A two-scale framework for coupled mechanics-diffusion-reaction processes

There is a wide range of industrially-relevant problems where mechanical stresses directly affect kinetics of chemical reactions. For example, this includes formation of oxide layers on parts of micro-electro-mechanical systems (MEMS) and lithiation of Si in Li-ion batteries. Detailed understanding of these processes requires thermodynamically-consistent theories describing the coupled thermo-chemo-mechanical behaviour of those systems. Furthermore, as the majority of materials used in those systems have complex microstructures, multiscale modelling techniques are required for efficient simulation of their behaviour. Hence, the purpose of the present paper is two-fold: (1) to derive a thermodynamically-consistent thermo-chemo-mechanical theory; and (2) to propose a two-scale modelling approach based on the concept of computational homogenisation for the considered theory. The theory and the two-scale computational approach are implemented and tested using a number of computational examples, including the case of the reaction locking due to mechanical stresses.