Effects Of Material Properties Research Articles

Exact solution of Eshelby's inhomogeneity problem in strain gradient theory of elasticity and its applications in composite materials

A new micromechanical approach to deal with the problem of Eshelby's inhomogeneity is developed for the prediction of the effective properties of composite materials according to the strain gradient elasticity theory. The method is based on the Green's function technique leading to an integral equation of the heterogeneous elastic problem. Within the simplified strain gradient elasticity theory, the integral equation for an infinite heterogeneous medium subjected to non-homogeneous boundary conditions is acquired. Thanks to this integral equation, the exact solution of Eshelby's inhomogeneity problem is detailed for spherical inhomogeneity and isotropic elastic behavior. From the expression of strain localization relations, the effective elastic properties of a two-phase composite material are then predicted through Mori Tanaka's homogenization scheme. To test the relevance of the suggested approach, its predictions are compared with results issued from some reference models and experimental data.

Learning from 2D: Machine learning of 3D effective properties of heterogeneous materials based on 2D microstructure sections

Microstructure—property relationships are key to effective design of structural materials for advanced applications. Advances in computational methods enabled modeling microstructure-sensitive properties using 3D models (e.g., finite elements) based on microstructure representative volumes. 3D microstructure data required as input to these models are typically obtained from either 3D characterization experiments or digital reconstruction based on statistics from 2D microstructure images. In this work, we present machine learning (ML) approaches to modeling effective properties of heterogeneous materials directly from 2D microstructure sections. To this end, we consider statistical learning models based on spatial correlations and convolutional neural networks as two distinct ML strategies. In both strategies, models are trained on a dataset of synthetically generated 3D microstructures and their properties obtained from micromechanical 3D simulations. Upon training, the models predict properties from 2D microstructure sections. The advantage of the presented models is that they only need 2D sections, whose experimental acquisition is more accessible compared to 3D characterization. Furthermore, the present models do not require digital reconstruction of 3D microstructures.

Level set-based topological design of multiphase micro-architectured materials using alternating active-phase method

Micro-architectured materials with periodically configured microstructures are widely used in various engineering fields due to their superior mechanical properties. Compared with conventional topology design with one single material, topological design with multiple materials can provide a better solution as the expanded design freedom. This paper presents a level set-based multi-material topological design method for micro-architectured materials involving three phases or more. In this method, a difference-set-based multi-material level set model is employed to represent the topology of each phase, in which N + 1 phases can be precisely represented by the sequential difference-set of N level set functions without any overlaps and redundant regions. By using an alternating active-phase algorithm, the multi-material topology design problem with N + 1 phases is splitted into N(N + 1)/2 binary-phase topological design sub-problems, where each sub-problem involves fewer design variables and volume constraints. The effective properties of multiphase micro-architectured materials are evaluated by a numerical homogenization approach, and their topological evolutions of two active phases in each sub-problem can be readily achieved by updating a single level set function, which greatly facilitate the extension to topological design problems with more phases. Both numerical examples and additive-manufactured specimens demonstrate the effectiveness of the proposed method for designing multiphase micro-architectured materials.

Thermomechanical vibration and stability of effectively homogenized FGM beam with temperature-dependent shear correction factors

Thermomechanical characteristics in the Functionally Graded Materials (FGMs) have been investigated in depth for the precise modeling and analysis of structures in ultimate thermal environments. On this subject, the micro-mechanical interactions of particles in the mixtures of FGMs is necessary to consider the more accurate estimation of structural model. Therefore, the effective material properties are obtained by using homogenization technique based on Mori-Tanaka scheme (MTS) with temperature-dependent material properties. In this regard, present research studies detail temperature-dependent frequencies and thermal buckling behavior of beam model. Then, the physical neutral surface concept is adopted to formulate the decoupled set of stress–strain relations for the FGM models. Also, the First-order Shear Deformation Theory of Beam with rectangular cross-sectional shape including temperature-dependent shear correction factors is developed to improve the practical applications. Furthermore, the results compared with previous data, and the present model is studied in the broad range of temperatures. Specifically, the correlations of shear correction factors and neutral surface shifts are discussed for the models according to temperature and volume fractions. Finally, the thermal stability and the natural frequencies of vibration behaviors are discussed as a result of the mixture ratio for the materials. Furthermore, the mutual interactions of micro-mechanical behavior with the correction factors are especially investigated for thermomechanical analysis.

