Recent development in modeling and analysis of functionally graded materials and structures

Effect of density grading on the mechanical behaviour of advanced functionally graded lattice structures

Lattice structures have found significant applications in the biomedical field due to their interesting combination of mechanical and biological properties. Among these, functionally graded structures sparked interest because of their potential of varying their mechanical properties throughout the volume, allowing the design of biomedical devices able to match the characteristics of a graded structure like human bone. The aim of this works is the study of the effect of the density grading on the mechanical response and the failure mechanisms of a novel functionally graded lattice structure, namely Triply Arranged Octagonal Rings (TAOR). The mechanical behaviour was compared with the same lattice structures having constant density ratio. Electron Beam Melting technology was used to manufacture titanium alloy specimens with global relative densities from 10% to 30%. Functionally graded structures were obtained by increasing the relative density along the specimen, by individually designing the lattice's layers. Scanning electron and a digital microscopy were used to evaluate the dimensional mismatch between actual and designed structures. Compressive tests were carried out to obtain the mechanical properties and to evaluate the collapse modes of the structures in relation to their average relative density and lattice grading. Open-source Digital Image Correlation algorithm was applied to evaluate the deformation behaviour of the structures and to calculate their elastic moduli. The results showed that uniform density structures provide higher mechanical properties than functionally graded ones. The Digital Image Correlation results showed the possibility of effectively designing the different layers of functionally graded structures selecting desired local mechanical properties to mimic the different characteristics of cortical and cancellous bone.

Advancement in total hip implant: a comprehensive review of mechanics and performance parameters across diverse novelties

The UK's National Joint Registry (NJR) and the American Joint Replacement Registry (AJRR) of 2022 revealed that total hip replacement (THR) is the most common orthopaedic joint procedure. The NJR also noted that 10-20% of hip implants require revision within 1 to 10 years. Most of these revisions are a result of aseptic loosening, dislocation, implant wear, implant fracture, and joint incompatibility, which are all caused by implant geometry disparity. The primary purpose of this review article is to analyze and evaluate the mechanics and performance factors of advancement in hip implants with novel geometries. The existing hip implants can be categorized based on two parts: the hip stem and the joint of the implant. Insufficient stress distribution from implants to the femur can cause stress shielding, bone loss, excessive micromotion, and ultimately, implant aseptic loosening due to inflammation. Researchers are designing hip implants with a porous lattice and functionally graded material (FGM) stems, femur resurfacing, short-stem, and collared stems, all aimed at achieving uniform stress distribution and promoting adequate bone remodeling. Designing hip implants with a porous lattice FGM structure requires maintaining stiffness, strength, isotropy, and bone development potential. Mechanical stability is still an issue with hip implants, femur resurfacing, collared stems, and short stems. Hip implants are being developed with a variety of joint geometries to decrease wear, improve an angular range of motion, and strengthen mechanical stability at the joint interface. Dual mobility and reverse femoral head-liner hip implants reduce the hip joint's dislocation limits. In addition, researchers reveal that femoral headliner joints with unidirectional motion have a lower wear rate than traditional ball-and-socket joints. Based on research findings and gaps, a hypothesis is formulated by the authors proposing a hip implant with a collared stem and porous lattice FGM structure to address stress shielding and micromotion issues. A hypothesis is also formulated by the authors suggesting that the utilization of a spiral or gear-shaped thread with a matched contact point at the tapered joint of a hip implant could be a viable option for reducing wear and enhancing stability. The literature analysis underscores substantial research opportunities in developing a hip implant joint that addresses both dislocation and increased wear rates. Finally, this review explores potential solutions to existing obstacles in developing a better hip implant system.

Large Amplitude Vibration of FG-GPL Reinforced Conical Shell Panels on Elastic Foundation

