Elasto-plastic constitutive equations for short fiber reinforced polymers

Short fiber-reinforced thermoplastics show nonlinear response under different sorts of loadings. The nonlinear behavior is referred to the plasticity-induced deformation in the short fiber reinforced materials. Proper constitutive equations are required to describe their mechanical response. These materials are considered transversely-isotropic, while an elastic-plastic model is introduced for the plasticity induced nonlinearity. The so-called non-local damage model is used to govern the post plasticity damage phenomenon. The model is founded on the representation theory of the basic invariants of the transversely isotopic materials. Since we deal with non-metallic materials, then the elasto-plastic model must be non-associated, which requires a potential function be defined as well as a yield function. These requirements along with the proper invariants for the transversely isotropic materials are introduced and discussed. The elasto-plasticity model is implemented into the Finite Element Method software ABAQUS using a properly conceived UMAT subroutine in an implicit fashion. Simulation results are validated with the basic tensile and compression experimental results for the material PA6GF60 for a single element and the complete geometry of the specimens.