Inconsistency of uhyper and umat in Abaqus for compressible hyperelastic materials

TL;DR

This paper clarifies the conditions under which uhyper and umat implementations in Abaqus produce consistent results for compressible hyperelastic materials, emphasizing the importance of the stress update method used.

Contribution

It clarifies the relationship between uhyper and umat implementations in Abaqus, highlighting that differences arise only with hypoelastic incremental stress updates.

Findings

Uhyper and umat produce identical results with total stress updates.

Differences occur only with hypoelastic incremental stress updates.

Clarifies implementation assumptions for hyperelastic models in Abaqus.

Abstract

In this article, we revisited Ba\v{z}ant's comments on the implementation of hyperelastic material models in commercial finite element software. We would like to clarify that our assertions only apply if the material models are implemented as hypoelastic, i.e. by incremental stress updates, in common interfaces (including, in particular, umat in Abaqus). This assumption was not made sufficiently clear in the article. If, on the other hand, the stress calculations are implemented using the umat interface with absolute (or "total") stress updates, as is also assumed in the uhyper interface, there is no difference in the internal processes or the results between the umat and the uhyper implementation. This applies to highly compressible formulations as well, where the Kirchhoff and Cauchy stress tensors are clearly distinguished.