Abstract
The complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells are discussed in more detail. They are formulated from restrictions imposed by the resultant 2D entropy imbalance according to Coleman–Noll procedure extended by a set of 2D constitutive equations based on heuristic assumptions.
Highlights
Different approaches to description of thermodiffusion phenomena in 3D bodies were proposed in the literature, see the historic review by [38]
One has to base the continuum shell thermodiffusion model on 3D nonlinear continuum thermodynamics supplemented by appropriate general relations accounting for influence of diffusing species
Our 2D model is fully nonlinear, the 3D-to-2D reduction procedure is based on throughthe-thickness integration of 3D basic balance laws and entropy imbalance of continuum thermodiffusion, and 2D laws are given in the Lagrangian description
Summary
Different approaches to description of thermodiffusion phenomena in 3D bodies were proposed in the literature, see the historic review by [38]. Most theories of diffusion in 3D bodies are based on the random walk theory and laws of statistical physics They are used to model and analyse many processes in modern micro- and nanotechnology leading to development of such devices as computer chips, accumulator batteries, solid-state lasers, elements of mobile phones and so on. We are interested in developing the alternative nonlinear phenomenologic continuum model of thermodiffusion as applied to thin-walled solid shell structures. One has to base the continuum shell thermodiffusion model on 3D nonlinear continuum thermodynamics supplemented by appropriate general relations accounting for influence of diffusing species. Our 2D model is fully nonlinear, the 3D-to-2D reduction procedure is based on throughthe-thickness integration of 3D basic balance laws and entropy imbalance of continuum thermodiffusion, and 2D laws are given in the Lagrangian description. For thermoelastic shells with diffusion, the entropy production reduces to more simple form called the reduced entropy inequality which restricts the possible forms of the 2D heat, species mass and other fluxes
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