We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner principle). A novelty of this work is that we introduce a less restrictive assumption on the stress-assisted diffusion coefficient, requiring an analysis of the perturbed diffusion equation using Banach spaces. The solvability of the continuous and discrete problems is established using a suitable modification of the abstract theory for perturbed saddle-point problems in Banach spaces (which is in itself a new result of independent interest). In addition, we establish optimal a priori error estimates. The method and its analysis are robust with respect to the poromechanical parameters. We also include a number of numerical examples that illustrate the properties of the proposed scheme.
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