An inf-sup stable phase-field formulation for fracture of thermo-responsive hydrogels: Isotropic and transversely isotropic material models

Abstract

This investigation presents a comprehensive phase-field formulation for fracture analysis of thermo-responsive hydrogels, encompassing both isotropic and transversely isotropic material models within an integrated thermo- chemo-mechanical framework. The proposed numerical approach addresses computational challenges through a mixed variational formulation that ensures inf-sup stability while maintaining robust fracture simulation capabilities. The finite element implementation employs quadratic interpolation functions for the displacement field and linear shape functions for the chemical potential (fluid pressure), temperature, and fracture fields. This formulation is implemented as a user-element subroutine UEL in ABAQUS, utilizing a Q2Q1Q1Q1 finite element formulation. The validation strategy comprises two key investigations. First, a comparative analysis against the foundational work of Böger et al. (2017), pinpoints the capacity of the current formulation to achieve numerical stability while accurately capturing fracture limit states across varying temperature conditions. Second, the methodology is applied to simulate complex material behavior through the analysis of pre-notched specimens under combined swelling and mechanical loading conditions. This thorough assessment provides valuable insights into the coupled chemical and mechanical responses of thermo-responsive hydrogels, demonstrating the ability of the proposed formulation in simulating these advanced materials.