modulus of elasticity in compression and direct tension were measured. Additionally, a factor was determined to convert the cubic strength to cylindrical. Based on the test results, the mixture with high volume (6%) and a combination of two lengths of steel fibres (3% each), water to binder ratio of 0.16% and 6.1% of superplasticizer to binder ratio exhibited the highest strength and presented great deformability in the plastic region. A numerical simulation developed using ABAQUS was capable of capturing very well the experimental three-point bending response of the UHPFRC best-performed mixture.

A Three-Phase Transport Model for High-Temperature Concrete Simulations Validated with X-ray CT Data

Concrete exposure to high temperatures induces thermo-hygral phenomena, causing water phase changes, buildup of pore pressure and vulnerability to spalling. In order to predict these phenomena under various conditions, a three-phase transport model is proposed. The model is validated on X-ray CT data up to 320 °C, showing good agreement of the temperature profiles and moisture changes. A dehydration description, traditionally derived from thermogravimetric analysis, was replaced by a formulation based on data from neutron radiography. In addition, treating porosity and dehydration evolution as independent processes, previous approaches do not fulfil the solid mass balance. As a consequence, a new formulation is proposed that introduces the porosity as an independent variable, ensuring the latter condition.

Effect of Manufacturing on the Transverse Response of Polymer Matrix Composites

The effect of residual stress build-up on the transverse properties of thermoset composites is studied through direct and inverse process modeling approaches. Progressive damage analysis is implemented to characterize composite stiffness and strength of cured composites microstructures. A size effect study is proposed to define the appropriate dimensions of Representative Volume Elements (RVEs). A comparison between periodic (PBCs) and flat (FBCs) boundary conditions during curing is performed on converged RVEs to establish computationally efficient methodologies. Transverse properties are analyzed as a function of the fiber packing through the nearest fiber distance statistical descriptor. A reasonable mechanical equivalence is achieved for RVEs consisting of 40 fibers. It has been found that process-induced residual stresses and fiber packing significantly contribute to the scatter in composites transverse strength. Variation of ±5% in average strength and 18% in standard deviation are observed with respect to ideally cured RVEs that neglect residual stresses. It is established that process modeling is needed to optimize the residual stress state and improve composite performance.

A multiscale four-layer finite element model to predict the effects of collagen fibers on skin behavior under tension

Human skin is a complex multilayered multiscale material that exhibits nonlinear and anisotropic mechanical behavior. It has been reported that its macroscopic behavior in terms of progression of wrinkles induced by aging is strongly dependent on its microscopic composition in terms of collagen fibers in the dermis layer. In the present work, a multiscale four-layer 2D finite element model of the skin was developed and implemented in Matlab code. The focus here was to investigate the effects of dermal collagen on the macroscopic mechanical behavior of the skin. The skin was modeled by a continuum model composed of four layers: the Stratum Corneum, the epidermis, the dermis, and the hypodermis. The geometry of the different layers of the skin was represented in a 2D model with their respective thicknesses and material properties taken from literature data. The macroscopic behavior of the dermis was modeled with a nonlinear multiscale approach based on a multiscale elastic model of collagen structure going from cross-linked molecules to the collagen fiber, combined with a Mori-Tanaka homogenization scheme. The model includes the nonlinear elasticity of the collagen fiber density, the fiber radius, the undulation, and the fiber orientation. An axial tension was applied incrementally to the lateral surfaces of the skin model. A parametric study was performed in order to investigate the effect of the collagen constituents on the macroscopic skin mechanical behavior in terms of the predicted macroscopic stress-strain curve of the skin. The results of the FE computations under uniaxial tension showed that the different layers undergo different strains, leading to a difference in the transversal deformation at the top surface. In addition, the parametric study revealed a strong correlation between macroscopic skin elasticity and its collagen structure.

