Implementation of Hencky’s elasticity model in Abaqus UELs for robust modelling of finite deformation

Abstract

Hencky’s elasticity model extends Hooke’s law from infinitesimal to large deformation and has been shown to accurately describe the mechanical behavior of materials at moderately large deformation. However, the native implementation of Hencky's model in Abaqus yields poor convergence. In this work, Abaqus user element subroutines (UELs) are developed to address this issue. Consistent tangent moduli are derived within a total Lagrangian framework to ensure robust convergence. Several benchmark examples demonstrate that the developed UELs can robustly model large-scale finite deformations with substantially improved convergence compared to the Abaqus built-in implementation. The developed UELs are of practical value for research and industry applications and have been made publicly available as supplementary materials.