基于偶应力理论的格栅材料等效介质模型

考察了结构最小尺寸与材料特征长度量级相当的格栅材料等效性能，建议了 基于偶应力理论的格栅材料等效介质模型以及确定等效模量的代表体元模型，给出了相应的 位移边界条件. 在此基础上导出了正交各向异性偶应力介质的特征长度表达式和偶应力介质 梁的抗弯刚度表达式，定义了偶应力影响因子\delta 以表征梁的偶应力效应. 具体计算了几种典型的格栅材料的等效偶应力模量以及格栅梁在一 定工况下的挠曲线，并与相应的有限元离散解进行对比，结果表明，等效结果具有较 高精度，且当宏观结构的尺寸和微结构尺寸相差不大时，宏观结构表现出强烈的偶应力效应. 偶应力介质的特征长度表征了偶应力效应的强弱，进而分析了格栅材料的相对密度，单 胞尺寸以及几何构型对等效介质特征长度的影响.

EFFECTIVE CONTINUUM MODEL OF GRID MATERIAL BASED ON COUPLE-STRESS THEORY

The effective properties of grid material based on classical continuum model have been widely investigated. Moreover, grid material is often used as thin-walled structures and the corresponding size of macro-structure (L) has the same magnitude with the characteristic length (l_{m}) of the grid material. The purpose of this paper is to introduce an effective couple-stress continuum model to describe the performance of grid material when L \approx l_{m} and to recommend a method to calculate the effective moduli of the model. The representative volume element (RVE) method Dirichlet boundary conditions is proposed. The effective beam stiffness of couple-stress continuum is deduced with a new parameter \delta as for the couple-stress influence factor. The theoretical analysis is validated with finite elements (FE) solutions with the cases of some typical grid materials. The results show that couple-stress continuum model can be used to evaluate grid material and obtain the effective material parameters. The couple-stress effect is obvious only when L \approx l_{m}. Furthermore, the characteristic length of the grid material is influenced by the relativity density, the size of the base cell and the geometry.