A finite element framework for continua with boundary energies. Part III: The thermomechanical case

This paper, in line with the previous works (Javili and Steinmann [28,29]), is concerned with the numerical implementation of boundary potential energies and the study of their impact on the deformations of solids. Thereby, the main thrust in this contribution is the extension to thermomechanical effects. Although boundary effects can play a dominant role in material behavior, the common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. In the approach of this contribution the boundary is equipped with its own thermodynamic life, i.e. we assume separate boundary energy, entropy and the like. Furthermore, the generalized local balance laws are given according to Javili and Steinmann [30]. ards, the derivations of a generalized weak formulation, including boundary potentials, completely based on a tensorial representation are carried out which is employed for the discretization and finite element implementation. Eventually, numerical examples are presented to demonstrate the boundary effects due to the proposed thermohyperelastic material model.