Continuity equation of elastic damage in Riemannian space obtained by topological method

There are many models for various material or the different damaging process in the Damage Mechanics,but there is no uniform model.And there are more difficulties when more complicated problems of damage are solved.The correlation between elastic damage defect and Riemannian space is established in this paper by topological method.The physical defect of material is translated into geometric defect by topological method.The quasi-plastic damage coefficient tensor is defined with continuous damaging variable,and the continuity equation of elastic damage in Riemannian space is obtained with the quasi-plastic strain tensor.So a physical nonlinear problem is taken apart into a physical linear problem together with a bending space.