Variational asymptotic method for unit cell homogenization of periodically heterogeneous materials

A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.     

A combined viscoelastic–viscoplastic behavior of particle reinforced composites

This study formulates a micromechanical model for predicting effective viscoelastic–viscoplastic responses of composites. The studied composites consist of solid spherical particle reinforcements dispersed in a homogeneous matrix. The particle constituent is assumed linear elastic, while the matrix exhibits combined viscoelastic–viscoplastic responses. The Schapery integral model is used for the 3D isotropic non-linear viscoelastic responses. Two viscoplastic models are considered: the Perzyna model, having a rate-independent yield surface and an overstress function, and the Valanis endochronic model based on an irreversible thermodynamics without a yield surface. The Valanis model is suitable for materials when viscoplastic responses occur at early loadings (small stress levels). A unit-cell model with four particle and polymer sub-cells is generated to obtain homogenized responses of the particle-reinforced composites. Available micromechanical models and experimental data in the literature are used to verify the proposed micromechanical model in predicting effective time-dependent and inelastic responses of composites. Field variables in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having detailed particle geometries, are modeled using finite element (FE) method.     

Thermomechanical properties of smart composites

The smart composite materials reinforced by SMA show a high performance and special deformation behavior. The thermomechanical constitutive formulas of the composites are derived by means of Eshelby's equivalent inclusion method and Mori-Tanaka's mean field concept. The interaction between the inclusion and crack and toughening mechanism are considered and the energy release rate of a crack in the smart composite is calculated. This work shows that there are the multiple mechanisms contributing to the toughening of the smart composite materials reinforced by SMA.This project is supported by the National Natural Science Foundation of China.     

Constitutive Relations of Nonlinear Thermoelasticity of Anisotropic Bodies

Quasilinear relations for finite reversible deformation of anisotropic materials are obtained using a thermomechanical approach. Free energy is written as a function of temperature and compatible invariants of the logarithmic strain measure and basis tensors. Nonlinear thermomechanical effects including different types of material behavior in tension and compression and the temperature dependence of the elastic tensor are taken into account.     

Stress analysis of notched anisotropic finite plates under mechanical and hygrothermal loads

Summary Notch-induced stress concentrations in anisotropic composite materials depend on their directional material properties, especially for uniaxially reinforced composites with high-modulus fibres. The design of notched high-performance composites requires therefore a special proof of their notched strength, which includes the structural parameters of the fibre/matrix combination, fibre orientation and layer arrangement. The assessment of the effects of the finite outer boundary is of practical importance when dimensioning critical notched regions. An anisotropic plate with finite dimensions and a hole in its center will be used here to model stress concentrations. The calculation is based on conformal mappings combined with complex-valued stress functions. The outer boundary is described using point-matching and the least-squares method. The solutions are conducive to the assessment of the essential influencing factors of material properties, geometry and loads. Notched finite plates made of fibre/matrix composites, mainly carbon-fibre reinforced polymers, will be presented as illustrations. Received 29 June 1998; accepted for publication 22 October 1998     

THERMOMECHANICAL RESPONSE OF SMA FIBER COMPOSITES WITH NON-UNIFORM TEMPERATURE DISTRIBUTION

A micromechanics method based on the High-Order-Theory developed by Aboudi et al. is used to predict the thermomechanical response of composites reinforced by shape memory alloy (SMA) fibers, and the non-uniform thermal distribution in composite arising from the process of heating or cooling is considered. The numerical development based on this model was coded to predict the thermomechanical response of shape memory alloy fiber/elastomer matrix composite subjected to thermal cycle loading. When the composite is heated, two heating ways, thermal gradients and heat source by passing an electric current through the SMA fibers are imposed on the composite respectively. Upon cooling, the first thermal boundary condition and the second thermal boundary condition are subjected to the composite respectively. A series of stress distributions and temperature distributions for different instants are calculated to reveal the interaction between the SMA material and matrix. It is useful to analyze and design the SMA actuator driven by heat source or the surface temperature.     

Homogenization and dimensional reduction of composite plates with in-plane heterogeneity

The variational asymptotic method is used to construct a new model for composite plates which could have in-plane heterogeneity due to both geometry and material. We first formulate the original three-dimensional problem in an intrinsic form which is suitable for geometrically nonlinear analysis. Taking advantage of smallness of the plate thickness and heterogeneity, we use the variational asymptotic method to rigorously construct an effective plate model unifying a homogenization process and a dimensional reduction process. This approach is implemented in the computer code VAPAS using the finite element technique for the purpose of dealing with realistic heterogeneous plates. A few examples are used to demonstrate the capability of this new model.     