Functionally graded (FG) composite structures reinforced by graphene platelets (GPL) have been widely adopted as a state-of-the-art structural element due to their preeminent properties and functional designability. However, most studies are confined to beams, plates, and cylindrical panels, relying on the numerical differential quadrature method (DQM) and the finite element numerical method. In this context, the current study intends to investigate the nonlinear free vibration of FG-GPL-reinforced composite (RC) conical panels resting on an elastic medium by developing a 2-D planar meshfree method-based nonlinear numerical method. The nonlinear free vibration problem is expressed by the first-order shell deformation theory and the von-Kármán nonlinearity. The complex conical neutral surface of the panel is transformed into a 2-D rectangular plane to avoid painstaking mathematical manipulation. The troublesome shear-membrane locking is suppressed by employing the MITC3+shell element, and the derived nonlinear modal equations are solved by introducing a three-step direct iterative scheme. The present method is compared with the DQM through the benchmark experiment, from which a good agreement between the two methods is observed. And, the nonlinear free vibration characteristics of FG-GPLRC conical panels on an elastic foundation are profoundly investigated, and it is found that those are significantly influenced by the foundation stiffness, the amount and dispersion pattern of GPLs, the panel geometry sizes, and the boundary condition.

Soft Functionally Gradient Materials and Structures - Natural and Manmade: A Review

Functionally gradient materials (FGM) have gradual variations in their properties along one or more dimensions due to local compositional or structural distinctions by design. Traditionally, hard materials (e.g., metals, ceramics) are used to design and fabricate FGMs; however, there is increasing interest in polymer-based soft and compliant FGMs mainly because of their potential application in the human environment. Soft FGMs are ideally suitable to manage interfacial problems in dissimilar materials used in many emerging devices and systems for human interaction, such as soft robotics and electronic textiles and beyond. Soft systems are ubiquitous in everyday lives; they are resilient and can easily deform, absorb energy, and adapt to changing environments. Here, the basic design and functional principles of biological FGMs and their manmade counterparts are discussed using representative examples. The remarkable multifunctional properties of natural FGMs resulting from their sophisticated hierarchical structures, built from a relatively limited choice of materials, offer a rich source of new design paradigms and manufacturing strategies for manmade materials and systems for emerging technological needs. Finally, the challenges and potential pathways are highlighted to leverage soft materials' facile processability and unique properties toward functional FGMs.

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.

Review of Additive Manufacturing Techniques for Large-Scale Metal Functionally Graded Materials

Functionally graded materials (FGMs), which constitute a new type of composite material, have received considerable attention in industry because of the spatial gradient of their composition and the microstructure-induced gradient in their material performance, which make them better suited for high-performance multifunctional applications. Additive manufacturing (AM) has become one of the most promising techniques for the manufacture of materials and structures because of its high flexibility. The combination of advanced materials (FGMs) and advanced manufacturing methods (AM) is expected to facilitate the further development of such engineering materials. In this paper, the definition, historical development and material gradient types of FGMs are introduced. The classification, process principle and typical research results of the AM of metal FGMs are summarized and discussed. In particular, the research status of wire and arc additive manufacture (WAAM), which is more suitable for the preparation of large-scale metal FGMs, is reviewed in detail according to the types of FGMs, and a double-wire bypass plasma arc additive manufacturing technique, which is suitable for inducing a gradient along the direction of single-pass cladding, is proposed. On the basis of this summary of the important achievements made to date, future research is proposed.

Lamb Waves Propagation Characteristics in Functionally Graded Sandwich Plates

Functionally graded materials (FGM) have received extensive attention in recent years due to their excellent mechanical properties. In this research, the theoretical process of calculating the propagation characteristics of Lamb waves in FGM sandwich plates is deduced by combining the FGM volume fraction curve and Legendre polynomial series expansion method. In this proposed method, the FGM plate does not have to be sliced into multiple layers. Numerical results are given in detail, and the Lamb wave dispersion curves are extracted. For comparison, the Lamb wave dispersion curve of the sliced layer model for the FGM sandwich plate is obtained by the global matrix method. Meanwhile, the FGM sandwich plate was subjected to finite element simulation, also based on the layered-plate model. The acoustic characteristics detection experiment was performed by simulation through a defocusing measurement. Thus, the Lamb wave dispersion curves were obtained by V(f, z) analysis. Finally, the influence of the change in the gradient function on the Lamb wave dispersion curves will be discussed.

Thermal Conductivity Identification in Functionally Graded Materials via a Machine Learning Strategy Based on Singular Boundary Method

A machine learning strategy based on the semi-analytical singular boundary method (SBM) is presented for the thermal conductivity identification of functionally graded materials (FGMs). In this study, only the temperature or heat flux on the surface or interior of FGMs can be measured by the thermal sensors, and the SBM is used to construct the database of the relationship between the thermal conductivity and the temperature distribution of the functionally graded structure. Based on the aforementioned constructed database, the artificial neural network-based machine learning strategy was implemented to identify the thermal conductivity of FGMs. Finally, several benchmark examples are presented to verify the feasibility, robustness, and applicability of the proposed machine learning strategy.

