GEOMETRICAL TOPOLOGY OF ELASTIC DAMAGE THEORY

The microscopic geometrical defects of materials are usually taken into account in the constitutive equation as a physical nonlinear problem. In this paper, the geometrical topology of elastic damage theory is given and the microscopic geometrical defects of materials are translated into the bending of the space, which is reflected in the geometrical equations. At first, this paper defines some quasi-plastic tensors with continuous damage tensor, which satisfy the continuity equations and the geometric laws. As a result, the corresponding relation between elastic damage defects and Riemann Space is established, and the physical nonlinear problem is converted to a physical linear problem together with a bending of space. Finally, an example of anisotropic damage of isotropic materials in two-dimensions is discussed.