Distribution Of Material Properties Research Articles

Limit elastic speed analysis for functionally graded rotating beam

This study aims to determine the limit elastic angular speed of the rotating beam made up of functionally graded material. The speed at which the material yielding is instigated is termed as limit elastic speed. Assuming material distribution as function of power law, modified rule of mixture was used to determine the distribution of material properties and later was used to calculate the effective yield stress for different volume fraction index. A metal matrix of aluminium has been considered with a reinforcement of silicon carbide. The B-spline collocation method has been used to solve the governing equation obtained using the principle of virtual work. This paper outlines the effect of volume fraction on the deformation and stress at limit elastic speed; influence of slenderness ratio on the limit speed was also reported.

Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment

Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.

Compressible cementitious composite materials: Multiscale modeling and experimental investigation

Tunnel linings installed in difficult geological conditions characterized by a high expansion potential, such as Opalinus Clay and rocks containing anhydrite, may exhibit a loss of integrity due to excessive ground deformations in case water penetrates the rocks. One of the potential remedies against lining deterioration and failure of the tunnel structure is the incorporation of a compressible cementitious layer around the tunnel. This compressible layer serves as a cushion that protects the tunnel structure by tolerating a certain amount of deformations prior to collapse. The deformation capacity of the compressible layer can be enhanced by introduction of various soft inclusions or air bubbles in the cementitious mix. However, such soft inclusions reduce the overall elasticity modulus and strength of the composite. Hence, it is crucial to determine the optimal mix that provides the required compaction potential without compromising on stiffness and strength. For this design purpose computational modeling can be adopted. The model should be able to account for the material properties of the individual components and their volume fraction, which strongly influence the overall behavior of the cementitious composite, and to capture the main features characterizing compressible composites, such as a yielding plateau after a certain threshold loading has been reached. The compaction process of such a composite is described by a voxel model with a discrete distribution of material properties, where the voxels are compacted by applying an Eigenforce when the local stress state reaches a threshold value. This threshold is determined within the framework of continuum micromechanics on the scale of individual inclusions. The model predictions are compared with data from experimental investigations on the compression behavior of different cementitious mixes.

Closed Form Expressions for Nonlinear Analysis of FG-GPLRC Beam Under Thermal Loading: Thermal Postbuckling and Nonlinear Bending

Considering that the exact solution for thermal buckling and post-buckling of the graphene platelets (GPLs)-reinforced composite beam in exposure to temperature changes has not been so far addressed, this problem is investigated in this research. The governing equations of the beam under thermal buckling load were acquired using the principle of virtual work, first-order shear deformation theory, and von Kármán strain field. The effective properties of the materials were then determined using the Halpin–Tsai model and rule of mixtures. Three coupled nonlinear equations are established and solved directly. Results are obtained for beams with clamped and simply supported edges. After validating the results, the effects of changing the GPLs distribution pattern and weight fraction changes on the critical thermal buckling load were evaluated. It is highlighted that for beams with simply supported edges and asymmetric distribution of material properties, the response is not of the bifurcation type.

Flutter of carbon-based nanohybrid composite panels

Recently, carbon-based composite aerospace and mechanical structures have considerable attention due to their great material and mechanical properties. Carbon nanotubes (CNTs) or graphene platelets (GPLs) reinforcements for different matrices are common for the design of modern multilayer structures. In the present paper, the supersonic flutter of nanohybrid composite multilayer panels is examined and discussed. The nanohybrid multilayer panel is made of different technologically justified configurations of polymer layers reinforced by CNTs and GPLs The effective material properties of each CNTs and GPLs layer are determined according to two well-established homogenization techniques: the Mori–Tanaka scheme and the modified Halpin–Tsai model, respectively. Reddy’s third-order shear deformation theory is applied to avoid determining shear correction factors for different distributions of material properties. Hamilton’s principle and the first-order piston theory are applied to formulate aeroelastic coupled equations of motion of the panel. The numerical meshless method is employed to discretize dynamic equations and find generalized multi-parametric characteristic equations functionally dependent on the parameters of the structure with different boundary conditions. The accuracy of the obtained solution and results is examined by comparing the determined natural frequency and critical aerodynamic pressure with those obtained in previous studies. Then, a comprehensive parametric study is carried out to show the effects of hybridization of different distribution patterns of CNTs and GPLs, weight fractions, total layer number, and aspect ratio of hybrid composite panels on the flutter bounds. Results show that the present method provides a highly effective general numerical model for flutter analysis of hybrid nanocomposite panels with different boundary conditions for all thickness categories including thick plates. Moreover, an optimization nanoparticles distribution for the flutter of the nanohybrid composite panel has been obtained.

