Implicit implementation and consistent tangent modulus of a viscoplastic model for polymers

• An implicit implementation for the viscoplastic DSGZ model is proposed.
• The formulation uses the consistent tangent modulus.
• The formulation is validated with experiments in polypropylene.
• Impact loading test illustrates the implementation capabilities.

In this work, the phenomenological viscoplastic DSGZ model (Duan et al., 2001 [13]), developed for glassy or semi-crystalline polymers, is numerically implemented in a three-dimensional framework, following an implicit formulation. The computational methodology is based on the radial return mapping algorithm. This implicit formulation leads to the definition of the consistent tangent modulus which permits the implementation in incremental micromechanical scale transition analysis. The extended model is validated by simulating the polypropylene thermoplastic behavior at various strain rates (from 0.92 s−1 to 258 s−1) and temperatures (from 20 °C to 60 °C). The model parameters for the studied material are identified using a heuristic optimization strategy based on genetic algorithm. The capabilities of the new implementation framework are illustrated by performing finite element simulations for multiaxial loading.