Natural Frequencies Optimization of Thin-Walled Circular Cylindrical Shells Using Axially Functionally Graded Materials

One method to avoid vibration resonance is shifting natural frequencies far away from excitation frequencies. This study investigates optimizing the natural frequencies of circular cylindrical shells using axially functionally graded materials. The constituents of functionally graded materials (FGMs) vary continuously in the longitudinal direction based on a trigonometric law or using interpolation of volume fractions at control points. The spatial change of material properties alters structural stiffness and mass, which then affects the structure’s natural frequencies. The local material properties at any place in the structure are obtained using Voigt model. First-order shear deformation theory and finite element method are used for estimating natural frequencies, and a genetic algorithm is used for optimizing material volume fractions. To demonstrate the proposed method, two optimization problems are presented. The goal of the first one is to maximize the fundamental frequency of an FGM cylindrical shell by optimizing the material volume fractions. In the second problem, we attempt to find the optimal material distribution that maximizes the distance between two adjoining natural frequencies. The optimization examples show that building cylindrical shells using axially FGM is a useful technique for optimizing their natural frequencies.

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.

Stochastic Extended Finite Element Implementation for Natural Frequency of Cracked Functionally Gradient and Bi-Material Structures

In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

A review on fabrication and characteristics of functionally graded aluminum matrix composites fabricated by centrifugal casting method

This paper delivers a detailed review of the influence of material and process variables on the microstructure, mechanical and tribological characteristics of functionally graded aluminum matrix composites (FGAMCs) produced by the ex-situ centrifugal casting method from previous studies. Also, the basic principle and classification of centrifugal casting to produce FGAMCs are illustrated. The ceramic reinforcement particles are classified based upon their uses in the processing of FGAMCs through the ex-situ centrifugal casting technique. In addition, using the linear regression model, an effort has been made to optimize the material and process variables to get enhance the mechanical properties. It is seen from the optimization while mold preheating temperature ranges 250–350 °C, centrifugal speed kept between 600 and 1300 rpm, pouring temperature in the range of 740–760 °C having reinforcement particle of 10–15 wt%, with an average particle size of 18–50 µm yield the maximum of hardness and tensile strength. This paper aims to provide direction to future researchers to develop advanced material using this route and thus, to boost technological growth.

Optimization of Metal–Ceramic Functionally Graded Plates Using the Simulated Annealing Algorithm

This work involves the design optimization of metal–ceramic through the thickness of functionally graded material (FGM) plates subjected to thermomechanical loadings. Constrained optimization was performed for minimum mass and minimum material cost of the FGM plates. The design process of FGM plate structures requires a good choice of metal and ceramic materials and the adequate definition of the components volume fractions through the thickness direction in order to accomplish a certain structural behavior, while optimizing the material costs and/or the plate mass. Here, the optimization problems are solved with the simulated annealing (SA) algorithm, not requiring the calculation of the derivatives of the objective or constraint functions. Constrained single objective optimization cases are studied, and validated with alternative solutions, considering the p-index and the FGM plate thickness as design variables. New optimization cases, involving additionally the metal and ceramic materials as design variables, are presented both for benchmark purposes and to demonstrate the suitability of the SA algorithm to solve those optimization problems.

Influence of Material Stochasticity on Buckling Characteristics of Initially Imperfect Higher-Order Shear Deformable Gradient Plates

This paper demonstrates the influence of material stochasticity on buckling characteristics of higher-order shear deformable gradient plates with initial geometric imperfections. The gradient plates are assessed by smooth variation in the volume fraction of the constituents (i.e. ceramic and metal) as power-law distribution function in the thickness direction. The effective material properties are achieved by means of the Voigt model. Plate kinematic based on Reddy’s higher-order shear deformation theory (HSDT) associated with initial geometric imperfection in the transverse direction is employed. The governing differential equation is produced using a variational approach. The mean and standard deviation of the critical buckling load are evaluated using finite element method and a mean-centered first-order perturbation technique in order to highlight the variation in buckling response. Numerical results are compared both in deterministic and probabilistic frameworks along with convergence in support of efficacy and performance of the proposed model. Based on the results, it can be concluded that the combined influence of geometric imperfection and uncertain material properties prominently affect the buckling response of the gradient plates.