Using a split Hopkinson bar to specify the parameters of thermomechanical models of flow under high strain rate deformation

By way of numerical simulation, a method is developed to determine the parameters of the thermomechanical Bodner-Partom model of flow under high strain rate deformation using a split Hopkinson bar. The classical method is generalized in two directions. To evaluate the kinematic hardening parameters, the wave reflected from the free end of the bar is used. The thermomechanical parameters that are responsible for the stored energy of cold work are calculated from measurements of temperature changes in the specimen __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 81–92, June 2008.     

A thermomechanically coupled viscoelastic cohesive zone model at large deformation

A new viscoelastic cohesive zone model is formulated for large deformation conditions and within a fully coupled thermomechanical framework. The model is suitable for the simulation of a wide range of problems especially for polymeric materials. It can capture viscoelastic crack propagation as well as energy dissipation due to this process. Starting from the principles of thermodynamics, a 3D finite element formulation is derived for a fully coupled simultaneous solution of the thermal field and the deformation field. The viscoelastic model is constructed by extending an elastic exponential traction separation law using a simple rheology. The viscous part of the tractions is postulated to have the same characteristic length as the elastic part and that they are related by a single material parameter. A Newtonian dashpot is used to describe the evolution of the viscous separation. Furthermore, thermal effects are accounted for using temperature expressions in both the traction laws and the viscosity of the dashpot, and using a heat conduction law across the interface. The model is implemented within an implicit finite element code and the internal variable is calculated using an internal iteration. Different numerical examples are used to verify the model and a comparison with experimental data shows a satisfactory agreement.     

智能复合材料的热力学特性

由形状记忆合金丝或颗粒增强的智能复合材料具有特殊的力学性能，本文从理论上预测了智能复合材料的热力学特性。利用Ｅｓｈｅｌｂｙ的等效夹杂原理与Ｍｏｒｉ－Ｔａｎａｋａ的平均场理论导出了本构列式和相变条件，揭示了形状记忆合金在弹性介质约束下的相变机理与过程。     

A new formulation of the effective elastic–plastic response of two-phase particulate composite materials

In this paper the double-inclusion model, originally developed to determine effective linear elastic properties of composite materials, is reformulated and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The resulting problem of elastic–plastic deformation of a double-inclusion embedded in an infinite reference medium subjected to an incrementally applied far-field strain is solved by the finite element method. The proposed double-inclusion model is evaluated by comparison of the model predictions to the available exact results obtained by the direct approach using representative volume elements containing many particles. It is found that the double-inclusion formulation is capable of providing accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions.     

纤维/金属网增强层板低速冲击损伤机理和演化

本文首先通过落锤低速冲击实验测试了纯玻璃纤维增强环氧树脂复合材料和304不锈钢丝网(SSWM)/玻璃纤维混杂复合材料的力学性能,探究了SSWM嵌入数量对混杂复合材料抗冲击性能的影响．随后采用Abaqus有限元软件建立了混杂复合材料的低速冲击模型,分别采用三维Hashin失效准则和Jason-Cook破坏准则模拟了纤维/基体和SSWM的损伤;建立了基于表面接触的内聚力模型来模拟界面分层;编写了VUMAT用户子程序定义混杂复合材料层合板的渐进失效过程．结果表明：相较于纯玻璃纤维增强环氧树脂层合板,SSWM/玻璃纤维混杂增强环氧树脂层合板的抗冲击性能更优,其中铺层形式为铺层III的混杂复合材料抗冲击性能最佳．通过对比发现有限元仿真结果与实验结果吻合良好,表明建立的模型适用于SSWM/玻璃纤维混杂增强环氧树脂复合材料低速冲击损伤的评估．通过分析仿真结果发现混杂复合材料的低速冲击损伤主要是冲击区域的纤维断裂、基体破坏和层间分层;SSWM通过吸收和传递冲击能量从而提升了混杂复合材料的抗冲击性能．     

On a micromechanical fracture model for cracked reinforced composites

The fracture process of reinforced composite materials is examined. In the outer region of the crack tip anisotropic continuum mechanics is employed, while for the crack tip region a heterogeneous micromechanical model is proposed. A solution is obtained using combined boundary layer — non-linear finite elements.     

