Local stability of hydrostatic compression states of non-linearly thermo-visco-elastic bodies of differential type

The local Lyapunov stability of a hydrostatically stressed state of an isotropic, homogeneous, non-linearly thermo-visco-elastic body of differential type with complexity n and constant initial temperature is investigated in a dynamical formulation. The connection between the thermal and mechanical fields is taken into account. As a special case a model of an incompressible non-linearly visco-elastic body is investigated. Conditions that ensure the existence and uniqueness of generalized solutions of the linearized equations of motion and heat conduction and their vanishing with time are formulated. The example shows that violation of the conditions obtained can lead to the exponential growth of the solution. © 1992.