On the stability of the natural unstressed state op viscoelastic bodies : PMM vol. 39, n 6, 1975, pp. 1110–1117

Within the framework of the Cauchy problem, a class of models of a linearviscoelastic body subjected to the stability principle of the natural unstressed state state of viscoelastic bodies (Principle Y) is isolated in 1], The principle Y is formulated as follows. Let the boundary conditions be such that the appropriate elasticity theory problem has a zero solution. If a viscoelastic body is free of external loads at each instant t > 0, then for every initial state, strain of the body vanishes as t → ∞. The principle Y is called partial if it is satisfied only for some particular class of viscoelasticity problems. Sufficient conditions for compliance with the partial Y principle are obtained in this paper for models of viscoelastic bodies within the framework of the fundamental initial-boundary value problems for finite bodies.