Variational method of mechanics of heterogeneous nonlinearly viscoelastic solids

A mixed type variational method, in the geometrically nonlinear formulation, for determination of the stress-strain state of anisotropic nonlinearly viscoelastic bodies was analyzed. A homogeneous material rarely possesses the properties corresponding to the requirements of a particular application. Inhomogeneity can be considered either as an idealized continuous change of the physical and mechanical properties from point to point, or as a step-like change of the properties when crossing the interface. The method is formulated in terms of velocities and is mainly based on the combination of the variational principles with the principles of the theory of partial differential equations and on independent variation of the displacement velocity field and stress fields. The central point of the theory of nonlinear viscoelasticity is the problem of choosing a particular form of functions taken as kernels of integrals in hereditary governing equations.