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Variationally consi...
Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions
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- Kaessmair, Stefan (author)
- Friedrich-Alexander-Universität Erlangen Nurnberg (FAU)
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- Runesson, Kenneth, 1948 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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- Steinmann, Paul, 1964 (author)
- Friedrich-Alexander-Universität Erlangen Nurnberg (FAU)
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- Janicke, R. (author)
- Technische Universität Braunschweig
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- Larsson, Fredrik, 1975 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2021-08-13
- 2021
- English.
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In: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 122:22, s. 6429-6454
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Abstract
Subject headings
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- 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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Maskinteknik -- Teknisk mekanik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Mechanical Engineering -- Applied Mechanics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- failsafe
- Dirichlet and Neumann RVE-conditions
- variationally consistent
- computational homogenization
- weak periodicity
- chemomechanical coupling
Publication and Content Type
- art (subject category)
- ref (subject category)
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