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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We study the mechanico-diffusive phenomena of saturation of a sphere for the case of two routes of dopant migration. We establish the basic qualitative and quantitative regularities.The stress-strain state that arises as the result of mass-transfer processes and the redistribution of a dopant determines in many cases the mechanical exploitation properties of structural elements and machine parts [3,7]. Concentrated strains and stresses and changes in them depend essentially on the local structure of the material of the body [6,9,12]. This is particularly connected with the fact that particles of dopant of a single type may exist in physically different states within a small region of the body, and in these states they may differ in their diffusive mobility and coefficients of concentration expansion [1,2,10].Several authors [4,5,11] have proposed physico-mathematical models of the theory of solid matter to describe mechanico-heterodiffusive phenomena in bodies with a complicated internal structure. Heterodiffusion is understood to mean a redistribution of dopant particles of a single type by various routes as they move from one migration route to another. The number of diffusion routes corresponds to the number of different states of particles, and it is taken into account that in these states they cause different strains. On this basis in the present paper we consider mechanico-diffusive phenomena in the saturation of a sphere for the case of two migration routes for the dopant.The original relations. Suppose a certain region of an isotropic body contains, in addition to particles of the basic material, particles of a dopant in two physically different states. In macroscopic description we regard the body as a three-component solid substance. As the basic processes we take deformation, diffusion of the dopant by two routes, and the process of transition from one route of migration to the other. We assume that the mass transfer of the body with the environment occurs under isothermal conditions and that its intensity makes it possible to ignore the effects of adiabatic coupling and dynamic effects in studying nonstationary processes.Ignoring the physical and geometric nonlinearities, we assume that the coefficients (material characteristics) in the equations of state and the kinetic relations of the model are constant. We replace the substantial derivatives with respect to time in the corresponding balance equations by local ones. In the Cauchy relations, which determine the strain tensor in terms of the displacement vector we ignore the nonlinear terms. We also assume that there are no sources of external mass force.Under such assumptions the local thermodynamic state of the body is determined by the coupled parameters: p-lcraf~ -ga~, Pi -Ci, where p is the density, a~ are the components of the Cauchy stress tensor, E~Z are the components of the strain tensor, a,/? = 1, 3; #i = #~-#0 is the chemical potential of the ith component (i = 1,2), computed from the value of the chemical potential #0 of the main compone...