A thermodynamically consistent phase-field framework for crack-induced self-heating in linear thermoviscoelastic solids
摘要
Crack formation is often accompanied by a localized temperature rise, which in turn influences deformation and crack evolution. Although this phenomenon has been extensively studied in plastic solids, it remains less understood in thermoviscoelastic materials. This work presents a thermodynamically consistent phase-field framework for modeling crack-induced self-heating in Maxwell-type linear thermoviscoelastic solids. Two phase-field formulations are developed within a unified thermodynamic setting based on the microforce balance principle, while thermodynamic consistency is ensured through an energy dissipation identity derived from energy conservation and the Clausius–Duhem inequality. The formulation couples viscoelastic dissipation, stored viscoelastic energy, fracture surface energy, and thermal energy within a thermodynamically admissible structure. Numerical simulations are performed using an anisotropic adaptive finite element method implemented in FreeFEM. The results indicate that heat generation during crack propagation arises from irreversible viscoelastic dissipation; higher viscosity enhances self-heating and accelerates thermal softening; and self-heating and crack evolution are strongly coupled. The proposed framework provides a physically grounded approach for analyzing thermally induced fracture processes in thermoviscoelastic solids.