Thermomechanical Behavior of Thermoviscoelastic Solid during Dynamic Crack Propagation

The constitutive relations of the thermoviscoelasticity are rigorously formulated, and the corresponding finite-element equations are derived. Due to the second law of thermodynamics, a nonlinear term, which appears in both the energy equation and the Clausius-Duhem inequality, is incorporated in the finite-element equations. This work is focused on the effect of this dissipative energy term on the stress and temperature field of an isotropic thermoviscoelastic solid during dynamic crack propagation through a finite-element analysis. The numerical solutions clearly demonstrate that the temperature elevates on the cracked surface in the wake of the advancing crack tip. This is the consequence of truthfully incorporating the second law of thermodynamics in the analysis of the dynamic process for materials that possess viscosity. Meanwhile, the effect of different crack propagation speeds on the stress and temperature distributions is also investigated.