Finite element implementation of a macromolecular viscoplastic polymer model

This paper presents a time‐integration method for a viscoplastic physics‐based polymer model at finite strains. The macromolecular character of the model resides in (i) the viscoplastic law based on a double‐kink molecular mechanism, and (ii) a full chain network model inspired by rubber elasticity to describe the large‐strain orientation hardening. A back stress enters the constitutive model formulation. Essential aspects of a three‐dimensional finite‐element implementation are outlined, the main novelty being in the back stress formulation. The computational efficiency and accuracy of the algorithm are examined in a series of parameter studies. In addition, because a co‐rotational formulation of the constitutive equations is employed using the Jaumann rate in the hypoelastic equation and the back stress evolution equation a detailed analysis of stress oscillations is carried out up to very large strains in simple shear. Subsequently, three‐dimensional FE analyses of compression with friction and instability propagation in tension are used as a means to demonstrate the robustness of the implementation and the potential occurrence of stress oscillations and shear bands in large‐strain analyses. Copyright © 2013 John Wiley & Sons, Ltd.