  This paper aims first to perform robust continuous analysis of a mixed
nonlinear formulation for stress-assisted diffusion of a solute that interacts
with an elastic material, and second to propose and analyse a virtual element
formulation of the model problem. The two-way coupling mechanisms between the
Herrmann formulation for linear elasticity and the reaction-diffusion equation
(written in mixed form) consist of diffusion-induced active stress and
stress-dependent diffusion. The two sub-problems are analysed using the
extended Babu\v{s}ka--Brezzi--Braess theory for perturbed saddle-point
problems. The well-posedness of the nonlinearly coupled system is established
using a Banach fixed-point strategy under the smallness assumption on data. The
virtual element formulations for the uncoupled sub-problems are proven uniquely
solvable by a fixed-point argument in conjunction with appropriate projection
operators. We derive the a priori error estimates, and test the accuracy and
performance of the proposed method through computational simulations.
