Stability of chemical reaction fronts in solids: Analytical and numerical approaches

Localized chemical reactions in deformable solids are considered. A chemical transformation is accompanied by the transformation strain and emerging mechanical stresses, which affect the kinetics of the chemical reaction front to the reaction arrest. A chemo-mechanical coupling via the chemical affinity tensor is used, in which the stresses affect the reaction rate. The emphasis is made on the stability of the propagating reaction front in the vicinity of the blocked state. There are two major novel contributions. First, it is shown that for a planar reaction front, the diffusion of the gaseous-type reactant does not influence the stability of the reaction front – the stability is governed only by the mechanical properties of solid reactants and stresses induced by the transformation strain and the external loading, which corresponds to the mathematically analogous phase transition problem. Second, the comparison of two computational approaches to model the reaction front propagation is performed – the standard finite-element method with a remeshing technique to resolve the moving interface is compared to the cut-finite-element-based approach, which allows the interface to cut through the elements and to move independently of the finite-element mesh. For stability problems considered in the present paper, the previously-developed implementation of the cut-element approach has been extended with the additional post-processing procedure that obtains more accurate stresses and strains, relying on the fact that the structured grid is used in the implementation. The approaches are compared using a range of chemo-mechanical problems with stable and unstable reaction fronts.