Sensitivity analysis based crack propagation criterion for compressible and (near) incompressible hyperelastic materials

Abstract

Sensitivity analysis of an XFEM crack propagation model is developed for shape and material parameters, where the direct differentiation method is applied to large strain problems with hyperelastic neo-Hookean materials. The presence of level set functions to describe the crack position requires the development of a proper differentiation technique which is also addressed. In order to compute the analytical derivatives of such a complex numerical model the capabilities of the symbolic system AceGen are employed.A crack propagation criterion based on the sensitivity formulation is developed, allowing the direct calculation of the crack growth length and direction without post-processing. Special attention is paid to the ability of satisfying incompressibility and near-incompressibility conditions.The performance of the XFEM sensitivity analysis is assessed by the Cook's Membrane and Pre-crack Plate benchmark tests where sensitivities of displacements and crack propagation criteria based on potential energy have been analysed with respect to crack length and crack growth parameters. The techniques presented in this paper can be extended to anisotropic materials and non-linear materials exhibiting plasticity and viscoplasticity. Additionally, this formulation constitutes a base for further analysis of crack branching and crack joining problems.