Inhomogeneous Material Properties Research Articles

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Functionally graded piezoelectric structures (FGPSs) have excellent electromechanical properties and are promising for engineering applications. However, the inhomogeneous material properties and piezoelectric effects create great difficulties in the mechanical analysis of the FGPSs. In this paper, a Hermite interpolation element-free Galerkin method (HIEFGM) is proposed for the numerical analysis of the FGPSs. The HIEFGM utilizes a set of nodes to represent the problem domain, which can ideally reflect the inhomogeneous material properties of the FGPSs. Firstly, the governing equations of the FGPSs are derived through the constitutive equation, equilibrium equation, and boundary conditions. Secondly, the approximating function of the field quantities is obtained by the improved moving least-square method and Hermite interpolation. The HIEFGM formulation of the FGPSs is obtained using the variational principle. Furtherly, the influence of weight function, scaling parameter, and node densities on the HIEFGM of the FGPSs is discussed in detail through a parameter study. Finally, the availability of present method is estimated by several examples with different configurations and boundary conditions. The influence of gradation exponent on the electromechanical responses of the FGPSs is analyzed. The results show that the present method has excellent accuracy and stability in analyzing the FGPSs. As the gradation exponent increases, the distribution of the field quantities of the FGPSs exhibits nonlinear characteristics. This work may provide an effective methodology for the analysis of the FGPSs, and contribute to the theoretical research and engineering application of the FGPSs.

SWENet: A Physics-Informed Deep Neural Network (PINN) for Shear Wave Elastography.

Shear wave elastography (SWE) enables the measurement of elastic properties of soft materials in a non-invasive manner and finds broad applications in various disciplines. The state-of-the-art SWE methods rely on the measurement of local shear wave speeds to infer material parameters and suffer from wave diffraction when applied to soft materials with strong heterogeneity. In the present study, we overcome this challenge by proposing a physics-informed neural network (PINN)-based SWE (SWENet) method. The spatial variation of elastic properties of inhomogeneous materials has been introduced in the governing equations, which are encoded in SWENet as loss functions. Snapshots of wave motions have been used to train neural networks, and during this course, the elastic properties within a region of interest illuminated by shear waves are inferred simultaneously. We performed finite element simulations, tissue-mimicking phantom experiments, and ex vivo experiments to validate the method. Our results show that the shear moduli of soft composites consisting of matrix and inclusions of several millimeters in cross-section dimensions with either regular or irregular geometries can be identified with excellent accuracy. The advantages of the SWENet over conventional SWE methods consist of using more features of the wave motions and enabling seamless integration of multi-source data in the inverse analysis. Given the advantages of SWENet, it may find broad applications where full wave fields get involved to infer heterogeneous mechanical properties, such as identifying small solid tumors with ultrasound SWE, and differentiating gray and white matters of the brain with magnetic resonance elastography.

Shear wave propagation in a fiber-laden viscoelastic waveguide under prestress: Inverse modeling challenges

The functional role of skeletal muscle and the hierarchal microstructure and arrangement of fibers within it results in anisotropy and inhomogeneity in both material properties and imposed stresses. Dynamic elastography reconstruction methods for estimating muscle tissue viscoelastic properties that are based on assumptions of homogeneity, isotropy and only bulk wave motion may produce inaccurate estimates. Biases may be introduced in reconstruction by homogenizing muscle with axially aligned fibers and approximating it as transversely isotropic. The significance of these biases, and their interplay with imposed stresses and confounding waveguide effects due to small cross-sectional dimensions, is quantified with a series of numerical finite element and experimental elastography studies on cylindrically-shaped fiber-laden muscle phantoms, with varying fiber dimensions. Specifically, numerical simulations of elastography are conducted on 4-, 60- and 113-fiber models with the aligned fiber cross-sectional area fixed (reduced fiber diameter as fiber count increases) and comprising approximately 40% of the cross-sectional area of the cylindrical phantom that is also undergoing tensile axial pre-loading. Fiber elastic moduli twice that of connective tissue are considered. Experimental studies of the 4-fiber model are used to validate the numerical model. [Funding support: NSF 1852691 and NIH AR071162]