The Challenge of Dental Education After COVID-19 Pandemic - Present and Future Innovation Study Design

The present work suggests research and innovation on the topic of dental education after the COVID-19 pandemic, is highly justified and could lead to a step change in dental practice. The challenge for the future in dentistry education should be revised with the COVID-19 and the possibility for future pandemics, since in most countries dental students stopped attending the dental faculties as there was a general lockdown of the population. The dental teaching has an important curriculum in the clinic where patients attend general dentistry practice. However, with SARS-CoV-2 virus, people may be reluctant having a dental treatment were airborne transmission can occur in some dental procedures. In preclinical dental education, the acquisition of clinical, technical skills, and the transfer of these skills to the clinic are extremely important. Therefore, dental education has to adapt the curriculum to embrace new technology devices, instrumentations systems, haptic systems, simulation based training, 3D printer machines, to permit validation and calibration of the technical skills of dental students.

Thermal jet drilling of granite rock: a numerical 3D finite-element study

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage-viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m^-2) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Spatial extension of a bone remodeling dynamics model and its finite element analysis

There are many works dealing with the dynamics of bone remodeling, proposing increasingly complex and complete models. In the recent years, the efforts started to focus on developing models that not only reproduce the temporal evolution, but also include the spatial aspects of this phenomenon. In this work, we propose the spatial extension of an existing model that includes the dynamics of osteocytes. The spatial dependence is modeled in terms of a linear diffusion, as proposed in previous works dealing with related problems. The resulting model is then written in its variational form, and fully discretized using the well-known finite element method and a combination of the implicit and explicit Euler schemes. The numerical algorithm is then analyzed, proving some a priori error estimates and its linear convergence. Finally, we extend the examples already published for the temporal model to one and two dimensions, showing the dynamics of the solution in the spatial domain.

A mathematical model for bleb regulation in zebrafish primordial germ cells

Blebs are cell protrusions generated by local membrane-cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane-cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion-advection-reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.

Single‑Stroke Attachment of Sheets to Tube Ends Made from Dissimilar Materials

This paper presents a new joining method by a forming process for attaching sheets to tube ends. The process consists of two different forming stages carried out sequentially in a single stroke. Firstly, the free tube end is flared by compression with a contoured die, then is squeezed (indented) against the sheet surface to create a mechanical interlocking. The new process is carried out at an ambient temperature and, in contrast to existing joining by forming operations based on tube expansion, it avoids seal welds, tube protrusions above the sheet surfaces, and machining of grooves on the sheet holes to obtain the form-fit joints. The paper starts by analyzing the process deformation mechanics and its main operating variables and finishes by presenting examples that demonstrate its effectiveness for attaching sheets to tube ends made from polyvinylchloride and aluminum. Experimental and numerical simulation work provides support to the presentation.

Machine Vision for As-Built Modeling of Complex Draped Composite Structures

The transition in the use of fiber composite structures from special applications to application in the mass market is accompanied by high demands in quality assurance. The consequential costs of unclear process design, unknown fiber orientations, and uncertainty regarding the effects of any fiber angle deviations can lead to market considerations (higher costs/time for development) in mass production that advise against the use of fiber composites, despite their superiority compared with conservative materials. Active monitoring of the deposited reinforcement layers and an evaluation of the real fiber orientation can form the basis of a robust industrial use of fiber composites by a first-time right production that is able to reduce the process variability. This paper describes the application of an image analysis system to provide both geometric topology and local reinforcement fiber orientation feedback to a finite-element (FE) model. The application during an industrial composite part production is described, and the possibilities of using it for the improvement of the lightweight character, the reduction of rejects, and the realization of a quality management system are shown. The determined component data are made directly available for use in numerical simulations and, thus, they serve as a non-destructive evaluation of the components under real conditions in which all production-dependent influences that affect the fiber orientation are incorporated.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

Numerical and experimental analyses of the use of double vertical barrier walls for groundwater protection

