含微缺陷金属材料损伤理论的几何拓扑

本文针对含微缺陷金属材料损伤理论进行几何拓扑,采用非完整标架的方法把金属材料内部微观几何缺陷拓扑为材料空间的弯曲,并体现在几何方程中。首先通过释放应力将平直Euclid空间缺陷物质流形与Riemann流形建立对应关系,给出Riemann流形中含微缺陷金属材料的应变、应力状态以及几何法则、静力平衡方程,将物理非线性问题转化为物理线性问题和材料空间弯曲之和。最后讨论了二维情况下金属材料受各向异性损伤的算例。

Topological Damage Theory of Metal with Defects

The purpose of this paper is to translate defects of mental materials into geometrical defects with geometrical topological method.Firstly,the corresponding relation between Euclid Space with damage defect and Riemann Space is established.Then the strain state and the stress state in Riemann Space are presented with the geometrical law.So a physical nonlinear problem is departed into a physical linear problem together with a bending space.Finally,an example of anisotropic damage of metal materials in two-dimensions is discussed.