周期性多孔材料等效剪切模量与尺寸效应研究  

NUMERICAL PREDICTIONS OF EFFECTIVE SHEAR MODULUS AND SIZE EFFECT FOR PERIODIC CELLULAR MATERIALS

作　　者：张卫红[1] 骆金威[1] 戴高明[1] 张进[1] 

机构地区：[1]西北工业大学现代设计与集成制造技术教育部重点实验室,西安710072

出　　处：《力学学报》2011年第1期144-153,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金项目(10925212;90916027);111项目(B07050)资助~~

摘　　要：提出了以圆筒扭转力学模型为基础,预测周期性多孔材料等效剪切模量及其研究尺寸效应的一种简单有效计算方法.以方形孔和圆形孔两种典型多孔材料为例进行了数值计算求解;同时,建立了几何参数随体胞尺寸缩放因子n的解析关系,证明了两种构型的周期性多孔材料的等效剪切模量均随尺寸缩放因子n的增大而减小.当n→∞时,即体胞尺寸相对整体结构无限小时,多孔材料的等效剪切模量趋近收敛于一个恒定值;当体胞的材料体分比增大时,多孔材料等效剪切模量也随之增大.此外,依据周期性多孔材料的结构对称特性,使用体胞子结构有限元计算模型进行等效剪切模量及其尺寸效应的预测,极大地提高了计算效率.Based on the classical cylinder torsion model,a simple and efficient method is proposed in this paper to predict the effective shear modulus and the size effect of periodic cellular materials.As representative examples,square-hole and circle-hole unit cells are used to clarify the problem and computing.Analytical expressions are established to determine the geometrical parameters of the cell in terms of the cell size factor n.Following conclusions can be drawn out from numeral results.The effective shear moduli of the two types of unit cells decrease as the scale factor n increases;when n→∞,i.e.,the size of the unit cell is small enough with respect to the size of the whole structure,the effective shear modulus tends to be a constant value.The increase of the material volume fraction of the unit cell will result in an increase of the effective shear modulus of the cellular material.Meanwhile,the unit cell substructure concept is proposed to predict the effective shear modulus and the size effect of the periodic cellular material based on its characteristic of structural symmetry. This modeling can greatly increase the computing efficiency.

关 键 词：周期性多孔材料 等效剪切模量 尺寸效应 材料体分比 体胞子结构 

分 类 号：O341[理学—固体力学]