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In this paper, the steady and transient heat transfer behaviours of multidirectional (1D/2D/3D) functionally graded composite plates are investigated. Also, two different porosity types, i.e., even and uneven distributions, are considered along with material gradation. Here, the spatial/temperature-dependent effective material properties of these highly heterogeneous composites with porosity are evaluated using the extended Voigt’s homogenisation scheme via multi-variable power-law functions and further verified with the representative volume element (RVE) scheme. In continuation, generalised mathematical models are developed by including material nonlinearity using the cubic-polynomial-based temperature-dependent constitutive model. The Poisson’s and Laplace’s equations are utilised for steady and transient heat transfer problems, respectively, and the weak form is derived using the Galerkin method. Further, coupled finite element method (FEM)–finite difference method (FDM) is adopted via Picard’s successive iteration and Crank–Nicolson technique to compute the nonlinear transient temperature. The proposed model is verified by comparing it with the previously reported results. In addition, the effects of heterogeneity, porosity, power-law indices and boundary conditions on the steady/transient heat transfer responses of multidirectional functionally graded plates are examined and discussed in detail. At last, the optimum material distributions are obtained using the response surface methodology (RSM) by minimising the heat transfer responses.

In recent times, hybrid composite materials have gained prominence as a replacement for conventional composite materials due to their superior characteristics. This study centers on assessing the elastic and thermal properties of unidirectional hybrid composites composed of natural fibers and polymers. These composites are developed by combining banana and jute fibers in four varying weight proportions, which are then impregnated with epoxy resin. The resulting specimens are manufactured and subjected to testing according to ASTM standards. The empirical findings serve as a benchmark against which outcomes from numerical simulations and analytical techniques are validated. The numerical aspect involves the implementation of a finite element model using ANSYS software. This model is based on a three-dimensional micromechanical Representative Volume Element (RVE) with both square and hexagonal packing configurations. This approach encapsulates the hybrid fiber composite’s structural characteristics. Additionally, various analytical methods, such as the rule of hybrid mixture, Halpin–Tsai, and Lewis and Nielsen approaches, are employed to calculate the elastic and thermal properties of the hybrid composite material. Comparing the results, it is evident that the outcomes derived from finite element analysis closely correspond to the experimental data and analytical predictions. Particularly noteworthy is the reduction in longitudinal and transverse thermal conductivity of the hybrid composites by 32.95% and 48.57%, respectively, at the highest fiber content. These changes are influenced by parameters like fiber loading, void fraction, and the chosen RVE. This study underscores the efficacy of employing the homogenization technique through finite element analysis for the advanced prediction of material properties. In summary, hybrid composite materials exhibit promising potential, and this research offers valuable insights into their behavior under varying conditions.

A simple model for describing the mechanical state associated with γ′-particles in Ni–Al superalloys is presented. The model is based on the properties of the anisotropic elastic Green function. The strain and stress fields produced by a single cubic particle are described. The self-energy for parallelepiped γ′-particles is calculated, finding the cubic geometry as the energetically most favorable particle shape. The anisotropy interaction between γ′-particles is investigated. The computed results are further examined considering the interaction energy between constituting elements of the particles. The configurational force acting on a γ′-particle during a creep test is analyzed.

Granular materials as typical soft matter, their transport properties play significant roles in durability and service life in relevant practical engineering structures. Physico-mechanical properties of materials are generally dependent of their microstructures including interfacial and porous characteristics. The formation of such microstructures is directly related to particle components in granular materials. Understanding the interactive mechanism of particle components, microstructures, and transport properties is a problem of great interest in materials research community. The resulting rigorous component-structure-property relations are also valuable for material design and microstructure optimization. This review article describes state-of-the-art progresses on modeling particle components, interfacial and porous configurations and incorporating these internal structural characteristics into modeling transport properties of granular materials. We mainly focus on three issues involving the simulation for geometrical components, the quantitative characterization for interfacial and porous microstructures, and the modeling strategies for diffusive behaviors of granular materials. In the first aspect, in-depth reviews are presented to realize complex morphologies of geometrical particles, to detect the overlap between adjacent nonspherical particles, and to simulate the random packings of nonspherical particles. In the second aspect, we emphasize the development progresses on the interfacial thickness and porosity distribution, the interfacial volume fraction, and the continuum percolation of soft particles representing compliant interfaces and discrete pores. In the final aspect, a literature review is also provided on modeling of transport properties on the forefront of the effective diffusion and anomalous diffusion in multiphase granular materials. Finally, some conclusions and perspectives for future studies are provided.

