On the connection of dissipation and deviatoric stress in the continuum theory of defects

In a material space-time manifold an expression for the entropy production is developed. It is based on a Lagrangian formulation for a hyperelastic solid. The material structure and heat transfer are represented by a tetrad field. The derivatives of the Lagrangian with respect to the time-like vector of the tetrad yields entropy density and current. An identity for the divergence of this four-current follows from the invariance of the Lagrangian and yields the entropy production due to heat transfer and defect movement. The latter part only depends on a kind of deviatoric stress if the conservation of mass is considered. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)