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

Abstract

In this work, the phenomenological viscoplastic DSGZ model[Duan, Y., Saigal, A., Greif, R., Zimmerman, M. A., 2001. A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers. Polymer Engineering and Science 41 (8), 1322-1328], 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 0:92s-1 to 258s-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.