Computational homogenization of transient chemo-mechanical processes based on a variational minimization principle
Open Access
- 25 July 2020
- journal article
- research article
- Published by Springer Science and Business Media LLC in Advanced Modeling and Simulation in Engineering Sciences
- Vol. 7 (1), 1-26
- https://doi.org/10.1186/s40323-020-00161-6
Abstract
We present a variational framework for the computational homogenization of chemo-mechanical processes of soft porous materials. The multiscale variational framework is based on a minimization principle with deformation map and solvent flux acting as independent variables. At the microscopic scale we assume the existence of periodic representative volume elements (RVEs) that are linked to the macroscopic scale via first-order scale transition. In this context, the macroscopic problem is considered to be homogeneous in nature and is thus solved at a single macroscopic material point. The microscopic problem is however assumed to be heterogeneous in nature and thus calls for spatial discretization of the underlying RVE. Here, we employ Raviart–Thomas finite elements and thus arrive at a conforming finite-element formulation of the problem. We present a sequence of numerical examples to demonstrate the capabilities of the multiscale formulation and to discuss a number of fundamental effects.Keywords
Funding Information
- Deutsche Forschungsgemeinschaft (327154368)
- Deutsche Forschungsgemeinschaft (390740016)
This publication has 38 references indexed in Scilit:
- Transient computational homogenization for heterogeneous materials under dynamic excitationJournal of the Mechanics and Physics of Solids, 2013
- Homogenization in finite thermoelasticityJournal of the Mechanics and Physics of Solids, 2011
- A modified least‐squares mixed finite element with improved momentum balanceInternational Journal for Numerical Methods in Engineering, 2009
- Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structuresJournal of the Mechanics and Physics of Solids, 2008
- Computational homogenization for heat conduction in heterogeneous solidsInternational Journal for Numerical Methods in Engineering, 2007
- On the effects of microstress on macroscopic diffusion processesActa Mechanica, 1999
- Primal hybrid finite element methods for 2nd order elliptic equationsMathematics of Computation, 1977
- Molecular volumes and the Stokes-Einstein equationJournal of Chemical Education, 1970
- A variational approach to the theory of the elastic behaviour of multiphase materialsJournal of the Mechanics and Physics of Solids, 1963
- The Elastic Behaviour of a Crystalline AggregateProceedings of the Physical Society. Section A, 1952