A note on the implementation of the hyperelastic Kilian model in the Abaqus

TL;DR

This paper verifies the implementation of the Kilian hyperelastic model in Abaqus/Standard, focusing on strain locking behavior and comparing it with the Gent model through numerical tests.

Contribution

It identifies an additional numerical procedure affecting the Kilian model implementation not documented in Abaqus.

Findings

Kilian model's strain locking is correctly implemented in Abaqus/Standard.

A discrepancy exists in the UHYPER procedure's handling of strain locking.

The study highlights the need for additional numerical procedures for accurate Kilian model simulation.

Abstract

The main goal of the article is to verify the implementation of the Kilian material model in the Abaqus/Standard. The key feature of the model is that it describes so called strain locking, which results directly from a structure of the stored energy function. Basic properties of the considered incompressible material model are illustrated base on three types of homogeneous deformations. To compare response of the material model, the Gent model is considered as well. Verification of the implementation concerns simple numerical tests based on the built-in Kilian model and the UHYPER procedure. We show that in the first case the locking constraint is satisfied while in the second one it is not. This indicates an existence of an additional numerical procedure which is not mentioned in the software documentation.