Formulation of Inelastic Constitutive Model for Fiber-Reinforced Composite Materials.

Abstract

Constitutive model to describe rate-dependent nonlinear inelastic behavior of unidirctionally fiber-reinforced composites is developed from phenomenological and continuum mechanics points of view. The fibrous composite is treated as a homogeneous medium which hardens with inelastic deformation. The inherent anisotropy due to the fibers is assumed to be transversely isotropic. We first derive a kinematic hardening model in invariant form. The constitutive modeling is based on the well-established thermodynamic formalism for internal state variable theories, where the thermodynamic potentials are defined by using a transversely isotropic tensor of fourth rank. In this model the evolution of the internal state variable is prescribed by the nonlinear kinematic hardening format of Armstrong-Frederick type. This enables us to describe the rate-dependence of the nonlinear anisotropic inelastic behavior of fibrous composites. Then, an isotropic hardening model is derived from this model by using an empirical method which assumes a particular representation of the kinematic hardening variable. Finally, some generalized expressions which are implied by these formulations are presented.