MatNLI: An open-source MATLAB-based solver for the non-linear inversion in elastography

Elastography has emerged as one of the most promising non-invasive clinical tools. In elastography, a stiffness map or elastogram is generated by solving an inverse problem of elasticity utilizing the tissue motion data acquired using magnetic resonance imaging or ultrasound. Among various inverse algorithms devoted to elastography, non-linear inversion coupled with the finite element method has demonstrated excellent applicability in extracting complex physics of the tissue. The development and implementation of such an inverse algorithm are challenging and often unavailable to clinicians. In the present work, we offer an open-source parallel MATLAB implementation of an efficient non-linear inversion algorithm based on the finite element method for different isotropic material models, viz., linear elastic and viscoelastic materials in the regime of compressible and nearly incompressible materials. Additionally, the framework has been extended to account for anisotropy by assuming transversely isotropic material. For the optimization module, the gradient of the objective function to the model parameters has been computed using the Adjoint method. Different case studies involving smooth variations and piece-wise discontinuities in the material property distribution are explored, and the efficacy of the inversion algorithm in reconstructing the stiffness map is discussed. In addition, noise is added to the synthetic data to depict a realistic setup, i.e., to prevent inverse crimes, and enhance the numerical stability and robustness of the current implementation. The present framework with general-purpose computer implementation could be beneficial for academic and clinical uses and may aid researchers in strengthening their existing frameworks and developing new algorithmic ideas.

Higher-order model with interlaminar stress continuity for multi-directional FG-GRC porous multilayer panels resting on elastic foundation

In this paper, the bending behaviors of multilayer panels composed of multi-directional functionally graded porous graphene reinforced composites (GRCs) resting on a two-parameter Winkler-Pasternak elastic foundation are investigated for the first time based on a higher-order layerwise model with interlaminar stress continuity. Since the material properties are discontinuously distributed through the thickness of specific multilayer structure and multi-directional graded in each layer of the panels caused by the distribution of both graphene and porosities, traditional higher-order plate theories have difficulty in predicting continuous stress fields efficiently. For this reason, the proposed model adopts higher-order interpolation functions and piecewise descriptions for transverse shear-stress fields to obtain accurate results satisfying continuity of interlaminar stresses, accounting for the distribution of material properties along the thickness direction and multilayer structure of the panel. Furthermore, to perform efficient numerical results for multi-directional functionally graded materials, the proposed higher-order layerwise model is combined with graded finite element method (GFEM) by sampling material properties directly at the Gaussian points within each element. Lastly, numerical examples are presented to verify the accuracy and efficiency of the proposed model, and the effects of porosity and graphene distribution patterns, graphene weight fraction, porosity coefficient, and elastic foundation parameters are investigated.

A new finite element for the analysis of functionally graded shells

This paper presents the development of a finite element model for functionally graded shells. The formulation solves the equations of the Stress Approach Model for Functionally Graded shells (SAM-FG) developed and validated by Rubio Rascón et al. (2020). SAM-FG involves only 5 generalized displacements and its equations differ from those of classical first order shear deformation theories mainly in the expressions of the generalized stiffnesses and the approximation of stresses. A 10-node isoparametric triangular element using cubic shape functions and 5 degrees of freedom per node is proposed. The equations of the numerical method were implemented in a program called FESAM-FG. The finite element code enables to calculate and visualize generalized fields on the middle surface of the shell and stress components at a given position across the thickness of the structure. To test the accuracy and convergence of FESAM-FG results, the numerical tool is applied to the structural analysis of four families of functionally graded shells with various distributions of material properties and thickness-to-radius ratios. Results are compared to those obtained by solid finite elements, a higher order shear deformation theory developed by Viola et al. (2014) and two shell models used for laminated composite structures: an equivalent single layer model and a layerwise model, both using 30 fictitious layers.