ANALYTICAL AND NUMERICAL ANALYSIS OF SOLID CYLINDER MADE OF RADIALLY NONUNIFORM MATERIAL UNDER EXTENSION

Functionally graded materials are inhomogeneous composite materials, composed of two or more constituents selected to achieve desirable properties for specific applications. In this work, a solid cylindrical tube made of inhomogeneous composite materials under tensile action was analyzed within the context of three-dimensional elasticity theory. An analytical solution was obtained for computing the displacement and stress fields. It has been assumed that the elastic stiffness is varying through the functionally graded material according to radial variation laws: linear, power, and exponential laws, while Poisson's ratio is considered as constant. In order to check the relevance of the analytical solution, a finite element model of the cylindrical tube was constructed, taking into account variations in Young's modulus. Very good agreement has been found between the numerical results and the predictions of the analytical solution, which confirms the accuracy of our model. Numerous curves were plotted by adjusting the inhomogeneity parameter and the elongation value, revealing a significant effect. Thus, the inhomogeneity in material properties can be exploited to optimize stress distribution. Indeed, by tailoring the material properties to match the stress distribution in a specific load scenario, stress concentrations can be minimized in high-stress areas.

Estimation of longitudinal elasticity modulus of anisotropic FDM-structure in CAE analysis systems and using full-scale experimen

The first approximation substantiate is given for the application of the theory of effective material to determine the effective elastic modulus of the FDM structure using the combined use of numerical analysis in a CAE environment and a full-scale testing. A specialized module for evaluating the effective properties of inhomogeneous materials of the russian Fidesys software system allowed us to obtain the values of effective elastic modulus for the FDM structure filling the volume under study. Full-scale tests of specimens, the printing pattern of which corresponds to a digital model in the automated environment of the Fidesys system, confirmed the results obtained.

Microstructurally-informed stochastic inhomogeneity of material properties and material symmetries in 3D-printed 316 L stainless steel

Microstructurally-informed stochastic inhomogeneity of material properties and material symmetries in 3D-printed 316 L stainless steel

Surface and subsurface material modifications and graded material properties in sheet steel 1.0338 (DC04) and their influence on forming processes

For bulk material it is very well known, that the material properties differ between the material near the surface and the inner material (i.e. segregations). However, for sheet material a gradient of material properties in depth direction and its influence on forming processes was not yet investigated. Within experiments on sheet steel 1.0338 (DC04) a gradient in material properties was proven by hardness measurements for both unprocessed material as well as after conducting forming and milling processes. The characterisation shows a gradient in material hardness over the entire sheet thickness. The experimental results regarding forming processes, such as rolling and bending, additionally show an increase of the materials hardness due to work hardening. The problem from the inhomogeneous material properties leads to an inaccurate prediction of the forming behaviour of the workpiece in further processing. Machining experiments were conducted for transferring the knowledge of modified surface and subsurface layers onto forming processes and their simulation. The bending experiments and the corresponding process simulation of the spring back behaviour show, that the implementation of an inhomogeneous material property increases the prediction accuracy. Notably the prediction of the spring back behaviour of thinner sheet metals is highly improved. Therefore, an analysis of sheet metal properties in thickness direction and their consideration in forming process simulations is inevitable for the implementation of accurate material models.

Effect of high-frequency induction weld seam on the deformation of M1700 ultra-high strength steel shell structures considering residual tensile stress

The feasible cold forming procedure to massively manufacture ultra-high strength steel (UHSS) light-weighting profiles so far in industrial fields consists of roll forming, welding, cutting and bending. To reveal the role the high-frequency induction weld (HFIW) line plays in the subsequent plastic forming, a serials of deliberately designed collapse tests of the shell structures taken from M1700 roof rail pillar with a wall-thickness of 2 mm and triangle cross-section were conducted. Real geometries and inhomogeneous material properties of the weld seam and heat-affected zone (HAZ), together with the residual tensile stresses within the weld seam after HFIW, were fully considered in the numerical simulation. The Brozoo's modified CL damage model and Oyane damage model were employed and compared. The results show that the deformation resistance of the shell structures is modified by the material accumulation around the HFIW seams during the collapse tests. The cracks mainly occur within the critical HAZ outside the tube and the temper softening zone inside the tube under the action of softening effect in the HAZ of M1700 steel. The residual tensile stresses increase the crack probability of weld seams. The predicting accuracy of fracture location of the Oyane damage model is higher than that of the Brozoo's modified CL damage model.

