On thermomechanical solids with boundary structures

This paper, in line with the previous works (Javili and Steinmann, 2009 and Javili and Steinmann, 2010), is concerned with the thermomechanically consistent theory and formulation 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 the material behavior, the common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. In this approach the boundary is equipped with its own thermodynamic life, i.e. we assume separate boundary energy, entropy and the like. Afterwards, the derivations of generalized balance equations, including boundary potentials, completely based on a tensorial representation is carried out. The formulation is exemplified for the example of thermohyperelasticity.