Design and fabrication of multi-material broadband electromagnetic absorbers for use in cavity-backed antennas

We investigated the feasibility of designing and fabricating novel broadband radiofrequency (RF) absorbers for use in cavity-backed antennas. Fabricating the absorber involved a multi-material additive manufacturing (AM) approach that combined two polymer filaments: a low-loss dielectric filament and a lossy carbon-loaded filament. An iterative optimization algorithm was developed to deploy these filaments and create gradient distributions of material properties that minimize reflectance over a desired frequency band and a range of incident angles to achieve wideband electromagnetic absorption. The chosen material profiles were effectively realized using a spatially varying subwavelength lattice structure printed via fused filament fabrication. Experimentally, validation results demonstrated low reflectance over a wide frequency band, 10 to 40 GHz, and a range of incident angles, 0°–50°. Finally, this printed multi-material absorber was integrated within a cavity-backed spiral antenna and used to suppress backlobe radiation while maintaining an acceptable radiation pattern in the forward direction. While this study investigated cavity-backed antennas, these computational and experimental methods are potentially useful for a wide range of other applications.

Geometric part error and material property profile separation technique of the additively manufactured and post-processed rods.

This paper presents novel surface profilometry for both geometric part error and metallurgical material property distribution measurements of the additively manufactured and post-processed rods. The measurement system, the so-called fiber optic-eddy current sensor, consists of a fiber optic displacement sensor and an eddy current sensor. The electromagnetic coil was wrapped around the probe of the fiber optic displacement sensor. The fiber optic displacement sensor was used to measure the surface profile, and the eddy current sensor was used to measure the change in permeability of the rod under varying electromagnetic excitation conditions. The permeability of the material changes upon exposure to mechanical forces, such as compression or extension and high temperatures. The geometric part error and material property profiles of the rods were successfully extracted by using a reversal method that is conventionally used for spindle error separation. The fiber optic displacement sensor and the eddy current sensor developed in this study have a resolution of 0.286 µm and 0.00359μr, respectively. The proposed method was applied not only to characterize the rods but also to characterize composite rods.

Effect of Uneven Distribution of Material Property on Buckling Behavior of Strip during Hot Finishing Rolling

Effect of Uneven Distribution of Material Property on Buckling Behavior of Strip during Hot Finishing Rolling

Effect of a new transpedicular vertebral device for the treatment or prevention of vertebral compression fractures: A finite element study

BackgroundA finite element study was performed to investigate the biomechanical performance of a novel transpedicular implant (V-STRUT©, Hyprevention, France) made of PEEK (polyetheretherketone) material in terms of strengthening the osteoporotic vertebra and the thoraco-lumbar spine.The objective was to assess numerically the efficacy of the implant to reduce the stress distribution within bone and absorb part of the stress by the implant thanks to its optimized material selection close to that of normal bone. MethodsA numerical model was generated based on a scan of an osteoporotic patient. The model is composed of three consecutive vertebrae and intervertebral discs. A heterogeneous distribution of bone material properties was assigned to the bone.In order to investigate the rationale of the device material selection, three FE models were developed (i) without the device to serve a reference model, (ii) with device made in Titanium material and (iii) with device made in PEEK material.Stiffness and stress distribution within the spine segment were computed and compared in order to assess the implants' performances. FindingsThe results obtained by the simulations indicated that the novel transpedicular implant made of PEEK material provided support to the superior vertebral endplate, restored the thoraco-lumbar spine segment stiffness and reduced the stress applied to the vertebrae under the compressive load. InterpretationImplant geometry in combination with its material properties are very important factors to restore vertebral strength and stiffness and limiting the risk of fracture at the same vertebra or adjacent ones.

Stress wave propagation analysis of 2D-FGM axisymmetric finite hollow thick cylinder

In this paper, a numerical axisymmetric elastic stress wave propagation analysis of the 2D-FGM hollow thick finite cylinder has been performed. The new accurate material distribution model based on Mori-Tanaka scheme and third-order transition function for 2D-FGMs has been implemented in the graded finite element method with higher-order quadrilateral elements. A non-uniform impulsive pressure has been applied on the one-third of the top inner cylinder wall. Consequently, different wave velocities and reflections from the boundaries have been observed due to the graded distribution of material along with two directions. Moreover, the effects of two-dimensional material property distributions on the stress wave propagations and displacements through the cylindrical wall at different locations have been studied systematically. Normalized effective stresses based on von-Mises criteria has been performed in comparison with the internal impulsive pressure amplitude to provide a measure of the cylinder wall response to the mechanical impact loading, the effective stresses are nearly 2.5 times the internal pressure loading amplitude, closed to the impact location. According to the results, 2D material property gradations has effected the stresses significantly. Alternatively, desired stress values can be achieved through optimal design and appropriate choice of property distribution.