Mechanical evaluation of revision surgery for femoral shaft nonunion initially treated with intramedullary nailing: Exchange nailing versus augmentation plating

IntroductionExchange nailing (EN) or augmentation plating (AP) has been employed to treat nonunions after intramedullary nailing for femoral shaft fractures. Although instability is a factor in hypertrophic nonunion, mechanical evaluations have been limited because the contribution of the callus to fracture site stability varies with healing. Our previous study illustrated the potential for evaluation using a finite element analysis (FEA) that incorporates callus material properties. This study aimed to mechanically evaluate revision surgery for nonunions using FEA. Materials and methodsA quantitative computed tomography-based FEA was performed on virtual revision models of a patient with suspected nonunion after intramedullary nailing. In addition to the initial nailing model (IN) with an 11-mm diameter (D) and 360-mm length (L), four EN models with D12mm (EN1), D13mm (EN2), D12mm-L400mm (EN3), and D13mm-L400mm (EN4) nails and three AP models with 5- (AP1), 6- (AP2), and 7-hole (AP3) plates were created. As with bone, callus was assigned inhomogeneous material properties derived from density based on an empirical formula. The hip joint reaction force and muscle forces at maximum load during the gait cycle were applied. The volume ratio of the callus at the fracture site with a tensile failure risk of ≥1 (tensile failure ratio) and bone fragment movement were evaluated. ResultsThe tensile failure ratio was 11.6 % (IN), 10.1 % (EN1), 6.3 % (EN2), 10.9 % (EN3), 6.2 % (EN4), 6.4 % (AP1), 7.2 % (AP2), and 7.7 % (AP3), respectively. The bone fragment movement showed an opening on the lateral side with the initial intramedullary nailing. However, both revision surgeries reduced the opening, leading to compression except in the EN1 model. The proximal bone fragments were internally rotated relative to the distal fragments, and the rotational instability was more suppressed in models with lower tensile failure ratio. ConclusionsFor EN, the increase in diameter, not length, is important to suppress instability. AP reduces instability, comparable to a 2 mm increase in nail diameter, and screw fixation closer to the fracture site reduces instability. This study suggest that AP is mechanically equivalent to EN and could be an option for revision surgery for femoral shaft nonunions.

Robust Optimization of UOE Forming Process Considering Inhomogeneity of Material Properties

Abstract The properties inhomogeneity of steel plates will result in uncertainty of forming quality of large diameter UOE oil pipes and increase the risk of pipeline failure. In this paper, a robust design method for UOE forming process based on support vector machine and sequential response surface modeling and considering the variation of steel plates′ properties is proposed. A hundred of mechanical experiments are first carried out and the variation of X80 steel's properties is statistically evaluated. The varied properties are assigned to partitioned steel segments and taken as the noise factor in process design. The ovality of the UOE pipe is employed as the optimization objective, and the forming quality indicators including convex amount, mean outside diameter, yield strengths and Ys/Uts7, O-forming gap, the width of the U-shaped plate, inclined angle of straight arm of the U-shaped plate, etc., are taken as the constraints. Based on the semi-analytical computation of C-, U- and O-forming processes and finite element simulation of expanding process, a sequential response surface model is established by using the support vector machine method. Finally, a Monte Carlo sampling is performed to demonstrate the effectiveness of the proposed method. Compared to conventional optimization method, the robust optimization performs obviously better in reducing the ovality and increasing the robustness of UOE forming process.

