High-order FEMs for thermo-hyperelasticity at finite strains

Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a 'monolithic' high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.