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates

This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM) rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials. The series solutions were established by satisfying governing equations and boundary conditions in the expanded space of the Fourier cosine series. The proposed solutions were validated through comprehensive convergence studies on the first six vibration frequencies of square plates under four combinations of boundary conditions and through comparison of the obtained convergent results with those in the literature. The convergence studies indicated that the solutions obtained for different modes could converge from the upper or lower bounds to the exact values or in an oscillatory manner. The present solutions were further employed to determine the first six vibration frequencies of FGM rectangular plates with various aspect ratios, thickness-to-width ratios, distributions of material properties and combinations of boundary conditions.

Review of Functionally Graded Thermal Sprayed Coatings

The paper briefly describes major thermal spray techniques used to spray functionally graded coatings such as atmospheric plasma spraying, high velocity oxy-fuel spraying, suspension and solution precursor plasma spraying, and finally low and high pressure cold gas spray method. The examples of combined spray processes as well as some examples of post spray treatment including laser and high temperature treatments or mechanical one, are described. Then, the solid and liquid feedstocks used to spray and their properties are shortly discussed. The reviewed properties of functional coatings include: (i) mechanical (adhesion, toughness, hardness); (ii) physical (porosity, thermal conductivity and diffusivity, thermal expansion, photo-catalytic activity), and; (iii) bioactivity and simulated body fluid (SBF) corrosion. These properties are useful in present applications of functionally graded coatings as thermal barriers, the bioactive coatings in prostheses, photo-catalytic coatings in water treatment, coatings used in printing industry (anilox and corona rolls). Finally, some of the future possible fields of functional thermal sprayed coatings applications are discussed, e.g., to coat polymer substrates or to use the cheap technology of low pressure cold gas spray method instead of expensive technology of vacuum plasma spraying to obtain bond coatings.

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

Mechanical and Dielectric Strength of Laminated Epoxy Dielectric Graded Materials

Laminated epoxy dielectric graded material is a commonly used insulating material with broad application prospects in power equipment. The interlaminar interfaces of laminated epoxy dielectric material between different layers form during its lamination process, and these interfaces are the crucial characteristic structures determining the mechanical and dielectric properties of laminated materials. Therefore, in order to gain a thorough understanding of physic properties behind a certain structural motif, it is necessary to study how these interfacial structures influence the mechanical and dielectric performances of graded materials. In this study, double-layered epoxy resin samples with an interlaminar interface are prepared to study their mechanical and dielectric strength. More importantly, the formation mechanism of the interface, as well as its influence on the mechanical and dielectric strength of this laminated material, is discussed. We found that a cross-linking reaction may take place between epoxy resins at the interlaminar interface, and the degree of cross-linking at the interface should be less than that in the bulk. The mechanical strength of the interlaminar interface is weaker than that of the bulk, and it is reduced by less than 40%. Moreover, the interlaminar interface is inclined to trap carriers, which improves the breakdown strength and arc ablation resistance of the laminated material. Our study of interlaminar interface properties could help in designing epoxy dielectric graded materials with better mechanical and dielectric properties.

Versatile Macroscale Concentration Gradients of Nanoparticles in Soft Nanocomposites

Nanocomposite materials benefit from the diverse physicochemical properties featured by nanoparticles, and the presence of nanoparticle concentration gradients can lend functions to macroscopic materials beyond the realm of classical nanocomposites. It is shown here that linearity and time-shift invariance obtained via the synergism of two independent physical phenomena-translational self-diffusion and shear-driven dispersion-may give access to an exceptionally high degree of flexibility in the design of scalable and programmable long-range concentration gradients of nanoparticles in solidifiable liquid matrices.

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones.