Biomechanical modeling of rice seedling stalk based on multi-scale structure and heterogeneous materials

Rice seedling stalks are biologically characterized by multilayer porous structure and multiphase inhomogeneous material properties. This biological properties make it challenging to reveal the biomechanical behavior and damage mechanism of rice seedling stalks under mechanical load. In this research, the mechanical properties of the cell wall in each leaf sheath of rice seedling stalk were measured by nanoindentation, and a three-dimensional (3D) structure model of rice seedling stalk was established using micro-computed tomography (Micro-CT). According to the gray value difference in the CT images, rice seedling stalk was defined as three types of materials: protoplasts, parenchyma cell wall and collenchyma cell wall. A 3D finite element model of rice seedling stalk with heterogeneous material distribution was established based on the mapping relationship of gray value-density-elastic modulus. The accuracy of the model was verified by radial compression and axial tensile tests from three aspects: macroscopic mechanical response, microscopic mechanical behavior, and actual load effect. The results show that the modeling method is fast and reliable, and effectively improves the analytical accuracy of biomechanical properties for living plant materials with multi-layer porous structure characteristics, heterogeneous anisotropic material properties, and high moisture content. It also provides a useful tool for revealing the damage mechanism and quantitative damage evaluation of living plants under mechanical loading. This will be of great help to the optimization of the structure and working parameters of transplanting mechanism.

Analyzing the Performance of Thermoelectric Generators with Inhomogeneous Legs: Coupled Material–Device Modelling for Mg2X-Based TEG Prototypes

Thermoelectric generators (TEGs) possess the ability to generate electrical power from heat. As TEGs are operated under a thermal gradient, inhomogeneous material properties—either by design or due to inhomogeneous material degradation under thermal load—are commonly found. However, this cannot be addressed using standard approaches for performance analysis of TEGs in which spatially homogeneous materials are assumed. Therefore, an innovative method of analysis, which can incorporate inhomogeneous material properties, is presented in this study. This is crucial to understand the measured performance parameters of TEGs and, from this, develop means to improve their longevity. The analysis combines experimental profiling of inhomogeneous material properties, modelling of the material properties using a single parabolic band model, and calculation of device properties using the established Constant Property Model. We compare modeling results assuming homogeneous and inhomogeneous properties to the measurement results of an Mg2(Si,Sn)-based TEG prototype. We find that relevant discrepancies lie in the effective temperature difference across the TE leg, which decreases by ~10%, and in the difference between measured and calculated heat flow, which increases from 2–15% to 9–16% when considering the inhomogeneous material. The approach confirms additional resistances in the TEG as the main performance loss mechanism and allows the accurate calculation of the impact of different improvements on the TEG’s performance.

Hip joint load prediction using inverse bone remodeling with homogenized FE models: Comparison to micro-FE and influence of material modeling strategy

Background and objectiveMeasuring physiological loading conditions in vivo can be challenging, as methods are invasive or pose a high modeling effort. However, the physiological loading of bones is also imprinted in the bone microstructure due to bone (re)modeling. This information can be retrieved by inverse bone remodeling (IBR). Recently, an IBR method based on micro-finite-element (µFE) modeling was translated to homogenized-FE (hFE) to decrease computational effort and tested on the distal radius. However, this bone has a relatively simple geometry and homogeneous microstructure. Therefore, the objective of this study was to assess the agreement of hFE-based IBR with µFE-based IBR to predict hip joint loading from the head of the femur; a bone with more complex loading as well as more heterogeneous microstructure. MethodshFE-based IBR was applied to a set of 19 femoral heads using four different material mapping laws. One model with a single homogeneous material for both trabecular and cortical volume and three models with a separated cortex and either homogeneous, density-dependent inhomogeneous, or density and fabric-dependent orthotropic material. Three different evaluation regions (full bone, trabecular bone only, head region only) were defined, in which IBR was applied. µFE models were created for the same bones, and the agreement of the predicted hip joint loading history obtained from hFE and µFE models was evaluated. The loading history was discretized using four unit load cases. ResultsThe computational time for FE solving was decreased on average from 500 h to under 1 min (CPU time) when using hFE models instead of µFE models. Using more information in the material model in the hFE models led to a better prediction of hip joint loading history. Inhomogeneous and inhomogeneous orthotropic models gave the best agreement to µFE-based IBR (RMSE% <14%). The evaluation region only played a minor role. ConclusionshFE-based IBR was able to reconstruct the dominant joint loading of the femoral head in agreement with µFE-based IBR and required considerably lower computational effort. Results indicate that cortical and trabecular bone should be modeled separately and at least density-dependent inhomogeneous material properties should be used with hFE models of the femoral head to predict joint loading.

