A finite strain framework for steady-state problems: Hyperelasto-viscoplasticity

A numerical framework for analyzing steady-state elastic–plastic material deformation at finite strains is developed and demonstrated in the present work. The framework is an extension of the original method by Dean and Hutchinson (1980) develop to analyze steady-state crack propagation, under a small strain assumption, in which the history-dependent material response is captured through streamline integration.

Steady-state problems are encountered in numerous engineering processes, and the original studies of crack growth have already been extended to include rolling and drawing, though within a small strain framework. However, the investigation of such manufacturing processes, where strains greater than 10% easily develop, requires a finite strain formulation to provide accurate results.

The framework proposed in the present work offers an efficient and accurate method to extract the steady-state solution at finite strains without encountering the numerical issues related to traditional Lagrangian procedures. Furthermore, the framework also accounts for elastic unloading compared to many existing numerical steady-state schemes as they are often restricted to rigid plasticity.

The new numerical framework employs a hyperelastic material model, in terms of a Neo-Hookean material, combined with an isotropic viscoplastic material behavior. However, the framework is not limited to any specific hyperelastic material model, nor any specific model for the plastic behavior. The finite strain steady-state framework has been verified through comparison to a traditional Lagrangian analysis conducted in ANSYS.

The benchmark case constitutes a plane strain drawing process where the thickness of the specimen is reduced by drawing it between two circular cylindrical tools.