Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions

A variationally consistent model-based computational homogenization approach for transient chemomechanically coupled problems is developed based on the classical assumption of first-order prolongation displacement, chemical potential, and (ion) concentration fields within a representative volume element (RVE). The presence potential as primary global represents mixed formulation, which has definite advantages. Nonstandard diffusion, governed by Cahn–Hilliard type gradient model, considered under restriction miscibility. Weakly periodic boundary conditions pertinent provide general variational setting uniquely solvable RVE-problem(s). These are introduced with novel in order to control stability discretization, thereby circumventing need satisfy LBB-condition: penalty stabilized Lagrange multiplier enforces at cost an additional each weakly field (three current problem). In particular, neat result that Neumann condition obtained when becomes very large. numerical examples, we investigate following characteristics: mesh convergence different approximations, sensitivity choice parameter, influence RVE-size macroscopic response.