On the sensitivity of the rate of global energy dissipation due to configurational changes

The thermodynamic framework for combined configurational and deformational changes was recently discussed by [Runesson, K., Larsson, F., Steinmann, P., 2009. On energetic changes due to configurational motion of standard continua. Int. J. Solids Struct, 46, 1464–1475.]. One key ingredient in this setting is the (fixed) absolute configuration, relative to which both physical and virtual (variational) changes of the material and spatial configurations can be described. In the present paper we consider dissipative material response and emphasize the fact that it is possible to identify explicit energetic changes due to configurational changes for “frozen” spatial configuration (a classical view) and the configuration-induced material dissipation. The classical assumption (previously adopted in the literature) is to ignore this dissipation, i.e. the internal variables are considered as fixed fields in the material configuration. In this paper, however, we define configurational forces by considering the total variation of the total dissipation with respect to configurational changes. The key task is then to compute the sensitivity of the internal variable rates to such configurational changes, which results in a global tangent problem based on the balance equations (momentum and energy) for a given body. In this paper we restrict to quasistatic loading under isothermal conditions and for elastic-plastic response, and we apply the modeling to the case of a moving interface of dissimilar materials.