The groundwater contamination and its impacts on the hydrologic systems and society are critical environmental concerns in the world. This research presents insights from the numerical (SEEP/W and CTRAN/W) and the experimental (sandbox model) analyses of the use of double vertical barrier walls for groundwater protection. The main objective was to evaluate contaminant transport under the effect of several variables. The arrival time increases with increasing the distance between the pollutant source and the first wall, first wall depth of penetration, the distance between the two walls and also increases at smaller hydraulic head differences, and lower conductivities. Furthermore, using double barrier walls would significantly reduce contaminant concentration at the downstream area. This control is most significant when the depth of first wall penetration is larger than that of the second wall. Results proved consistent with several similar studies and advantageous over many of them by the integrated use of both techniques with more variable parameters evaluated. PRACTITIONER POINTS: The research will introduce insights from the effect of using double barrier walls on the hydraulic control of contaminant transport. The effect of several variables on the contaminant arrival time and concentration is investigated. Using double barrier walls has a significant impact on contamination transport through the soil. This control is most significant when the penetration depth of the first wall is larger than that of the second.

Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

Finite Element Analysis of a Novel Aortic Valve Stent

Worldwide, one of the leading causes of death for patients with cardiovascular disease is aortic valve failure or insufficiency as a result of calcification and cardiovascular disease. The surgical treatment consists of repair or total replacement of the aortic valve. Artificial aortic valve implantation via a percutaneous or endovascular procedure is the minimally invasive alternative to open chest surgery, and the only option for high-risk or older patients. Due to the complex anatomical location between the left ventricle and the aorta, there are still engineering design optimization challenges which influence the long-term durability of the valve. In this study we developed a computer model and performed a numerical analysis of an original self-expanding stent for transcatheter aortic valve in order to optimize its design and materials. The study demonstrates the current valve design could be a good alternative to the existing commercially available valve devices.

Cold Forming of Al-TiB2 Composites Fabricated by SPS: A Computational Experimental Study

The mechanical response and failure of Al-TiB₂ composites fabricated by Spark Plasma Sintering (SPS) were investigated. The effective flow stress at room temperature for different TiB₂ particle volume fractions between 0% and 15% was determined using compression experiments on cylindrical specimens in conjunction with an iterative computational methodology. A different set of experiments on tapered specimens was used to validate the effective flow curves by comparing experimental force–displacement curves and deformation patterns to the ones obtained from the computations. Using a continuum damage mechanics approach, the experiments were also used to construct effective failure curves for each material composition. It was demonstrated that the fracture modes observed in the different experiments could be reproduced in the computations. The results show that increasing the TiB₂ particle volume fraction to 10% results in an increase in material effective yield stress and a decrease in hardening. For a particle volume fraction of 15%, the effective yield stress decreases with no significant influence on the hardening slope. The ductility (workability) of the composite decreases with increasing particle volume fraction.

Gradient-Enhanced Modelling of Damage for Rate-Dependent Material Behaviour-A Parameter Identification Framework

The simulation of complex engineering components and structures under loads requires the formulation and adequate calibration of appropriate material models. This work introduces an optimisation-based scheme for the calibration of viscoelastic material models that are coupled to gradient-enhanced damage in a finite strain setting. The parameter identification scheme is applied to a self-diagnostic poly(dimethylsiloxane) (PDMS) elastomer, where so-called mechanophore units are incorporated within the polymeric microstructure. The present contribution, however, focuses on the purely mechanical response of the material, combining experiments with homogeneous and inhomogeneous states of deformation. In effect, the results provided lay the groundwork for a future extension of the proposed parameter identification framework, where additional field-data provided by the self-diagnostic capabilities can be incorporated into the optimisation scheme.

Analysis of a bone remodeling model with myeloma disease arising in cellular dynamics

In this work we study a bone remodeling model for the evolution of the myeloma disease. The biological problem is written as a coupled nonlinear system consisting of parabolic partial differential equations. They are written in terms of the concentrations of osteoblasts and osteoclasts, the density of the relative bone and the concentration of the tumor cells. Then, we deal with the numerical analysis of this variational problem, introducing a numerical approximation by using the finite element method and a hybrid combination of both implicit and explicit Euler schemes. We perform some a priori error estimates and show a few numerical simulations to demonstrate the accuracy of the approximation. Finally, we present the comparison with previous works and the behavior of the solution in two-dimensional examples.

