On consequences of the principle of stationary action for dissipative bodies

Abstract

The aim of this note is to show possible consequences of the principle of stationary action formulated for dissipative bodies. The material structure with internal state variables is considered for those bodies. The appropriate action functional is proposed for a typical dissipative body. Possible variations of fields of dependent state variables are introduced together with a non-commutative rule between operations of taking variations of the field and their partial time derivatives. Assuming vanishing of the first variation of the functional, the balance of linear momentum in differential form is received together with evolution equations for internal state variables and stress boundary condition.