Computational design for 4D printing of topology optimized multi-material active composites

Recent efforts on design for four-dimensional (4D) printing have considered the spatial arrangement of smart materials and energy stimuli. The development of multifunctional structures and their desired mechanical/actuation performances require tackling 4D printing from a multi-material design perspective. With the materials distributions there is an opportunity to increase the spectrum of design concepts with computational approaches. The main goal being to achieve the “best” distribution of material properties in a voxelized structure, a computational framework that consists of a finite element analysis-based evolutionary algorithm is presented. It fuses the advantages of optimizing both the materials distribution and material layout within a design space via topology optimization to solve the inverse design problem of finding an optimal design to achieve a target shape change by integrating void voxels. The results demonstrate the efficacy of the proposed method in providing a highly capable tool for the design of 4D-printed active composites.

Probabilistic Stress Intensity Factor Prediction of Surface Crack Using Bootstrap Sampling Method

Fatigue cracks commonly occur for in-service engineering structures. The main parameter for fatigue crack is the stress intensity factor (SIF). The SIF is an indicator of the fatigue crack growth and remaining life of a structure. Nonetheless, a problem was raised when determining the remaining life since the SIF could not be presented in physical phenomena. Thus, a technique is required to predict the range of SIF. Maximum and minimum bounds of SIF help estimate the range of remaining life. This paper aims to predict a structure's safe and failure region during the fracture process based on the SIFs.The primary tool is S-version Finite Element Model (S-FEM). Yet, S-FEM unable to compute random variables in analysis. Thus, the Bootstrap is developed and embedded into S-FEMfor computing random variables in the analysis. The random variables areutilised to predict a range of SIFs. The SIFs are generated based on one hundred samples. The samples arerandomly generated based on the distribution of material properties. A lognormal distribution is used to generate the material properties. The sampling process is computed based on the bootstrap method. The embedded Bootstrap in S-FEM was introduced as BootsrapS-FEM. When the samples exceedthe fracture toughness of 29 MPa.√m, the failure region is indicated at the angle 2φ/π = 0.627 to 1 with 6% of failure samples. The saferegion is observed at angle 2φ/π = 0 to 0.626 with 94% of the samples. The failure region is essential in this analysis to prevent unstable crack growth.

DETECTION OF NONLOCAL CALIBRATION PARAMETERS AND RANGE INTERACTION FOR DYNAMICS OF FGM POROUS NANOBEAMS UNDER ELECTRO-MECHANICAL LOADS

The present investigation examines the range of effect of nonlocal parameters on dynamic behavior of a smart beam-like nanostructure modeled as sandwich functionally graded porous nanobeam with piezoelectric layers. Therefore, the study is concentrated on determining length of the structure for which nonlocal effects are observed for vibration of nanobeam under in-plane electro-mechanical forces. The nanobeam-based NEMS device model is obtained based on assumptions of the nonlocal strain gradient theory in conjunction with Reddy higher-order shear deformation theory. The investigation present differences in obtained results for nanostructure’s free vibration based on classical and nonlocal assumptions. To study range of application of nonlocal parameters for different length of simply supported nanobeam, defined eigenvalue problem is solved in view of variation of length to thickness ratio, distribution of material properties, as well as electro-mechanical loads. What is more, the study attempts to determine and calibrate values of size-dependent coefficients based on expected natural frequencies, material properties, and applied loads. The results are completed with extensive discussion on the dependence of nonlocal parameters on nanobeam’s dynamic response, thus may be an important step forward to extend understanding of ultra-small structure’s behavior.

Probabilistic failure assessment of an irradiated DEMO breeding blanket component under ferromagnetic loads: Impacts of material data scattering and uncertainty in local stress intensities

The most significant technical challenge in developing structural materials for in-vessel components in the Demonstration Power Plant (DEMO) fusion reactor is to qualify the lifetime of material to guarantee the lifetime of components. The qualification needs to be conducted theoretically rather than empirically because it is conducted based on the knowledge and data acquired in fission neutron irradiation experiments and various simulation irradiation experiments rather than in experiments performed in the actual fusion environment. Such experiments will not be achievable until the DEMO fusion reactor becomes operational. Consequently, various uncertainties are expected in irradiation data and loading conditions.The probabilistic approach, where the probability of failure is calculated based on the probability density function of postulated load distribution and material property distribution, is one path to mitigate such uncertainties. In this approach, those probabilities constitute the subjective probability based on the theoretical understanding of fusion neutron irradiation effects on materials to maximize the confidence in the estimated value.A case study of the Japanese DEMO breeding blanket is the basis for the discussion of the technical issues involved in the probabilistic approach. The breeding blanket design was simplified, the failure probability was estimated, and the impact of electromagnetic force on ferromagnetic material caused by a strong magnetic field induced by toroidal field coils was considered. The discussion of the impact of the irradiation damage is based on the irradiation data for F82H reduced-activation ferritic/martensitic steel. A direction for the development of fusion structural materials is suggested in terms of design technology and the statistical quality of the irradiation database.

