Thermodynamics of continua with complex rheology

The present study deals with the thermodynamic approach for modelling of the elastic-creep-plastic material behaviour. The proposed theory of finite elastic-creep-plastic deformations is based on the classical formalism of non-equilibrium thermodynamics. Reversible and irreversible components of total deformations are defined by the constitutive differential balance equations following from the multiple subdivision of metric tensor. The least action principle and the formalism of field theory are used for derivation constitutive equation and conservation laws. The energy balance equation is specified for elastic-creep-plastic continuum. The constitutive stress-strain equations are obtained for isothermal isotropic non-linear elastic material. The specific form of elastic strain energy has been specified in terms of invariants of reversible strain tensor. The least action principle is generalized for dissipative behaviour of the materials. The specific features of dissipation function construction for creep and plastic materials are proposed and discussed. The boundary value problem on elastic-creep material is considered in the frameworks of the proposed model. Some results of the numerical simulation under axisymmetric conditions are discussed.