胞元材料拓扑构型与力学性能的相关性

为了进一步探索胞元材料力学性能与材料拓扑构型的相关性,分析了不同二维和三维胞元材料的拓扑构型特征以及材料的模量与强度,得到了拉伸主导型和弯曲主导型胞元材料的力学性能与材料相对密度之间的关系,并对各种构型的力学性能进行了对比分析。在Deshpande拓扑规则的基础上,由等效连续介质刚度矩阵的非奇异性特征得到了拉伸主导型胞元材料的基本拓扑构型特征。研究表明:平面条件下拉伸主导型胞元材料必须具有3组或3组以上不同方向的连续杆件,而空间状态下拉伸主导型胞元材料必须具有6组或6组以上不同方向的连续杆件。

Relation between topology and mechanical properties of cellular materials

The periodic structure and mechanical behavior of typical two-dimensional and three-dimensional cellular materials were analyzed to relate the mechanical behavior to the topologies of the cellular materials.The strengths and stiffnesses of various stretching and bending dominated materials were compared along with the relative densities of these materials.The stretching dominated materials were much stronger and stiffer than the bending dominated materials,with the basic topological characteristics of stretching dominated materials determined based on the non-singularity of the stiffness matrix of the equivalent continuous media using the Deshpande topology criterion.The results show that not less than three stacks of continuous struts with different directions are needed for 2-D stretching dominated cellular materials,with not less than six stacks needed for 3-D materials.