Linear Elastic FE-Analysis of Porous, Laser Welded, Heat Treatable, Aluminium High Pressure Die Castings Based on X-Ray Computed Tomography Data

The welding of aluminium high pressure die castings is a well known and broadly investigated challenge in various fields of industry and research. Prior research in this specific field mainly focused on the optimisation of the welding and the casting process and on the cause of the frequently occurring porosity and incomplete fusion phenomena, whereas the impacts of these defects have hardly been addressed. Therefore, the underlying study presents the investigation of weldments in EN AC-AlSi10MnMg high pressure aluminium die castings by linear elastic finite element analysis based on X-ray computed tomography as a novel approach. Hereby, four laser weldments with differing surfaces and pore contents were investigated by X-ray computed tomography and tensile testing. Based on the voxel datasets of the porous weldments, triangular finite element meshes were generated and a numerical finite element analysis was conducted. Good agreement of the stress-strain curves between the simulations and the experiments was achieved.

Mathematical modeling of mass and energy transport for thermoembolization

Background: Thermoembolization presents a unique treatment alternative for patients diagnosed with hepatocellular carcinoma. The approach delivers a reagent that undergoes an exothermic chemical reaction and combines the benefits of embolic as well as thermal- and chemical-ablative therapy modalities. The target tissue and vascular bed are subjected to simultaneous hyperthermia, ischemia, and chemical denaturation in a single procedure. To guide optimal delivery, we developed a mathematical model for understanding the competing diffusive and convective effects observed in thermoembolization delivery protocols.Methods: A mixture theory formulation was used to mathematically model thermoembolization as chemically reacting transport of an electrophile, dichloroacetyl chloride (DCACl), within porous living tissue. Mass and energy transport of each relevant constituent are considered. Specifically, DCACl is injected into the vessels and exothermically reacts with water in the blood or tissue to form dichloroacetic acid and hydrochloric acid. Neutralization reactions are assumed instantaneous in this approach. We validated the mathematical model predictions of temperature using MR thermometry of the thermoembolization procedure performed in ex vivo kidney.Results: Mathematical modeling predictions of tissue death were highly dependent on the vascular geometry, injection pressure, and intrinsic amount of exothermic energy released from the chemical species, and were able to recapitulate the temperature distributions observed in MR thermometry.Conclusion: These efforts present a first step toward formalizing a mathematical model for thermoembolization and are promising for providing insight for delivery protocol optimization. While our approach captured the observed experimental temperature measurements, larger-scale experimental validation is needed to prioritize additional model complexity and fidelity.

An Experimental and Numerical Analysis of the Compression of Bimetallic Cylinders

This paper investigates the upsetting of bimetallic cylinders with an aluminum alloy center and a brass ring. The influence of the center-ring shape factor and type of assembly fit (interference and clearance), and the effect of friction on the compression force and ductile damage are comprehensively analyzed by means of a combined numerical-experimental approach. Results showed that the higher the shape factor, the lower the forces required, whereas the effect of friction is especially important for cylinders with the lowest shape factors. The type of assembly fit does not influence the compression force. The accumulated ductile damage in the compression of bimetallic cylinders is higher than in single-material cylinders, and the higher the shape factor, the lower the damage for the same amount of stroke. The highest values of damaged were found to occur at the middle plane, and typically in the ring. Results also showed that an interference fit was more favorable for preventing fracture of the ring than a clearance fit. Microstructural analysis by scanning electron microscopy revealed a good agreement with the finite element predicted distribution of ductile damage.