Numerical modelling on polymer composites prepared via large area extrusion-deposition additive manufacturing: fibre orientation, material inhomogeneity, and thermal-mechanical responses during material loading process

ABSTRACT The flow-induced fibre orientation formed during polymer extrusions causes the composite to exhibit non-homogeneous thermal-mechanical behaviours during Large Area extrusion-deposition Additive Manufacturing (LAAM) processes. This study numerically evaluates the fibre orientation state of a 20 wt.% short carbon fibre reinforced polyethylenimine fabricated by LAAM. The fibre orientation state of the solidified deposited bead is determined by a fully coupled flow/orientation simulation approach. The material properties of deposited composites are computed by assuming that the deposited bead has heterogeneous regions with varying local fibre orientation states. A finite element simulation is performed to model the LAAM process of a thin-wall structure, where the predicted inhomogeneous material properties are employed. Computed results show notable differences between simulations performed by employing homogenous properties and those obtained using heterogeneous properties. The bead-direction tensile stress contours computed under the heterogeneous assumption are comparable to experimental data in the literature, supporting our numerical approach.

Effect of material non-uniformity and residual stress on wear and transient rolling contact behaviour in laminar plasma quenched (LPQ) rails

Laminar plasma discrete quenching of rail surfaces significantly improves the wear resistance of quenched rails by forming a discrete hardened layer on the rail surface, while also introducing residual compressive stress. However, in practice, laminar plasma quenched (LPQ) rails demonstrate numerous fine cracks and spalling at the edges of the hardened layer, potentially threatening the safety of railway traffic. However, most previous studies have focused on the microstructure of LPQ materials and two-disc tests, with few of them including a finite element analysis of the mechanical properties of the quenched rails. In this paper, an ANSYS/LSDYNA explicit finite element (FE) model of the transient rolling contact between the quenched rail and the wheel is developed for the rolling contact behaviour and wear characteristics of the LPQ rail. The innovation of the model is the fact that it takes the inhomogeneous material properties between the substrate and the hardened layer of the rail surface into account, as well as the real residual stress. It was found that the inhomogeneous material properties of the substrate and the hardened layer may be the main cause of micro-cracking at the edges of the hardened layer. Residual compressive stress within the hardened layer has a non-negligible effect on the rolling contact characteristics of the rail. The research methodology in this paper further develops the FE model for LPQ rails, while the results obtained will be important for controlling rail damage.

Parametric design of the human bone with the aim of promoting dynamic resistance

In sports practices, the intensity and type of forces exerted on the human body are totally different from everyday living. Harsh movements and impact loadings are very common in sports and sometimes cause severe injuries to both muscles and bones. In a specific case, in volleyball games, the lower arm of the player is continuously exposed to heavy impacts by the ball. The main part of the body enduring these impact loads are the two ulna and radius bones in the lower arm. Therefore, in this type of ball impacts it is important to investigate the effect of ball movement and condition on the stress-induced in bones. In the present study, using numerical finite element and generalized differential quadrature (GDQ) methods, stability conditions in the ulna and radius bones in volleyball players under several static and harmonic loading types are investigated. Furthermore, change in the ball mass in the standard range is also considered in analyses. The bone structure is modeled as a cylindrical shell with classical elasticity theory and for inhomogeneous material properties. The results obtained using the numerical method are presented with a focus on the state of stability of the both ulna and radius bones.

