nonlinearity, viscoelasticity, pressure, deformation, a variation, heterogeneity, interface.

The formulation and the proof of the mixed variational principle for the threedimensional theory of nonlinear viscous-elasticity, allowing to set independently the presumable fields of pressure and movings is given here. Instant elastic-plastic deformation is considered. the exact expressions for a component of deformation tensor through the movings are used. Procedure of its updating on a case of the kusochno-non-uniform body made of the final number of the parts is resulted. the interface conditions on the contact surfaces are essentially various and consist or in their full coupling, or in intense landing. Modification of the constructed functionals on a case of the elasto-plastic (nonlinear-elastic) deformations is given