材料高温力学性能理论表征方法研究进展

随着科学技术的迅猛发展,材料在高温领域的应用越来越广泛。然而高温下材料的力学性能和常温相比有很大差异,材料的高温力学性能研究和表征已成为当前的研究热点。论文文对材料在高温下力学行为理论表征方法研究的最新进展进行了总结和回顾。着重介绍了近年来高温陶瓷材料的断裂强度、金属材料的屈服强度、弹性模量与本构关系的温度相关性理论表征方法的研究进展。最后,总结已有研究工作的特点和不足之处,对材料高温力学性能理论表征方法的后续研究进行了展望,就进一步研究提供建议。     

Development of constitutive laws for thermomechanical behaviors of composites containing multi-type ellipsoidal reinforcements

Composite materials are widely used in industrial applications because of their excellent properties and behaviors. While a composite material is defined as a mixture of two or more different materials, many research works in the literature dealt with composites of only two constituents, which are matrix and one type of particles. On the other hand, the theoretical research works that dealt with more than two constituents are rare. Using some additives affects the sintering behavior, the tribological behavior and the fracture mechanics behavior of composites. For example, a suitable amount of additives as sintering aids, in the sintering process, could lower the sintering temperature, enhance phase wettability and bonding strength and improve the interlaminar fracture resistance of a composite. Therefore, it is worthwhile to develop the constitutive laws that describe the behavior of such composite materials. Accordingly, the aim of this paper is to modify the previous paper, Shabana (2003) [Shabana, Y.M., 2003. Incremental constitutive equation for discontinuously reinforced composites considering reinforcement damage and thermoelastoplasticity. Computational Materials Science 28, 31–40], in order to propose constitutive laws that predict the thermomechanical behavior of composites containing multi-type ellipsoidal reinforcements. This includes reinforcements with different materials and/or different shapes that are represented by aspect ratios. These constitutive laws not only predict the macroscopic and microscopic thermoelastoplastic behaviors of composites containing multi-type ellipsoidal reinforcements, but also characterize their different overall effective properties such as modulus of elasticity, Poison’s ratio and thermal expansion coefficient in different directions. Beside this, they are applicable for porous materials and composites with multiple reinforcements and porosities of different shapes and distributions. In the present numerical analyses, composites with two, three and four constituents considering different materials and aspect ratios as well as reinforcement damage are discussed.     

增强纤维材料高温烧蚀-相变特性的细观研究

通过高温环境下多种纤维材料的体积烧蚀机理的分析,利用细观力学的 Eshelby等效夹杂方法研究了材料烧蚀-相变特性和高温力学性能变化规律.假设材料体积烧蚀后热解相（真空）和氧化相（空气）介质统计均匀分布,考虑了热化学反应产生的气孔与固体相介质之间的相互作用,预报了不同纤维材料弹性模量随温度、加温速率之间的变化关系,并与实验结果对照,吻合较好.     

Stochastic homogenization of reinforced polymer with very small carbon inclusions

In this study, we wish to determine a homogenized model of a material reinforced by spherical inclusion that is randomly distributed in space. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional. In this study, we want to determine a homogenized model of a material reinforced by a spherical inclusion distributed randomly in space. The peculiarity here is that these particles are of very small size, this generating an energy due to the strong contrast of microstructure. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. The random distribution is taken into account during the transition of scales, so as to preserve the statistical information, and that in spite of the passage to the limit. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional.     

Analysis of Composite Molding Using the Homogenization Method

In this paper, we present an application of the homogenization method to the analysis of Resin Transfer Molding (RTM) and Structural Reaction Injection Molding (SRIM). RTM and SRIM are relatively new molding processes for manufacturing continuous fiber reinforced polymer composites. First, the mold flow is analyzed. In the molding process, the resin experiences significant temperature changes as it fills the mold and forms a free boundary with air as it pushes out the air. In addition, the flow domain is the mold cavity packed with fiber perform, which is a porous medium. Here, the homogenization method is used to model the non-isothermal flow through porous media with free boundaries. A computer program is developed which is capable of simulating a three-dimensional mold flow using the finite element approximation. An example is provided for a three-dimensional part. Then, an analysis of the residual stress developed in the curing stage is given. The curing stage starts when the mold is completely filled and it involves chemical reaction and large temperature variation. In curing, the resin part undergoes larger volume shrinkage than the fiber part, and the residual stresses are developed due to this volume mismatch. In some cases, these stresses are large enough to cause micro-cracking and to exhaust the strength of the material. Here, a brief discussion of the application of the homogenization method to a residual stress analysis is given and one example is provided.