Numerical modelling of swelling and fracture events in thermoresponsive hydrogels
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We present a comprehensive computational framework for the thermo-chemo-mechanical simulation of thermoresponsive hydrogels, encompassing both swelling and fracture phenomena. An inf-sup stable FE formulation is proposed, approximating the displacement field via quadratic shape functions while employing linear functions for the chemical potential (fluid pressure) and temperature fields. For fracture analysis, the framework is extended to incorporate a phase-field approach for damage evolution, maintaining the same stability characteristics. The formulations are implemented as user-element subroutines (UEL) in Abaqus, denoted as Q2Q1Q1 for swelling analysis and Q2Q1Q1Q1 when incorporating fracture mechanics, where the additional field corresponds to the phase-field damage variable. The proposed methodology addresses both isotropic and transversely isotropic material models within the integrated framework. Initial validation focuses on capturing the upper/lower critical solution temperature behaviors of thermoresponsive hydrogels through several examples of transient diffusion-driven swelling deformation comparing with [1]. Numerical analyses investigate the effect of temperature-dependent swelling ratio on the mechanical behavior of spheres undergoing compression, with accuracy assessed by replicating seminal experiments exploring the influence of crosslinking density on thermally driven swelling of PNIPAAm hydrogels. The fracture analysis capabilities are validated through comparative studies against [2], demonstrating the formulation's capacity to achieve numerical stability while accurately capturing fracture limit states across varying temperature conditions. The methodology is further applied to simulate pre-notched specimens under combined swelling and mechanical loading conditions, providing valuable insights into the coupled thermo-chemo-mechanical responses and fracture behavior of these advanced materials.
