An anisotropic finite elastic-plastic model for fiber-matrix materials

Abstract

This chapter presents a constitutive model for anisotropic finite strain plasticity that takes into account the major effects of the macroscopic behavior of materials that consists out of matrix and fibers. The matrix material is isotropic, and the anisotropy is induced by the fiber material. The free energy function is additively split into a part that is related to the matrix and in parts that correspond to the fibers. The deformation gradient is multiplicatively decomposed into elastic and plastic parts. The principle of the maximum plastic dissipation yields the evolution equations of the plastic variables for the matrix and for the fibers. An implicit integration algorithm for the fiber is proposed that leads to the classical return-mapping scheme. A numerical example demonstrates the anisotropic behavior of the introduced material model. The anisotropic effect is induced by the fibers that are described by macroscopic one-dimensional material models.