Effect of defects and reinforcements on the mechanical behaviour of a bi-layered panel

This paper investigates the mechanical behaviour of a bi-layered panel containing many particles in one layer and demonstrates the size effect of particles on the deflection. The inclusion-based boundary element method (iBEM) considers a fully bounded bi-material system. The fundamental solution for two-jointed half spaces has been used to acquire elastic fields resulting from source fields over inclusions and boundary-avoiding multi-domain integral along the interface. Eshelby’s equivalent inclusion method is used to simulate the material mismatch with a continuously distributed eigenstrain field over the equivalent inclusion. The eigenstrain is expanded at the centre of the inclusion, which provides tailorable accuracy based on the order of the polynomial of the eigenstrain. As a single-domain approach, the iBEM algorithm is particularly suitable for conducting virtual experiments of bi-layered composites with many defects or reinforcements for both local analysis and homogenization purposes. The maximum deflection of solar panel coupons is studied under uniform vertical loading merged with inhomogeneities of different material properties, dimensions and volume fractions. The size of defects or reinforcements plays a significant role in the deflection of the panel, even with the same volume fraction, as the substrate is relatively thin.

Stress analysis of rotating thick-walled nonhomogeneous sphere under thermomechanical loadings

In this work, a rotating thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure under thermal loading was analyzed within the context of three-dimensional elasticity theory. An analytical formulation was established for computing the displacement and stress fields. It has been assumed that the mechanical and thermal properties are varying through thickness of the functionally graded material (FGM) according to a power-law nonlinear expression, while Poisson's ratio is considered as constant. Based on equilibrium equation, Hooke's law, stress-strain relationship in the spheres and other theories from mechanics a second-order ordinary differential equation well-known as Navier equation is obtained that represents the thermoelastic field in hollow FGM sphere. Navier equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Different results of thermoelastic field are presented across the thickness of the sphere. The analysis of the different results reveals that stress and strain in the FGM sphere are significantly depend upon variation made in temperature profile, rotation and inhomogeneity parameter on the thermoelastic field. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.

Process-Specific Topology Optimization Method Based on Laser-Based Additive Manufacturing of AlSi10Mg Components: Material Characterization and Evaluation

In the laser powder bed fusion process (PBF-LB), components are built up incrementally by locally melting metal powder with a laser beam. This process leads to inhomogeneous material properties of the manufactured components. By integrating these specific material properties into a topology optimization algorithm, product developers can be supported in the early phases of the product development process, such as design finding. For this purpose, a topology optimization method was developed, which takes the inhomogeneous material properties of components fabricated in the PBF-LB process into account. The complex pore architecture in PBF-LB components was studied with micro-computed tomography (µCT). Thereby, three characteristic regions of different porosity were identified and analyzed. The effective stiffness in each of these regions was determined by means of resonant ultrasonic spectroscopy (RUS) as well as finite element analysis. Afterward, the effective stiffness is iteratively considered in the developed topology optimization method. The resulting design proposals of two optimization cases were analyzed and compared to design proposals derived from a standard topology optimization. To evaluate the developed topology optimization method, the derived design proposals were additionally manufactured in the PBF-LB process, and the characteristic pore architecture was analyzed by means of µCT.

Elastic and strength properties of statistical volume elements: Determination of isotropic and homogeneous size limits

In this paper, a method is presented to describe the statistical behavior of mesoscale material property fields, which are useful in macroscopic fracture simulation. The use of representative volume element-based properties can result in unsatisfactory fracture patterns because this approach eliminates random variations. In contrast, statistical volume elements can approximate random and inhomogeneous material properties. We compare two material property convergence metrics based on 1) vanishing variations of a property and 2) the convergence of property mean value versus volume element size. We examine the trends with which the properties of a two-phase composite tend toward homogeneous and isotropic limits. Compared to fracture properties, elastic properties reach their homogeneous and isotropic limit at smaller sizes. Accordingly, a volume element size can be chosen such that only the apparent fracture strength remains random and inhomogeneous. This reduces the computational cost and has proven useful in capturing realistic fracture results. In addition, the geometry of the mesoscale partitioning scheme has an important effect on homogenized properties. The intersection of straight edges with inclusions results in nonphysical size effects, increases anisotropy of properties, and results in 30 to 60 times larger representative volume elements compared to a partitioning scheme based on Voronoi homogenization.