A multiplicative finite strain finite element framework for the modelling of semicrystalline polymers and polycarbonates

This paper presents a phenomenological model for the simulation and analysis of stress-induced orientational hardening in semicrystalline polymers and polycarbonates at finite strains. The notion of intermediate (local) stress-free configuration is used to develop a set of constitutive equations, and its relation to the multiple natural (stress-free) configurations in the class of materials being considered here is discussed. A hyperelastic stored energy function, written with respect to the intermediate stress-free configuration is presented to model the finite elastic response. It is then combined with the J₂-flow theory to model the finite inelastic response. The isochoric constraint during inelastic deformation is treated via an exact multiplicative decomposition of the deformation gradient into volume-preserving and spherical parts. The numerical solution algorithm is based on the use of operator splitting technique that results in a product formula algorithm with elastic-predictor/inelastic-corrector components. Numerical results are presented to show the behaviour of the model.