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

Käßmair S, Runesson K, Steinmann P, Jänicke R, Larsson F (2021)


Publication Type: Journal article

Publication year: 2021

Journal

DOI: 10.1002/nme.6798

Abstract

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

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APA:

Käßmair, S., Runesson, K., Steinmann, P., Jänicke, R., & Larsson, F. (2021). Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions. International Journal for Numerical Methods in Engineering. https://dx.doi.org/10.1002/nme.6798

MLA:

Käßmair, Stefan, et al. "Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions." International Journal for Numerical Methods in Engineering (2021).

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