Numerical predictions of effective shear modulus and size effect for periodic cellular materials
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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$n \to \infty$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.
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关键词:
- 体胞子结构
Abstract: Based on the classical cylinder torsion model, a simpleand efficient method is proposed in this paper to predict the effectiveshear modulus and the size effect of periodic cellular materials. Asrepresentative examples, square-hole and circle-hole unit cells are used toclarify the problem and computing. Analytical expressions are established todetermine the geometrical parameters of the cell in terms of the cell sizefactor $n$. Following conclusions can be drawn out from numeral results. Theeffective shear moduli of the two types of unit cells decrease as the scalefactor $n$ increases; when $n \to \infty $, i.e., the size of the unit cell issmall enough with respect to the size of the whole structure, the effectiveshear modulus tends to be a constant value. The increase of the materialvolume fraction of the unit cell will result in an increase of the effectiveshear modulus of the cellular material. Meanwhile, the unit cellsubstructure concept is proposed to predict the effective shear modulus andthe size effect of the periodic cellular material based on itscharacteristic of structural symmetry. This modeling can greatly increasethe computing efficiency.-
Key words:
- unit cell substructure
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