A Finite Strain Plasticity Theory for Transversely Isotropic Materials

Abstract

A finite strain theory for anisotropic elastic-plastic materials is presented. The example of a metal-matrix composite reinforced by aligned fibers is analyzed in detail. The plastic spin W ^p, which is the average spin of the continuum as seen by an observer spinning with the substructure (fiber), is shown to be W ^p = nn⋅D ^p-D ^p⋅nn, where D ^p is the plastic part of the deformation rate, and n is the unit vector in the direction of the fiber. The numerical implementation of the developed model is briefly discussed and the example of finite simple shear is presented.