In this research work, the nonlinear large-amplitude free vibration characteristics of composite microplates made of a porous functionally graded (PFG) material are addressed numerically in the presence of different size-dependent strain gradient tensors as microscale. Accordingly, for the first time, the effect of each microstructural tensor is analyzed separately on the nonlinear free oscillations of PFG microplates with and without a central cutout. In order to fulfill this goal, the isogeometric computation approach is engaged to integrate the finite element approach into the nonuniform B-spline-based computer aided design tool. Accordingly, the geometry of the microplate with a central cutout is modeled smoothly to verify C⁻¹ continuity based upon a refined higher-order plate formulations. In this regard, the microstructural-dependent frequency responses associated with the nonlinear free oscillations of microplates are traced. In both the cases of simply supported and clamped boundary conditions, it was revealed that the fundamental frequency is enhanced about 1.20% by considering only the symmetric rotation gradient tensor, about 3.27% by taking only the dilatation gradient tensor, and 9.43% by considering only the deviatoric stretch gradient tensor. On the other hand, the anisotropic character of PFG composite microplates results in an unsymmetrical frequency response curve, as the nonlinear frequencies associated with negative oscillation amplitudes are a bit higher than those of positive ones.

In this study, our attention is mainly on elaborating a computational strategy to effectively predict the influence of prism profiles on the overall anisotropic property of human enamels (HEs). At first, two distinct schemes are developed separately with the aid of the polynomial fitting technique and the general power functions to mathematically describe the practical irregular and simplified regular profiles of enamel prisms. Hereafter, two parametric piecewise formulas, which facilitate the definition of anisotropic material properties of finite elements at different locations and make the numerical simulation of HE microstructures consisting of irregularly shaped prisms feasible, are presented to describe the orientation of hydroxyapatite (HAP) crystallites embedded in microprisms. The effective anisotropic moduli over a representative unit cell (RUC) under the periodic displacement constraint is concisely introduced according to the micromechanics, and a computational strategy is established to calculate these moduli numerically. Finally, the evaluations in the open literature are employed to demonstrate the validity of the elaborated computational strategy, and more investigations are conducted and yield the conclusions such that the material property of the inter-prism regions as well as the prism shapes plays a crucial role in determining the overall anisotropy of HEs.

This paper presents a numerical simulation method for the brittle rock failure process under compression, by combining the finite element method with micromechanics damage theory. When considering the rock as a homogeneous material, the initial elastic constant of each computational element is the same, but the microcrack distribution in the rock follows a statistical distribution. Consequently, in the loading process, microcrack propagation in each element is different, leading to an inhomogeneous distribution of changes in elastic constant. Under increased loading, this distribution will ultimately be reflected in the macro-failure mode of the rock. To investigate the macromechanics of the rock failure process, the damage variables and effective elastic constants are used to reflect the propagation of microcracks, thus coupling the micromechanics and macromechanics of the rock failure process. Finally, the paper demonstrates the numerical simulation method by simulating the failure of sandstone; these computational results show that the method performs well in simulating the mechanical characteristics of the brittle rock failure process.

A micromechanical damage model for the finite element modelling of historical masonry structures is presented in this article. Masonry is considered as a composite medium made up of a periodic assembly of blocks connected by orthogonal bed and head mortar joints. The constitutive equations, in plane stress, are based on the homogenisation theory and they consider the non linear stress-strain relationship in terms of mean stress and mean strain. Different in-plane damage mechanisms, involving both mortar and blocks, are considered and the damage process is governed by evolution laws based on an energetic approach derived from Fracture Mechanics and on a non-associated Coulomb friction law. The failure domain of the model is analysed both in the equivalent stress and in the principal stress space considering different orientations of the bed joints relative to the loading direction. A comparison with experimental results is provided. A numerical simulation of masonry walls subjected to horizontal forces proportional to their own weight is shown in order to discuss the model's capability of describing the influence of the masonry microstructure on its mechanical behaviour.

The paper presents an overview of multiscale modeling of advanced fibrous composite materials. Following the review, a nonlinear, fully three-dimensional, numerical model is proposed which is suitable for multiscale elastic and progressive failure analysis of plain-woven composite materials. The proposed model is developed for implementation into the Finite Element code ABAQUS/Explicit as a user-defined subroutine for constant stress (one integration point) solid elements.

