Accurate, Efficient and Robust Explicit and Implicit Integration Schemes for the Arruda-Boyce Viscoplastic Model

Abstract

Starting from the mathematical structure and kinematic framework of the Arruda-Boyce viscoplastic model, a great variety of ideas can be tested to develop advanced constitutive models for polymers, biomaterials and soft tissues. Moreover, the primitive Arruda-Boyce constitutive model has been the cornerstone for the development of quite sophisticated models to reproduce large-strain mechanical behavior of polymers and soft biological tissues.
However, it is noteworthy that it is still impossible to find a scientific article (or book) providing a detailed description of explicit or implicit integration schemes for this constitutive model. In fact, it is quite difficult to find numerical implementations of any unified viscoplastic model. For that reason, the authors present in this article two simple integration algorithms for the Arruda-Boyce viscoplastic model, one them explicit and the other one implicit.
The development of this algorithms required a thorough bibliographical review, searching and collecting the most convenient numerical strategies, revision of standard numerical practices (and eventually their avoidance) and of course the inclusion of the own ideas of the authors. The final result is a meticulous combination of elements which were carefully assembled into two numerical material routines, which up to the present date, have worked satisfactorily with all the finite element analyses carried out by the authors.