An elastic half space under the action of one-dimensional time-dependent diffusion perturbations

The paper deals with a one-dimensional problem of elastic diffusion for a single-component half space. We use a locally static geometrically linear model of elastic diffusion, which contains mass transfer equations and a coupled system of the motion equations of an elastic body. To build the solution, we apply the integral Fourier and Laplace transforms. The problem of inversion of the Laplace transforms reduces to the inversion of rational functions; the inverse Fourier transform is performed numerically. A fundamental solution to the problem is developed. We consider the case when the diffusion flux at the boundary is constant. The obtained results provide a theoretical framework for the analysis of the stress-strain state in aeronautical and space structures working in the conditions of multifactorial external influences.