The multiscale strategy applied in this paper uses a closed-form solution approach for homogenization of the mesoscale properties of a woven composite. A mosaic model of the woven composite's Representative Volume Element (RVE) is used for deriving the micromechanical relations used for homogenization. The composite RVE model used herein is composed of UD interlacing yarns (fill and warp yarns) and matrix-rich regions. For failure and damage analysis, the following features are implemented in this work: material nonlinearity for pure in-plane shear deformation; physically-based failure criteria for matrix failure in the UD yarns; maximum stress failure criteria for failure of fibers in the UD yarns and of the pure matrix in the resin-rich regions and energy-based damage mechanics.

The proposed strategy, which has been implemented and tested for a special case of an in-plane damage, has some evident advantages compared to the other approaches, especially for application to full-scale simulations, i.e., component and structural scales.

A comparison of the proposed model with experimental data shows a good correlation can be achieved.

Evaluation of the poroelastic properties of oil-well cement paste is essential for prediction of the performance of the cement sheath during the life of a well. A multiscale homogenization model is used to evaluate the poroelastic properties of different classes of oil-well cement paste. The model has been calibrated in a previous work based on the results of a laboratory study on a hardened class G cement paste. A hydration model is used to evaluate the volume fractions of different microstructure phases of cement paste based on the chemical composition of clinker and the water-to-cement ratio. Typical chemical compositions of API class A to class H oil-well cements with their corresponding water-to-cement ratios are used to evaluate the poroelastic parameters such as drained bulk modulus, Biot coefficient, Skempton coefficient, etc. The results show that the difference in the chemical compositions of these cements has not an important effect on the variations of the poroelastic properties. Contrarily, the water-to-cement ratio has an important effect on the variations of these parameters.

There has been increasing attention to utilizing carbon nanotubes (CNTs) as nano-fillers in polymers and polymer matrix composite materials, such as carbon fiber reinforced plastics. However, the understanding of how randomly oriented CNTs affect mechanical properties of such CNT-engineered composites is limited. This paper serves to develop an analytical model for determining the elastic properties of CNT-engineered composite materials using a mechanics of materials approach. Analysis of the properties was constructed progressively using material unit cells starting from the nano level, to the micro level, and finally, to the macro level. MATLAB programming platform was used to facilitate simulation of the modeling process. Typical simulation cases of the CNT-engineered composite materials are presented in comparison with published experimental and other data, where appropriate.

Advanced composites are increasingly being used as a structural material because of their balanced properties, higher impact resistance, and easier handling and fabrication compared with unidirectional composites. However, complex architecture of these composites leads to difficulties in predicting the mechanical response necessary for product design. Different methods for micromechanical analysis for the evaluation of effective mechanical properties of advanced composites are compared. Difficulties in modeling are highlighted and recommendations are given for micromechanical analysis using the finite element method.

In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a 3D grain boundary micro mechanical model. The volume fraction of pores, their size and distribution can be varied to better simulate the response of real porous materials. The formulation is built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi Tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are obtained through material homogenization, computing the volume averages of micro-strains and stresses and taking the ensemble average over a certain number of microstructural samples. The obtained results show the capability of the model to assess the macroscopic effects of porosity.

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

Structural performance of unidirectional composites (UD) is directly dependent on its ingredient’s properties, ply configurations and the manufacturing effects. Prediction of mechanical properties using multiscale manufacturing simulation and micromechanical models is the focus of this study. Particular problem of coupled dual-scale deformation-flow process such as the one arising in RTM, Vacuum-Assisted Resin Infusion (VARI) and Vacuum Bag Only (VBO) prepregs is considered. A finite element formulation of porous media theory framework is employed to predict the element-wise local volume fractions and the deformation of a preform in a press forming process. This formulation considers coupling effects between macro-scale preform processes and mesoscale ply processes as well as coupling effects between the solid and fluid phases. A number of different micromechanical models are assessed and the most suitable one is used to calculate mechanical properties from volume fractions. Structural performance of the “deformed” geometry is then evaluated in mechanical analysis. An integrated platform is designed to cover the whole chain of analysis and perform the properties’ calculation and transfer them between the modules in a smooth mapping procedure. The paper is concluded with a numerical example, where a compression-relaxation test of a planar fluid filled prepreg at globally un-drained condition is considered followed by a mechanical loading analysis. The development is user friendly and interactive and is established to enable design and optimization of composites.

