Finite Deformation Constitutive Relations for Elastic-Plastic Fibrous Metal Matrix Composites

This paper presents a finite strain formulation of a plasticity theory of fibrous composite materials. An additive decomposition is adopted to describe the kinematics of large deformations; a lattice is defined by the current fiber direction. Elastic and plastic constitutive relations are developed from the proposition that distortions take place relative to the fiber direction. A numerical method is proposed for integrating the constitutive equations. Finally, an illustrative example of the formulation indicates that when axial loads along the fiber direction are comparable to the instantaneous shear stiffness, the finite deformation formulation is needed even with small strains.