Dynamic Contact Response of a Thermo-Viscoelastic Rod with Damping Effects

We study a quasistatic contact problem involving a thermo-viscoelastic rod and a rigid obstacle. The material response follows a nonlinear Kelvin-Voigt law with thermal coupling, where the elasticity operator is locally Lipschitz. A generalized damped condition describes the contact interaction. By formulating the problem variationally, we establish existence and uniqueness of the weak solution through nonlinear evolutionary PDE techniques and fixed-point theory. Finally, we detail our numerical approach and demonstrate its performance through several one-dimensional numerical simulations based on the DGM-FEM algorithm.