A computational model of open-irrigated radiofrequency catheter ablation accounting for mechanical properties of the cardiac tissue

Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmias. Although generally safe, it is not completely exempt from the risk of complications. The great flexibility of computational models can be a major asset in optimizing interventional strategies if they can produce sufficiently precise estimations of the generated lesion for a given ablation protocol. This requires an accurate description of the catheter tip and the cardiac tissue. In particular, the deformation of the tissue under the catheter pressure during the ablation is an important aspect that is overlooked in the existing literature, which resorts to a sharp insertion of the catheter into an undeformed geometry. As the lesion size depends on the power dissipated in the tissue and the latter depends on the percentage of the electrode surface in contact with the tissue itself, the sharp insertion geometry has the tendency to overestimate the lesion obtained, which is a consequence of the tissue temperature rise overestimation. In this paper, we introduce a full 3D computational model that takes into account the tissue elasticity and is able to capture tissue deformation and realistic power dissipation in the tissue. Numerical results in FEniCS-HPC are provided to validate the model against experimental data and to compare the lesions obtained with the new model and with the classical ones featuring a sharp electrode insertion in the tissue.

A Finite Element Model for the Vibration Analysis of Sandwich Beam with Frequency-Dependent Viscoelastic Material Core

In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.

Numerical Modelling of Ballistic Impact Response at Low Velocity in Aramid Fabrics

In this study, the effect of the impact angle of a projectile during low-velocity impact on Kevlar fabrics has been investigated using a simplified numerical model. The implementation of mesoscale models is complex and usually involves long computation time, in contrast to the practical industry needs to obtain accurate results rapidly. In addition, when the simulation includes more than one layer of composite ply, the computational time increases even in the case of hybrid models. With the goal of providing useful and rapid prediction tools to the industry, a simplified model has been developed in this work. The model offers an advantage in the reduced computational time compared to a full 3D model (around a 90% faster). The proposed model has been validated against equivalent experimental and numerical results reported in the literature with acceptable deviations and accuracies for design requirements. The proposed numerical model allows the study of the influence of the geometry on the impact response of the composite. Finally, after a parametric study related to the number of layers and angle of impact, using a response surface methodology, a mechanistic model and a surface diagram have been presented in order to help with the calculation of the ballistic limit.

Modeling, Simulation, Experimentation, and Compensation of Temperature Effect in Impedance-Based SHM Systems Applied to Steel Pipes

Pipelines have been widely used for the transportation of chemical products, mainly those related to the petroleum industry. Damage in such pipelines can produce leakage with unpredictable consequences to the environment. There are different structural health monitoring (SHM) systems such as Lamb wave, comparative vacuum, acoustic emission, etc. for monitoring such structures. However, those based on piezoelectric sensors and electromechanical impedance technique (EMI) measurements are simple and efficient, and have been applied in a wide range of structures, including pipes. A disadvantage of such technique is that temperature changes can lead to false diagnoses. To overcome this disadvantage, temperature variation compensation techniques are normally incorporated. Therefore, this work has developed a complete study applied to damage detection in pipelines, including an innovative technique for compensating the temperature effect in EMI-based SHM and the modeling of piezoceramics bonded to pipeline structures using finite elements. Experimental results were used to validate the model. Moreover, the compensation method was tested in two steel pipes-healthy and damaged-compensating the temperature effect ranging from -40 °C to +80 °C, with analysis on the frequency range from 5 kHz to 120 kHz. The simulated and experimental results showed that the studies effectively contribute to the SHM area, mainly to EMI-based techniques.

Signatures of slip in dewetting polymer films

Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.

A Study of the Biomechanical Behavior of the Implantation Method of Inverted Shoulder Prosthesis (BIO⁻RSA) under Different Abduction Movements

The shoulder is the most mobile joint of the human body, but it is very fragile; several pathologies, and especially muscular degenerations in the elderly, can affect its stability. These are more commonly called rotator cuff fractures. In the case of this type of pathology, the mobility of the shoulder decreases and pain appears. In order to restore mobility and reduce pain, implantation of an inverted shoulder prosthesis is recommended. Unfortunately, over time a notch phenomenon has been observed. In the lower position of the arm, part of the implant comes into contact with the scapula and therefore causes deterioration of the bone. Among the solutions adopted is the lateralized method with bone grafting. However, a main disadvantage of this method concerns the reconstruction of the graft in the case of prosthesis revision. In this context, the aim of the present work was to reconstruct the shoulder joint in 3D in order to obtain a bio-faithful geometry, and then study the behavior of different types of biomaterials that can replace bone grafting. To this end, three arm abduction motions were examined for three individuals. From the results obtained, it appears that grafts in ultra-high molecular weight polyethylene (UHMWPE) exhibit a behavior closer to that of bones.

