A phase field model for thermoelastic fracture in hyperelastic solids under finite deformation

Abstract

This paper develops a phase field model for simulating crack propagation in hyperelastic solids subjected to coupled thermo-mechanical loading under finite deformation. The model integrates the Neo-Hookean constitutive law with a thermodynamically consistent framework that captures key multiphysics couplings: finite thermoelastic deformation, degradation of thermal conductivity with progressive damage, and heat convection across diffusely represented crack surfaces. A robust staggered solution algorithm is employed to solve the coupled system of displacement, temperature, and phase field equations. Numerical simulation of a notched tension specimen demonstrates the model’s capability to predict crack initiation and growth, while revealing the interdependent evolution of mechanical damage and thermal response. Results show that damage-induced thermal conductivity reduction leads to localized thermal gradients and “hot-spot” formation near the crack tip, while crack-surface convection significantly moderates the temperature field within the crack. Parametric studies elucidate the influence of thermal expansion and convection coefficients on the fracture process. This work provides a computational tool for failure analysis and design of rubber-like components in thermal environments.