本文研究了含非均匀界面相球形粒子填充复合材料的有效体积模量和有效热膨胀系数。本文采用的细观力学模型是包含界面相的复合球模型,界面相位于夹杂和基体之间(如图1)。在复合球的外边界施加静水压的边界条件,并假设复合球内有一个均匀的温度变化。首先求解复合球内的位移,对于均匀相(夹杂相和基体相),位移、应变和应力有通解,而对于不均匀的界面相,直接求解位移比较困难,本文将界面相剖分为n层等厚薄层(如图2),假设每层薄层性质是均匀的,将这些薄层由内而外编号为区域1到n,并定义夹杂相和基体相为区域0和区域n+1。薄层的性能参数取为界面相内模量和热膨胀系数分布函数在每层薄层中心处的值。

This paper studies the effective properties of multi-phase thermoelastic composites. Based on the Helmholtz free energy and the Gibbs free energy of individual phases, the effective elastic tensor, thermal-expansion tensor, and specific heats of the multi-phase composites are derived by means of the volume average of free-energies of these phases. Particular emphasis is placed on the derivation of new analytical expressions of effective specific heats at constant-strain and constant-stress situations, in which a modified Eshelby's micromechanics theory is developed and the interaction between inclusions is considered. As an illustrative example, the analytical expression of the effective specific heat for a three-phase thermoelastic composite is presented.

This paper studies the effective properties of multi-phase thermoelastic composites. Based on the Helmholtz free energy and the Gibbs free energy of individual phases, the effective elastic tensor, thermal-expansion tensor, and specific heats of the multi-phase composites are derived by means of the volume average of free-energies of these phases. Particular emphasis is placed on the derivation of new analytical expressions of effective specific heats at constant-strain and constant-stress situations, in which a modified Eshelby's micromechanics theory is developed and the interaction between inclusions is considered. As an illustrative example, the analytical expression of the effective specific heat for a three-phase thermoelastic composite is presented.

In this paper, a new method of topological cleanup for quadrilateral mesh is presented. The method first selects a patch of mesh around an irregular node. It then seeks the best connection of the selected patch according to its irregular valence using a new topological operation: small polygon reconnection (SPR). By replacing the original patch with an optimal one that has less irregular valence, mesh quality can be improved. Three applications based on the proposed approach are enumerated: (1) improving the quality of a quadrilateral mesh, (2) converting a triangular mesh to a quadrilateral one, and (3) adapting a triangle generator to a quadrilateral one. The presented method is highly effective in all three applications.

基体和夹杂之间的界面能对复合材料的宏观等效性质是有影响的,本文将黄筑平等人提出的界面能理论应用于包含单向纤维夹杂的复合材料等效性质的计算中,给出了考虑界面能效应之后横观各向同性的复合材料的5个独立的等效工程参数。其中,等效横观剪切模量是由广义自洽法得到的,其余四个等效参数是由"复合柱"模型得到的。

The surface/interface energy theory based on three configurations proposed by Huang et al. is used to study the effective properties of thermoelastic nanocomposites. The particular emphasis is placed on the discussion of the influence of the residual interface stress on the thermal expansion coefficient of a thermoelastic composite filled with nanoparticles. First, the thermo-elastic interface constitutive relations expressed in terms of the first Piola-Kirchhoff interface stress and the Lagrangian description of the generalized Young-Laplace equation are presented. Second, the Hashin's composite sphere assemblage (CSA) is taken as the representative volume element (RVE), and the residual elastic field induced by the residual interface stress in this CSA at reference configuration is determined. Elastic deformations in the CSA from the reference configuration to the current configuration are calculated. From the above calculations, analytical expressions of the effective bulk modulus and the effective thermal expansion coefficient of thermoelastic composite are derived. It is shown that the residual interface stress has a significant effect on the thermal expansion properties of thermoelastic nanocomposites.