Nonlocal fields and effective properties of piezoelectric material with a rigid line inclusion perpendicular to the poling direction

Nonlocal fields and effective properties of piezoelectric material with a rigid line inclusion perpendicular to the poling direction

Comparative Study of the Effective Properties of 0-3 and Gyroid Triply Periodic Minimal Surface Cement-Piezocomposites.

In the present numerical simulation work, effective elastic and piezoelectric properties are calculated and a comparative study is conducted on a cement matrix-based piezocomposite with 0-3 and gyroid triply periodic minimal surface (TPMS) inclusions. The present study compares the effective properties of different piezoelectric materials having two different types of connectivity of the inclusions namely, 0-3 inclusions where the inclusions are physically separated from each other and are embedded within the matrix and the second one is TPMS inclusions having interpenetrating phase type connectivity. Effective properties are calculated for four different materials at five different volume fractions namely, 10%, 15%, 20%, 25%, and 30% volume fractions of inclusion by volume. In terms of effective properties and direct piezoelectric effect, TPMS piezocomposite is found to perform better compared to 0-3 piezocomposite. Lead-free piezoelectric material 0.5Ba(Ca0.8Zr0.2)O3- 0.5(Ba0.7Ca0.3)TiO3 demonstrates better performance compared to all other material inclusions studied. The present study attempts to highlight improved piezoelectric effective properties of lead-free material-based piezocomposites with TPMS inclusions.

An Analytical Symplectic Method for Buckling of Ring-Stiffened Graphene Platelet-Reinforced Composite Cylindrical Shells Subjected to Hydrostatic Pressure

In this paper, a novel analytical approach for the buckling of ring-stiffened porous graphene platelet-reinforced composite cylindrical shells under hydrostatic pressure is proposed under the framework of symplectic mechanics. Three types of graphene platelet-reinforced patterns and porosity distributions are considered, and the effective material properties of porous graphene platelet-reinforced composite are determined with a modified Halpin–Tsai model. In the symplectic approach, the governing equations in the conventional Lagrangian system are transformed into a set of Hamiltonian canonical equations, and therefore, the buckling analysis is reduced into an eigenproblem in a symplectic space. Consequently, the accurate critical pressures and corresponding analytical buckling mode shapes are obtained simultaneously without any trial function. The numerical results are compared with the existing results, and good agreements are observed. A comprehensive parametric study of the geometrical parameters, boundary conditions, material properties, and ring-stiffener parameters on the buckling behavior of such shells is also presented.

STATIC INVESTIGATION OF A FUNCTIONALLY GRADED CARBON NANOTUBES REINFORCED COMPOSITE CYLINDRICAL SHELL, DOUBLE-ENDED CLAMPED SUBJECTED TO EXTERNAL PRESSURE LOADS

In this article, static analysis of clamped-clamped (C-C) functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical shell subjected to external pressure was conducted. The governing equations were established by using higher-order shear deformation theory (HSDT) taking transverse normal stress effect into account. In this theory, the transverse displacement w is not a constant but rather is the second order polynomial of the coordinate along the thickness direction. Distribution of carbon nanotubes (CNT) across the shell thickness is assumed to be uniform (UD) or functionally graded in four types: FG-Ʌ, FG-V, FG-O, and FG-X. Effective material properties of FG-CNTRC cylindrical shells were estimated by the rule of mixture. An analytical solution using the simple trigonometric series and the Laplace transformation to solve governing equations of shell with clamped boundary condition at the both ends is presented. The validation of the applied approach was examined by comparing the results based on 3D exact model. The effects of the CNT distribution, the CNT volume fraction, and the geometrical parameters on the static behaviour of cylindrical shells subjected to external pressure were investigated. The result is remarkable that the stress components near the outer or inner surface vary most strongly, and in the case of a short or/and thick shell, the geometric parameter greatly affects the stress of shell.

