A gradient enhanced constitutive framework for the investigation of ductile damage localization within semicrystalline polymers

The paper presents a gradient enhanced model dealing with nonlocal phenomena driven by the ductile damage in semicrystalline polymers that exhibit rate-dependent and rate-independent mechanisms. The study aims at capturing the material localization at high damage levels. To this end, a viscoelastic-viscoplastic constitutive model is formulated considering a gradient enhanced thermodynamic potential, function of local and nonlocal state variables. The model is based on two different options for the nonlocal state variable: the first option considers nonlocal damage scalar, while the second considers nonlocal hardening state variable. An appropriate user defined material subroutine is developed so as to define and to update the stress, the state variables, and the associated tangent moduli towards finite element structural computations. The analogy between the steady-state heat equation and the nonlocal gradient enhanced relation enables coupling the displacement and nonlocal fields within a finite element package code (i.e., ABAQUS). Structural analyses for polyamide 66 (PA66) material are presented to assess the efficiency of the developed nonlocal model. This research work demonstrates that the model is able to capture efficiently the ductile damage localization and simulate the related fields when using the nonlocal hardening or damage state variable. This study for the first time combines viscoelasticity, viscoplasticity, and damage with nonlocal approaches, and can be considered as an initial step towards developing a constitutive formulation towards multiscale analyses for polymer-based composites.