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.

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。