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

Based on the three‐dimensional (3D) consistent couple stress theory (CCST), we develop an asymptotic theory for the free vibration analysis of functionally graded (FG) microplates resting on an elastic medium. The material properties of the FG microplate are assumed to obey a power‐law distribution of the volume fractions of the constituents in the thickness direction, for which the effective material properties are estimated using the rule of mixtures. The interactions between the FG microplate and its foundation medium are simulated using a Winkler–Pasternak foundation. Carrying out the asymptotic expansion method, we obtain recursive sets of motion equations for various order problems. The CCST‐based classical plate theory is derived as a first‐order approximation of the 3D CCST. The asymptotic theory is shown to converge rapidly and to be in excellent agreement with the exact solutions for FG macroplates reported in the literature when the value of the material length scale parameter is assigned to be zero.

Nonlinear dynamic and forced vibration characteristic analysis of sandwich panel with double-U auxetic core and GPLRC facing sheets embedded with piezoelectric layers

The aim of the present research is to investigate the nonlinear dynamic and forced vibration of a composite sandwich panel embedded with piezoelectric layers under thermo-harmonic loading. The panel consists of a double-U auxetic honeycomb core made of aluminum alloy and graphene platelet reinforced composite (GPLRC) skins at the top and bottom surfaces. According to Gibson’s formula, the effective material properties of facing sheets and double-V auxetic core are considered. The nonlinear equations are obtained by applying Hamilton’s principles via von Karman’s nonlinear theory and higher-order shear deformation theory (HSDT). The governing equations of motion are solved by employing the differential quadrature method (DQM) and homotopy perturbation method, respectively. The accuracy of the current results has been verified by comparison with others in the literature. Finally, the influence of different parameters such as applied voltage, magnetic potential, temperature rise, different boundary conditions, and geometric parameters of core on the nonlinear frequency-amplitude response of cylindrical panels are analyzed. The numerical results show negative effect of temperature increment, positive influence of ratio of thickness to inclined length, core thickness, amplitudes of segments, considerable effect of the magnetic potential as well as small effect of applied voltage on the nonlinear vibration of sandwich panel. Finally, the important findings of this research indicate that the magnetic potential, amplitude segment, and length to inclined cell rib length have significant effects on nonlinear dynamic deflection and frequencies-amplitude response. Based on the results of this article, designers can develop different parts of aircraft.

Absence of hysteresis in n-k space during the phase transition of vanadium dioxide

Thermal hysteresis in the optical and electrical properties of VO2 when cycling the temperature through insulator-to-metal states is well known. Here we show that no hysteresis is observed in the co-evolution of the real and imaginary parts of the refractive index, or equivalently, in the evolution of the polarization state of light reflected from a film. Using models for the effective optical properties of inhomogeneous materials, we show that this observation is consistent with a two-phase composition having similar depolarization factors during the temperature cycling. Absence of hysteresis also rules out the possibility of light acquiring different polarization states when interacting with the material during a full cycle of the phase transition. Such considerations are important to understand the functioning of VO2-based photonic devices.

Thermal properties of HfN‐MoW surrogate cermet fuel for nuclear thermal propulsion

AbstractThe thermal properties of MoW‐HfN, a surrogate cermet for MoW‐UN nuclear thermal propulsion fuel, were characterized over a wide range of elevated temperatures. Thermal diffusivity, coefficient of thermal expansion (CTE), and heat capacity were measured. Optical and scanning electron microscopy were performed to characterize the microstructure and draw structure–property correlations. The thermal diffusivity was obtained using the laser flash method. Diffusivity values ranged from about 0.18 cm2/s at 200°C to 0.15 cm2/s at 1800°C. The CTE was measured using push‐rod dilatometry up to 1600°C, giving values between 6.0 and 9.0 μm/m. A scientific rationalization of the effective material properties is made using the rule‐of‐mixtures and other effective properties models.