The objective of this work is to numerically investigate the elastic–plastic deformation of closed-cell foams incorporating the effect of inner gas pressure. Both body-centered cubic (BCC) and face-centered cubic (FCC) arrangements of pores are considered in analysis. It is seen that the inner gas pressure has a significant effect on the plastic deformation of closed-cell foams, which is different for the foams with different microstructures and is discussed in detail. The inner gas pressure results in the asymmetry of uniaxial tensile-compressive stress–strain curves and the nominal Poisson's ratio. It is shown that the inner gas pressure makes the yield surface move to the negative direction of the hydrostatic axis in the plane of equivalent and hydrostatic stresses, and the moving distance is equal to the magnitude of inner gas pressure in the foams. Moreover, a new yield function incorporating the effect of inner gas pressure is developed for closed-cell foams. The material constants in the yield function depend on the microstructures of the foams.

Ionic polymer transducers (IPTs), also known as ionic polymer-metal composites (IPMCs), are smart sensors and actuators which operate through a coupling of micro-scale chemical, mechanical, and electrical interactions. It is known that ion movement, when a voltage is applied, causes stresses which lead to a net bending movement of a cantilevered transducer towards the anode. However, it is not well understood how these stresses arise, and it is not known how the material microstructure affects the observed macroscopic bending response. In this work, we apply a micromechanics modeling framework to analyze how assumptions of the material microstructure of an IPT affect local interactions and the resulting boundary layer stresses which lead to actuation. In the micromechanics framework, local equilibrium consists of a balance between internal cluster pressure and the stress developed in the polymer backbone. Here, we derive a generalized expression for the electrostatic cluster pressure and show how it depends on microstructure and microstructural evolution in the boundary layers. It is proposed that the boundary layer stiffness varies locally with changes in solvent uptake and charge density; this relationship is defined from micromechanics equilibrium conditions and includes effects of the generalized electrostatic cluster pressure. By assuming a relationship between ion and solvent movement, we then examine how boundary layer stresses are affected by assumptions of the material microstructure. The results and implications of the model are compared with recent experimental observations as well as other models of IPT actuation.

A micromechanics-based elastoplastic constitutive model for porous materials is proposed. With an assumption of modified three-dimensional Ramberg–Osgood equation for the compressible matrix material, the variational principle based on a linear comparison composite is applied to study the effective mechanical properties of the porous materials. Analytical expressions of elastoplastic constitutive relations are derived by means of micromechanics principles and homogenization procedures. It is demonstrated that the derived expressions do not involve any additional material constants to be fitted with experimental data. The model can be useful in the prediction of mechanical properties of elastoplastic porous solids.

In this paper, the bi-axial stretching effects on the electrical conductivity of carbon nanotube (CNT)-polymer composites are studied by a mixed micromechanics model with the consideration of the electrical conductive mechanisms. The bi-axial stretching effects are characterized by volume expansion of composite, re-orientation of CNTs and change of conductive networks. Simulation results demonstrate that the bi-axial stretching decreases the electrical conductivity of the composites due to the dominant role of the stretching-induced change in conductive networks, i.e., the increase in the percolation threshold, the separation distance among CNTs and the breakdown of the networks. It is also found that the bi-axial stretching enhances the decreasing rate of the electrical conductivity and increases the distribution randomness of the CNTs in the bi-axial stretching plane, as compared to a uni-axial stretching case. Furthermore, the dependency of the variation of electrical conductivity on the CNT concentration and sizes is also investigated. Possible reasons for the variation trends are interpreted. The study in this paper is expected to provide an increased understanding on the stretching effects upon the electrical conductivity of CNT-polymer composites.

Brittle creep in rock has great significance for the prediction of important geohazards and stability of deep underground excavations. A major challenge in this area is to link the time-dependent cracking with macroscopic mechanical behavior. In this paper, Ashby and Sammis’ microcrack model and Charles’ crack growth law are employed to investigate the time-dependent cracking during brittle creep in rock. Based on the macroscopic and micromechanical definition of damage in rock, a new theoretical model is suggested to establish the linkage between microcrack length and macroscopic strain. In order to verify the rationality of the suggested model, comparison between theoretical and experimental results is presented. Using this new model, brittle creep of Sanxia granite is investigated and discussed in detail. It is found that evolutions of wing crack length, strain, and damage perform a similar process during brittle creep and could be divided into three phases. Effects of model parameters on creep failure behaviors also are studied.