A Geometrical Description in Finite Elasto-Plastic Deformation

摘要

In the present paper, a fibre bundle model of material states, in which the microscopic and macroscopic states of material can be simultaneously described and treated, is given by using the properties of fibre bundle theory that can simultaneously study some different spaces and associated relations among these spaces. According to the different deformed paths of material, the decompositions of material deformation gradient by E.H. Lee and R.J. Clifton in finite elasto plastic deformation theory can be naturally described and some relevant analyses on these decompositions are given on the model. Finally, a evolution law of the plastic deformed states of material, which is induced by the internal state evolution laws of material, is obtained by the theory of fibre bundle.