On the Role of the Unloaded Configuration in Diffusion-Elasticity Problems

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Abstract Accumulation of impurities in material affects the stress-strain state of the host medium. The modeling of coupled mass transfer and deformation processes is typically performed under the assumption of small relative changes in the concentration of the diffusing species and in the deformation of the matrix. In this approach, the concentration and the small deformation tensor are considered as independent quantities, implying a direct influence of concentration on the stress field. Such models demonstrate good agreement with experimental data when the change in diffusant concentration only weakly affects the material behavior. However, they can be inadequate from a physical standpoint in the general case. The work proposes a more general approach, according to which changes in concentration within the material’s elementary fragments first alter their unloaded configuration, and the change in this unloaded configuration, in turn, leads to the development of stresses in the solid. The unloaded configuration is understood as the one that the fragment would assume in the absence of constraints from the surrounding medium. Numerical modeling has been performed based on this approach, and a comparison between the classical and the proposed methods has been made using an initial-boundary value problem for a long cylinder with a free surface. The ranges of parameters of the medium for which the models are equivalent, as well as those where significant discrepancies occur, have been identified. It is shown that the proposed approach can be applied to describe the behavior of a wide class of materials, including geometrically nonlinear ones.

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