The thermal-mechanical properties of functionally graded membrane electrode assembly of PEMFC

Proton exchange membrane fuel cell (PEMFC) is one of the most promising clean energy technologies in the future because of its advantages of having zero pollution and high-power generation efficiency. However, the commercialization of PEMFC is difficult because of the constraints of operational lifetime and cost. Membrane electrode assembly (MEA) is the core component, and its durability determines the performance and life of PEMFC. Owing to the different expansion properties of each layer in MEA, stress concentration and uneven distribution are easily occurred in the process of dynamic cycling of PEMFC, causing the electrode crack and delamination and highly dropping the cell performance. We established the sandwich molecular model of functionally graded membrane electrode assembly (FG-MEA) and investigated the coefficient of thermal expansion and elastic modulus by molecular dynamics simulation. The relationship between gradient structure of FG-MEA and thermomechanical properties was discussed. Three FG-MEA models were established by adding different volume fraction of platinum (Pt) particles along the thickness direction of the membrane. It was found that with the decrease of gradient value, the coefficient of volumetric thermal expansion decreases and elastic modulus along gradient direction slightly increases. The results were in agreement with the estimation of empirical formula of exponential function. The research provides an idea and theoretical reference for the design of FG-MEA materials.

Modeling guided wave propagation in functionally graded plates by state-vector formalism and the Legendre polynomial method

A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.

Junction Characterization in a Functionally Graded Aluminum Part

Aluminum alloys are widely used to produce automotive components, thanks to their great mechanical properties-to-density ratio. Engine components such as pistons are conventionally produced by casting of Al-Si eutectic alloys (Silumin alloys) such as EN AC 48000. Due to the harsh working conditions and the lower ductility if compared to aluminum-silicon alloys with lower silicon content, pistons made of this alloy are prone to fatigue failures in the skirt region. In order to overcome such limits, the use of a Functionally Graded Material (FGM) in the production of a piston is proposed. The adoption of a functionally graded architecture can maximize the properties of the component in specific areas. A higher level of thermal resistance in the crown of the piston can be achieved with EN AC 48000 (AlSi12CuNiMg), while higher elongation at rupture in the skirt region would be conferred by an EN AC 42100 (AlSi9Mg0.3). The FGM properties are strictly related to the metallurgical bonding between the alloys as well as to the presence of intermetallic phases in the alloys junction. In the present article, the characterization of gravity casted FGM samples based on Al-Si alloys with respect to microstructure and mechanical testing is presented, with a specific focus on the characterization by impact testing of the joint between the two alloys.

Self-Assembled Functionally Graded Graphene Films with Tunable Compositions and Their Applications in Transient Electronics and Actuation

The facile fabrication of functionally graded all-graphene films using a single-step casting process is reported. The films consist of a self-assembled graphene oxide (GO) precursor that can be reduced to different levels on an active metal substrate. Control of processing conditions such as the underlying substrate metal and the film-drying environment results in an ability to tailor the internal architecture of the films as well as to functionally grade the reduction of GO. A gradient arrangement within each film, where one side is electrically conductive reduced GO (rGO) and the other side is insulating GO, was confirmed by scanning electron microscopy, Raman, X-ray diffraction, Fourier transform infrared, and X-ray photoelectron spectroscopy characterization studies. All-graphene-based freestanding films with selectively reduced GO were used in transient electronic applications such as flexible circuitry and RFID tag antennas, where their decommissioning is easily achieved by capitalizing on GO's ability to readily dissociate and create a stable suspension in water. Furthermore, the functionally graded structure was found to exhibit differential swelling behavior, and its potential applications in graphene-based actuators are outlined.

Imperfection sensitivity in the vibration behavior of functionally graded arches by considering microstructural defects

In this paper, imperfection sensitivity in the vibration behavior of functionally graded arches with microstructural defects (porosity) has been studied. The temperature-dependent material properties of functionally graded arches are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on the Reddy’s higher order shear deformation theory using finite element method. Convergence and comparison studies have been performed to describe the efficacy of the present formulation. The obtained results have been compared with the limited available literature. The parametric studies have been performed to study the influence of the temperature rise, volume fraction index, and porosity index on the frequency response of the functionally graded arches. The effect of various modes of initial geometrical imperfections has also been examined. The obtained numerical results can be used as benchmark solutions for future researches in this field of study.

