We formulate the basic relations of a mathematical model of mechanics of elastic deformable systems that describes the formation of a near-surface inhomogeneity caused by both the process of local mass displacement and dissipative processes. On this basis, we solve the problem of the stationary stressstrain state of an infinite hollow cylinder. It is shown that the near-surface inhomogeneity of the distribution of stresses and chemical potential is characterized by two parameters. One of them is related to the local mass displacement, and the other is a consequence of dissipative processes in the body.

In the context of the continuous-thermodynamic approach we generalize the Gibbs equation and obtain the initial relations of local-gradient mechanicothermodiffusion.We state the relation between the thermodynamic flows and forces in the form of functionals. We find influence functions that cause expansion of the phase space that determines the thermodynamic potentials by the gradients of the intensive parameters of the equilibrium state of the system. It is shown that such influence functions are connected with the undamped memory of the body of the action at the initial time.Contemporary theoretical models of solid-state mechanics describe, along with the strain, processes of spatial redistribution of heat and mass, and take account on the macroscopic level of the actual microscopic structure of actual solid bodies. The initial relations of such models are usually obtained applying the methods of thermodynamics of nonequilibrium processes. In these processes local thermodynamic equilibrium and the homogeneity of an infinitesimal piece of a region of space are tacitly assumed. If essentially inhomogeneous (gradient) systems, bodies with a microstructure, or solid solutions with local changes of state are being considered, this hypothesis is generalized by including among the independent parameters that give the thermodynamic state of a small region of the body a number of new macroscopic variables connected with the intensity of nonequilibrium processes.The thermodynamic foundations and methods of construction of specific models of solid-state mechanics in which physical processes of diffusion type in deformable solid solutions are taken into account were laid in the work of the school of Ya. S. Pidstryhach [24-26, 28, 29] and developed for electrically conducting systems in [5] and, taking account of the possible change of state of particles of the admixture, in [2,6]. The problems of the continuous description of one-component and binary thermoelastic systems taking account of effects of elastic and polarization type are considered in [1,3,4,10].At the same time, it is known that rheological relations can also be used to describe the mechanothermodiffusion processes in such bodies, which in integral form take account of interactions that are nonlocal with respect to time (memory effects [13, 15-17, 23, 33]). Hence the question of joint analysis of these approaches and the possibility of combining them becomes interesting.We shall consider a solid deformable multicomponent nonferromagnetic electrically conducting body embedded in a three-dimensional affine space (a region V bounded by a surface ~V). The body is subject to conditions of force action and heat and mass exchange with the surrounding medium. We note that, along with strain, processes involving transport of charge, mass and energy occur in the body, as well as processes that are characteristic for phase changes or chemical reactions. In the macroscopic description we assign to each component of the body a separate continuum and to the body as a whole...

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