On the theory of viscoelastic mixtures and stability

A theory is developed for binary mixtures of viscoelastic materials. The basic equations of a nonlinear theory of heat conducting viscoelastic mixtures are derived in Lagrangian description. The individual components of the mixture are modeled as Kelvin—Voigt viscoelastic materials. A nonlinear constitutive relation which generalizes Darcy's law is derived. The linearized version of the theory is established. In the present theory the diffusive force depends on relative displacement and relative velocity. Stability results are presented in the context of materials which are non-conductor of heat.