The surface/interface energy theory based on three configurations proposed by Huang et al. is used to study the effective properties of thermoelastic nanocomposites. The particular emphasis is placed on the discussion of the influence of the residual interface stress on the thermal expansion coefficient of a thermoelastic composite filled with nanoparticles. First, the thermo-elastic interface constitutive relations expressed in terms of the first Piola-Kirchhoff interface stress and the Lagrangian description of the generalized Young-Laplace equation are presented. Second, the Hashin's composite sphere assemblage (CSA) is taken as the representative volume element (RVE), and the residual elastic field induced by the residual interface stress in this CSA at reference configuration is determined. Elastic deformations in the CSA from the reference configuration to the current configuration are calculated. From the above calculations, analytical expressions of the effective bulk modulus and the effective thermal expansion coefficient of thermoelastic composite are derived. It is shown that the residual interface stress has a significant effect on the thermal expansion properties of thermoelastic nanocomposites.

In subspace iteration method (SIM), the relative difference of approximated eigenvalues between two consecutive iterations is usually employed as the convergence criterion. However, though it controls the convergence of eigenvalues well, it cannot guarantee the convergence of eigenvectors in all cases. In the case when there is no shifting, the best choice for the convergence criterion of eigenvalues may generally be the computable error bound proposed by Matthies, which is based on an estimation of Rayleigh quotient of approximated eigenvalues expressed in the subspace. Matthies' form guarantees the convergence of both eigenvalues and eigenvectors and can be computed with almost negligible operations. However, it is not as popular as expected in implementations, partly because it does not consider the popular shifting acceleration technique of subspace iterations. In this paper, we extend Matthies' form to the case of nonzero shifting and prove that this extended error bound form with nonzero shifting can be used generally as a convergence criterion for eigenpairs. Besides, this paper details the derivation to illustrate that the extended error bound can also be applied to the case of positive semi-definite mass matrix by only slightly modifying the subspace iteration procedure. Numerical tests are presented to illustrate the motivation and to demonstrate the better performance of the modified computable error bound. The studies in this paper indicate that the modified Matthies' form of error bound can be effectively used as a preferred convergence criterion in the SIM. Copyright (C) 2009 John Wiley & Sons, Ltd.

In subspace iteration method (SIM), the relative difference of approximated eigenvalues between two consecutive iterations is usually employed as the convergence criterion. However, though it controls the convergence of eigenvalues well, it cannot guarantee the convergence of eigenvectors in all cases. In the case when there is no shifting, the best choice for the convergence criterion of eigenvalues may generally be the computable error bound proposed by Matthies, which is based on an estimation of Rayleigh quotient of approximated eigenvalues expressed in the subspace. Matthies' form guarantees the convergence of both eigenvalues and eigenvectors and can be computed with almost negligible operations. However, it is not as popular as expected in implementations, partly because it does not consider the popular shifting acceleration technique of subspace iterations. In this paper, we extend Matthies' form to the case of nonzero shifting and prove that this extended error bound form with nonzero shifting can be used generally as a convergence criterion for eigenpairs. Besides, this paper details the derivation to illustrate that the extended error bound can also be applied to the case of positive semi-definite mass matrix by only slightly modifying the subspace iteration procedure. Numerical tests are presented to illustrate the motivation and to demonstrate the better performance of the modified computable error bound. The studies in this paper indicate that the modified Matthies' form of error bound can be effectively used as a preferred convergence criterion in the SIM. Copyright (C) 2009 John Wiley & Sons, Ltd.

A thermal-elastoplastic constitutive model is proposed for particle-filled composites in this paper. Particles are assumed to be linear thermoelastic while the matrix follows the thermal-elastoplastic responses with the generalized Ramberg-Osgood relation. Based on the micromechanics methodology and homogenization procedures, the effective thermal-mechanical constitutive functions are derived including the macroscopic Helmholtz free energy and the macroscopic yield function.First, it is assumed that in the case of plastic unloading or stress-strain state being in the macroscopic yield surface, the constitutive relation of the composites is linear thermoelastic expressed by the macroscopic Helmholtz free energy. The micromechanics-based thermoelastic properties of the composite are obtained including the effective elastic moduli, thermal expansion coefficients, and specific heats.Furthermore, with the concept of linear comparison composites, the variational principle is extended to consider the thermal effect, from which the lower bound of the macroscopic stress potential for the nonlinear composites can be computed. The associated macroscopic plastic strain is defined, and the macroscopic yield function in the temperature-strain space is therefore determined.Finally, the above two constitutive functions are combined with the thermal-elastoplastic constitutive theory proposed by Huang (1994) to develop the loading-unloading criterion in the temperature-strain space and the incremental thermal-elastoplastic constitutive relations for particulate composites. The results can be useful in the study of the thermomechanical behavior of particle-filled composites at elevated temperatures.