Linear variational principle for Riemann mappings and discrete conformality

We consider Riemann mappings from bounded Lipschitz domains in the plane to a triangle. We show that in this case the Riemann mapping has a linear variational principle: It is the minimizer of the Dirichlet energy over an appropriate affine space. By discretizing the variational principle in a natural way we obtain discrete conformal maps which can be computed by solving a sparse linear system. We show that these discrete conformal maps converge to the Riemann mapping in [Formula: see text], even for non-Delaunay triangulations. Additionally, for Delaunay triangulations the discrete conformal maps converge uniformly and are known to be bijective. As a consequence we show that the Riemann mapping between two bounded Lipschitz domains can be uniformly approximated by composing the discrete Riemann mappings between each Lipschitz domain and the triangle.

Computational aeroacoustics to identify sound sources in the generation of sibilant /s/

A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large-scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.

A coupled approach for fluid saturated poroelastic media and immersed solids for modeling cell-tissue interactions

In this paper, we propose a finite element-based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume-coupled two-field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy-Brinkman flow. The fluid phase is formulated with respect to the Lagrangian finite element mesh, following the solid phase deformation. The ISM is discretized with an independent Lagrangian mesh and may behave arbitrarily complex (it may, eg, be compressible, grow, and perform active deformations). We model two distinct types of interactions, namely, (1) the immersed fluid-structure interaction (FSI) between the ISM and the fluid phase in the PM and (2) the immersed structure-structure interaction (SSI) between the ISM and the solid phase in the PM. Within each time step, we solve both FSI and SSI, employing strongly coupled partitioned schemes. This novel finite element method establishes a main building block of an evolving computational framework for modeling and simulating complex biomechanical problems, with focus on key phenomena during cell migration. Cell movement is strongly influenced by mechanical interactions between the cell body and the surrounding tissue, ie, the extracellular matrix (ECM). In this context, the PM represents the ECM, ie, a fibrous scaffold of structural proteins interacting with interstitial flow, and the ISM represents the cell body. The FSI models the influence of fluid drag, and the SSI models the force transmission between cell and ECM at adhesions sites.

A Non-Linear Model of an All-Elastomer, in-Plane, Capacitive, Tactile Sensor Under the Application of Normal Forces

In this work, a large deformation, non-linear semi-analytical model for an all-elastomer, capacitive tactile unit-sensor is developed. The model is capable of predicting the response of such sensors over their entire sensing range under the application of normal forces. In doing so the finite flat punch indentation model developed earlier is integrated with a capacitance model to predict the change-in-capacitance as a function of applied normal forces. The empirical change-in-capacitance expression, based on the parallel plate capacitance model, is developed to account for the fringe field and saturation effects. The elastomeric layer used as a substrate in these sensors is modeled as an incompressible, non-linear, hyperelastic material. More specifically, the two term Mooney-Rivlin strain energy function is used as a constitutive response to relate the stresses and strains. The developed model assumes both geometrical as well as material non-linearity. Based on the related experimental work presented elsewhere, the inverse analysis, combining finite element (FE) modeling and non-linear optimization, is used to obtain the Mooney-Rivlin material parameters. Finally, to validate the model developed herein the model predictions are compared to the experimental results obtained elsewhere for four different tactile sensors. Great agreements are found to exist between the two which shows the model capabilities in capturing the response of these sensors. The model and methodologies developed in this work, may also help advancing bio-material studies in the determination of biological tissue properties.