THERMODYNAMIC STABILITY OF EQUILIBRIUM IN PLASTICITY

Thermodynamic stability of equilibrium in solids with intrinsic dissipation of plastic type is investigated. Rate-dependent plastic behaviour and its rate-independent limit are described with the help of internal variables of averaging type. A general condition sufficient for the stability of equilibrium in the sense of Lyapunov is formulated for a continuous plastic body interacting with a reversible work source and a heat reservoir. The relation to the classical Gibbs condition is discussed. As an application, the second-order stability condition in time-independent plasticity is derived in various forms, depending on the class of disturbances under consideration.