A thermal-elastoplastic constitutive model is proposed for particle-filled composites in this paper. Particles are assumed to be linear thermoelastic while the matrix follows the thermal-elastoplastic responses with the generalized Ramberg-Osgood relation. Based on the micromechanics methodology and homogenization procedures, the effective thermal-mechanical constitutive functions are derived including the macroscopic Helmholtz free energy and the macroscopic yield function.First, it is assumed that in the case of plastic unloading or stress-strain state being in the macroscopic yield surface, the constitutive relation of the composites is linear thermoelastic expressed by the macroscopic Helmholtz free energy. The micromechanics-based thermoelastic properties of the composite are obtained including the effective elastic moduli, thermal expansion coefficients, and specific heats.Furthermore, with the concept of linear comparison composites, the variational principle is extended to consider the thermal effect, from which the lower bound of the macroscopic stress potential for the nonlinear composites can be computed. The associated macroscopic plastic strain is defined, and the macroscopic yield function in the temperature-strain space is therefore determined.Finally, the above two constitutive functions are combined with the thermal-elastoplastic constitutive theory proposed by Huang (1994) to develop the loading-unloading criterion in the temperature-strain space and the incremental thermal-elastoplastic constitutive relations for particulate composites. The results can be useful in the study of the thermomechanical behavior of particle-filled composites at elevated temperatures.

In this paper, a modified projection method is combined with a self-adaptive time step procedure to develop numerical scheme for large eddy simulation (LES) of low Ma number turbulent reactive flows. The projection method introduced by Chorin is modified in this study to satisfy the simulation requirement of low Ma number reactive flow. The time step in this computation is automatically determined according to the time scales of both chemical reaction and turbulent fluctuations. This enables the simulation to capture detailed flow structures with less computational time. Numerical simulation of methane-air jet flames is carried out as an example to validate the developed numerical scheme. The mechanism of a simplified 4-step chemical kinetics is applied for the methane-air reaction. The dynamic model is adopted for the turbulent motion of sub-grid scale (SGS). The dynamic similarity model is used as the SGS model for the reaction rate. The LES results satisfactorily depict the ignition process of the turbulent jet flames and illustrate lucid and detailed coherent structures of the fully developed turbulent reactive jet flow. The LES results also exhibit the mechanism and characteristics of local extinction. The method developed in this study provides an effective way to capture more flow details with less computational time. In addition the method also helps one to investigate the mechanism of ignition and local extinction in jet flames. Copyright (C) 2008 John Wiley & Sons, Ltd.

In this paper, a modified projection method is combined with a self-adaptive time step procedure to develop numerical scheme for large eddy simulation (LES) of low Ma number turbulent reactive flows. The projection method introduced by Chorin is modified in this study to satisfy the simulation requirement of low Ma number reactive flow. The time step in this computation is automatically determined according to the time scales of both chemical reaction and turbulent fluctuations. This enables the simulation to capture detailed flow structures with less computational time. Numerical simulation of methane-air jet flames is carried out as an example to validate the developed numerical scheme. The mechanism of a simplified 4-step chemical kinetics is applied for the methane-air reaction. The dynamic model is adopted for the turbulent motion of sub-grid scale (SGS). The dynamic similarity model is used as the SGS model for the reaction rate. The LES results satisfactorily depict the ignition process of the turbulent jet flames and illustrate lucid and detailed coherent structures of the fully developed turbulent reactive jet flow. The LES results also exhibit the mechanism and characteristics of local extinction. The method developed in this study provides an effective way to capture more flow details with less computational time. In addition the method also helps one to investigate the mechanism of ignition and local extinction in jet flames. Copyright (C) 2008 John Wiley & Sons, Ltd.