Transient analysis of functionally graded graphene oxide powders-reinforced porous composite beams resting on elastic foundations using the reproducing kernel particle meshless method

In this paper, we propose a numerical algorithm, combining the reproducing kernel particle collocation (RKPC) meshless method with the implicit Newmark time integration scheme to examine the transient response of porous composite beams (PCB) strengthened with functionally graded (FG) graphene oxide powders (GOP), and resting on elastic foundations (EF). The PCB are subjected to dynamic loads (DL) with different boundary conditions (BC), and rested on EF modeled using the Winkler–Pasternak foundation model. The first-order shear deformation theory (FSDT) is employed to model the studied PCB reinforced with FG-GOP. The Halpin–Tsai homogenization technique and the rule of mixture are used to determine the effective material properties of the PCB taking the porosity into consideration. The obtained equations of motion using the principle of virtual displacement, are rewritten in a matrix–vector strong form and solved using the adopted numerical strategy. The performance and efficiency of the present approach are validated by comparison with numerical results of the finite element method (FEM). Parametric studies are performed to investigate the effect of GOP weight fraction, GOP distribution patterns, boundary conditions, porosity volume fraction, size of GOP, and elastic foundation stiffness on the transient behavior of FG-GOP reinforced PCB.

Static bending mesh-free analysis of smart piezoelectric porous beam reinforced with graphene platelets

This paper presents static analysis and response of smart piezoelectric porous beams by mesh-free approach. The beam consists of a functionally graded porous core reinforced with graphene platelets (GPLs) and two piezoelectric face layers. The effective material properties of the core vary smoothly through the thickness direction, and they are estimated based upon Halpin–Tsai micromechanical model. The electric potential is assumed to vary linearly across the thickness of the piezoelectric layers. Polynomial basis function-based C1-Hermite interpolation for all displacement and electric potential variables of the problem is proposed for the mesh-free method to discretize the equilibrium equations. Parametric studies are carried out to investigate the effects of material parameters and boundary conditions on the deflection and stresses of the beam subjected to mechanical and/or electrical load(s). Furthermore, the study also highlights the piezoelectric effect on the static bending control of the proposed beam.

Effective elastic properties and wave surfaces of rock materials containing multiple cavities and cracks (effective field approach)

The paper is devoted to simulation of the effective elastic properties of rock materials containing two substantially different types of defects simultaneously: random sets of ellipsoidal pores (cavities) and elliptical cracks. For solution of the homogenization problem and calculation of the effective elastic properties of such materials, the self-consistent effective field method is used. For composites with one type of heterogeneities, the method coincides with the Mori–Tanaka method. The method allows deriving analytical expressions for the effective elastic stiffness tensors of the materials containing pores and cracks of various scales. These tensors have correct symmetry with respect to tensor indices and provide physically reasonable values of the effective elastic constants in wide regions of porosity and crack density. The materials with pores and cracks of substantially different sizes and of close sizes are considered. The method predicts substantially different effective elastic constants of the materials with these microstructures. Comparison of the components of the effective elastic stiffness tensors for the materials with various values of porosity and crack density are presented. Wave surfaces of acoustical waves in the materials containing pores and cracks are constructed. It is shown that for materials with spherical pores and circular cracks, the shapes of these surfaces are close to ellipsoidal. The results of the paper can be used for determination of fracture level in damaged rock materials by acoustical methods.

Influence of circular cutouts and elastic foundation on vibration characteristics of porous sandwich FGM plates under hygro-thermal environments

The present article investigates the effect of cutouts, porosity inclusion, and hygro-thermal environment on the vibrational characteristics of sandwich functionally graded material (FGM) plates resting on Pasternak elastic foundation. The governing equations for the sandwich FGM plates have been developed using the finite element method (FEM) with the conjunction of non-polynomial-based higher-order shear deformation theory (HSDT). The trigonometric shear-strain shape function has been used for the first time for sandwich FGM plates. The effective material properties with porosity inclusions have been computed using modified power–law distribution. The present results have been acquired by employing a C0 continuity isoparametric finite element (FE), using 4-noded elements with 7-DOF's per node. The accuracy of the current solution has been confirmed by convergence and validation studies. The influence of circular cutout, elastic foundations, hygro-thermal conditions, and geometric and boundary conditions on the vibrational frequency of porous sandwich FGM plates have been discussed in detail.