On the flexural and vibration behavior of imperfection sensitive higher order functionally graded material skew sandwich plates in thermal environment

This work presents an investigation on the flexural and vibration behavior of imperfection sensitive higher order functionally graded material skew sandwich plates in thermal environment. Material properties have been assumed to be temperature dependent and graded in transverse direction following the power law distribution. Reddy’s higher order shear deformation theory has been used to model displacement field kinematics of skew sandwich plate. Variational principle has been used for deriving the governing equations. Finite element methodology has been adopted to discretize plate domain. Convergence and comparison studies have been performed to demonstrate the reliability of present formulation. Effect of various system parameters such as thickness ratio, volume fraction index, skew angle, imperfection parameter, and boundary conditions on the flexural and vibration response have been investigated.

Stress Concentration and Optimized Analysis of an Arbitrarily Shaped Hole with a Graded Layer under Anti-Plane Shear

This paper provides a general solution to the anti-plane problem of an arbitrarily shaped hole reinforced with a functionally graded (FG) layer in a homogenous plate. By using the piece-wise homogeneous layers method and the conformal mapping technique, the complex potentials in the form of series in the FG layer are derived based on the theory of complex variable functions. The influence of the FG layer on the shear stress distributions around some typically shaped holes are discussed by numerical examples, and then the optimized analysis of the stress concentration factor (SCF) is performed. The results showed that the SCF of various shaped holes can be noticeably reduced by the optimum design of the material variations in the layer, and the most significant one in this paper is the triangular hole, whose SCF can be decreased by more than 50%.

Thermoelastic Vibration of Shear Deformable Functionally Graded Curved Beams with Microstructural Defects

In the present study, the thermoelastic vibration of shear deformable functionally graded material (FGM) curved beams with microstructural defects (porosity) has been analyzed by the finite element method. The formulation is based on the higher-order shear deformation theory. The material properties of FGM beams are allowed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Even and uneven distributions of porosities in the beam have been considered with temperature-dependent material properties. Comparison and convergence study has been performed to validate the present formulation. Parametric studies have been done to study the effect of different influencing parameters on the frequency of the FGM curved beam, i.e. porosity, temperature rise, volume fraction index and opening angle. Some new results are presented which can be used as benchmark solutions for future research.

3D Printing of Materials with Tunable Failure via Bioinspired Mechanical Gradients

Mechanical gradients are useful to reduce strain mismatches in heterogeneous materials and thus prevent premature failure of devices in a wide range of applications. While complex graded designs are a hallmark of biological materials, gradients in manmade materials are often limited to 1D profiles due to the lack of adequate fabrication tools. Here, a multimaterial 3D-printing platform is developed to fabricate elastomer gradients spanning three orders of magnitude in elastic modulus and used to investigate the role of various bioinspired gradient designs on the local and global mechanical behavior of synthetic materials. The digital image correlation data and finite element modeling indicate that gradients can be effectively used to manipulate the stress state and thus circumvent the weakening effect of defect-rich interfaces or program the failure behavior of heterogeneous materials. Implementing this concept in materials with bioinspired designs can potentially lead to defect-tolerant structures and to materials whose tunable failure facilitates repair of biomedical implants, stretchable electronics, or soft robotics.

Thermo-Mechanical Buckling Analysis of Functionally Graded Skew Laminated Plates with Initial Geometric Imperfections

The aim of the present study is to investigate thermo-mechanical buckling response of skew functionally graded laminated plates (FGLP) with initial geometric imperfections. The formulation has been performed using Reddy’s higher order shear deformation theory (HSDT) with the [Formula: see text] continuous displacement field. A nine-noded isoparametric element has been employed to discretize the domain of the plate. Variational principle has been used to derive the governing differential equation of the problem. Several examples with various comparison and parametric studies have been shown to prove the efficiency and effectiveness of the present formulation. The numerical results have been highlighted with different system parameters and boundary conditions.

Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment

This paper examines the influence of porosities on the flexural and free vibration response of functionally graded material (FGM) plates based on the authors’ recently developed non-polynomial higher-order shear and normal deformation theory. The theory accommodates the nonlinear variation in the in-plane and transverse displacements in the thickness coordinates. It also contains the hyperbolic shear strain shape function in the displacement field with only four unknowns. A new mathematical model has also been proposed to incorporate the effects of porosity in the FGM plate. Various numerical examples have been solved to ascertain the accuracy, efficiency, and applicability of the present formulation. The effects of porosity, volume fraction index, plate thickness, aspect ratio, boundary conditions and temperature have been discussed in details. The obtained results can be treated as a benchmark for future studies.