Estimation of spatial uncertainty in material property distributions within heterogeneous structures using optimized convolutional neural networks

Variations in material behaviors within structures built with heterogeneous materials lead to damage initiation and evolution in locally weak regions. Quantifying the property variability within the structure and forward propagation of the impact of the material property uncertainty on the structural response is critical for reliability analysis and structural performance maximization. Commonly, quantification of the variability requires either computationally expensive high-fidelity models of the underlying microstructure or extensive experimental testing. In this paper, we model the uncertainty with spatially correlated random fields and calibrate the model parameters from limited strain field observations using Neural Networks (NNs). The calibration is performed by trained NNs, which outputs best-fit parameters for the spatial correlation model by accepting filtered Digital Image Correlation (DIC) strain distributions as the input. We demonstrate that by training the NNs using simulated data, the resulting networks are able to calibrate the spatial distribution uncertainty models effectively for a set of Fused Filament Fabrication (FFF) printed structures. The methodology requires a limited number of experimental datasets and produces fast estimations of the best-fit parameters of the uncertainty model compared to optimization or inverse fitting methods. This method allows experimentalists to use the same DIC information routinely obtained during modulus or strength testing to calibrate a spatial property distribution uncertainty model for the underlying microstructure.

FEniCS implementation of the Virtual Fields Method (VFM) for nonhomogeneous hyperelastic identification

It is of great significance to identify the nonhomogeneous distribution of material properties in human tissues for different clinical and medical applications. This leads to the requirement of solving an inverse problem in elasticity. The Virtual Fields Method (VFM) is a rather recent inverse method with remarkable computational efficiency compared with the optimization-based methods. In this study, we aim to identify nonhomogeneous hyperelastic material properties using the VFM. We propose two novel algorithms, RE-VFM and NO-VFM. In RE-VFM, the solid is partitioned in different regions and the elastic properties of each region are determined. In NO-VFM, the distribution of elastic properties is completely reconstructed through the inverse problem without partitioning the solid. As the VFM requires to use virtual fields, we proposed an efficient way to construct them and implemented the approach in the FEniCS package. We validated the proposed methods on several examples, including a bilayer structure, a lamina cribosa (LC) model and a cube model embedded with a spherical inclusion. The numerical examples illustrate the feasibility of both RE-VFM and NO-VFM. Notably, the spatial variations of the Young's modulus distribution can be recovered accurately within only 5 iterations. The obtained results reveal the potential of the proposed methods for future clinical applications such as estimating the risk of vision loss related to glaucoma and detecting tumors.

Dynamic response characterization and simplified analysis methods for viscoelastic dampers considering heat transfer

AbstractViscoelastic (VE) dampers are sensitive to temperature, excitation frequency, and strain level. As they dissipate the kinetic energy from earthquake or wind‐induced structural vibrations, their temperature increases from the heat generated, consequently softening their VE materials and lowering their dynamic mechanical properties. Temperature increase can be significant for long‐duration loading, but can be limited by heat conduction and convection which depend on damper configuration. The writers analytically explored such effect on the six different dampers by using their previously proposed three‐dimensional finite‐element analysis method. Results provided better understanding of how heat is generated within the VE material, conducted and stored in different damper parts, and dispersed to the surrounding air. These results also led to characterization of both local (e.g., temperatures, properties, and strain energy density) and global (e.g., hysteresis loops, and stiffness) behavior of VE dampers, and provided a framework for a new simplified one‐dimensional (1D) modeling approach for time‐history analysis. This new proposed 1D method greatly improves the computation time of the previously proposed long‐duration method coupling fractional time‐derivatives VE constitutive rule with 1D heat transfer analysis. Unlike the previous method, it idealizes uniform shear strain and VE material property distributions for computational efficiency, but still simulating non‐uniform temperature distribution along the thickness direction of the VE material. Despite the approximations, it accurately predicts VE damper global responses.