The topology structures are investigated for Zener and Every anisotropy, universal elastic anisotropy, stress-strain, and brittleness in ZrC based on Bond matrix model and tensor theory. Although the mathematical expressions of these three kinds of anisotropy are different, they give the same results, that is, the anisotropy is along the directions of [100], [110] and [111] respectively. The study of the brittleness of ZrC shows that there is a one-to-one relationship between anisotropy and brittleness. The cause of this phenomenon can be explained from the 3-D spatial structure of its negative Cauchy pressure. The investigations mainly focus on the topological structures of stress - strain in ZrC induced by point force. The results indicate that the orientation of stress-strain is not only consistent with the direction of the anisotropy of the crystal, but also with the symmetry of the crystal.

基于Bond矩阵模型和张量理论，研究了ZrC中ZerC的Zener和Every各向异性、普遍弹性各向异性、应力-应变和脆性的拓扑结构。这三种各向异性的数学表达式虽然不同，但给出的结果是相同的，即各向异性分别沿[100]、[110]和[111]方向。对 ZrC 脆性的研究表明，各向异性与脆性之间存在一一对应的关系。这种现象的成因可以从其负柯西压力的3D空间结构来解释。研究主要集中在ZrC中由点力引起的应力-应变拓扑结构。