Computational thermomechanics with boundary structures

This contribution is concerned with the numerical implementation of boundary potential energies and the study of their impact on the deformations of thermomechanical solids. 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 (Int J Solids Struct, 47:3245–3253, 2010). Afterwards, derivations of a generalized weak formulation which is employed for the discretization and finite element implementation, including boundary potentials, are carried out completely based on a tensorial representation. Finally, numerical examples are presented to demonstrate the boundary effects due to the proposed thermohyperelastic material model