Integrated wavelet-learning method for macroscopic mechanical properties prediction of concrete composites with hierarchical random configurations

In this research, a novel integrated wavelet-learning approach with high-accuracy and efficient prediction capability is developed to predict the effective elastic properties of concrete composites with hierarchical random configurations and heterogeneous elasticity in multiple spatial scales. The significant contributions of this work include: (1) The random structural heterogeneities and material uncertainties of concrete composites in meso-scale and micro-scale are modeled on the basis of modified authors’ previous researches and Weibull probabilistic model separately. (2) Innovative stochastic three-scale asymptotic homogenization method (STAHM), background grid technique and padding strategy are presented to thoroughly acquire the doubly random geometry and material features of concrete composites with hierarchical random configurations for constructing concrete material databases. (3) The wavelet transform is utilized to preprocess the high-dimensional data features of the material databases, and the wavelet coefficients are employed as the novel input neurons for efficiently establishing more plain wavelet-neural networks that possess increasing capacity and resisting noise for approximating mappings of high complexity and nonlinearity. The numerical experiments and achieved results demonstrate that the integrated wavelet-learning approach is robust for the high-accuracy and efficient prediction of effective elastic properties of concrete materials with random heterogeneity patterns in multiple spatial scales.

How Far is the Difference Between Mechanical Behavior of Ideal and Non-Ideal FG-GPLRC Beams?

This study explored the disparities in bending, buckling, and vibration results of ideal and non-ideal functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams. The smooth and continuous profiles of material distributions of ideal FG-GPLRC beams were modified for making the controlling tracks to produce two different forms of non-ideal FG-GPLRC beams which had in-and out-stepwise distributions of material constituents across the beam’s thickness. The Halpin–Tsai model and the rule of mixture were used to predict the effective material properties of the nanocomposite beams. The closed-form solution possessing less time of computation was provided for predicting the mechanical behavior of the beams, and it was validated for accuracy by comparing with the results of the Ritz method. The study’s results suggest that non-ideal beams with an out-stepwise distribution of material constituents have a better dispersion of reinforcing nanomaterials than in-stepwise distribution. Therefore, the results of the beams with an out-stepwise distribution are closer to those of ideal beams than with in-stepwise distribution.

Thermo‐mechanical nonlinear stability analysis of geometrically imperfect functionally graded plates with microstructural defects using logarithmic structure kinematics: An unified expression

AbstractIn the present paper, thermo‐mechanical stability analysis of geometrically imperfect porous functionally graded plates (FGP) with geometric nonlinearity is presented. The equilibrium, stability, and compatibility equations are derived using Logarithmic structural kinematics in conjunction with the von‐Karman type of geometric nonlinearity. A logarithmic‐based shear‐strain function has been used for the first time for the buckling response of functionally graded material (FGM) plates. Generic imperfection function has been implemented to incorporate the various imperfection modes like sin‐type or global type in the formulation. The effective materials properties of the plates with porosity inclusion have been computed using modified power law. The plate is subjected to uniaxial and biaxial compression as well as combined compression and tension along with thermal loading. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGM plate for each loading case has been developed. After confirming the excellent accuracy of the current exact solutions, the effect of geometric imperfection, porosity inclusion, and geometric configurations on the nonlinear stability of the FGM plate have been discussed extensively. The results presented in this paper will be used as a benchmark for future research.

A specific eight-node hexahedral finite element for the analysis of 3D fibre-reinforced composites

This contribution deals with the development of an eight-node hexahedral finite element to estimate the effective elastic properties of fibre-reinforced composite materials and structures. This three-dimensional (3D) composite element is a combination of the standard eight-node hexahedral element, modelling a unit of the matrix domain, and 3D two-node truss elements that represent fibres crossing each matrix element. The so-called ‘Projected Fibre Approach’ is then considered to express the truss elements variables in terms of their corresponding matrix elements. Consequently, the obtained system of equations size is equivalent to that of a non-reinforced medium. In particular, we show that the proposed finite element formulation allows readily studying 3D composite structures with complex shape of the reinforcement like stitched sandwich panels.