Archive of Applied Mechanics

, Volume 88, Issue 1–2, pp 271–286 | Cite as

Computational first-order homogenization in chemo-mechanics



In the present contribution, we consider species diffusion coupled to finite deformations in strongly heterogeneous microstructures. A semi-dual energy formulation parameterized in terms of the chemical potential is obtained by Legendre transformation of the free energy. Doing so avoids the presence of higher gradients of the deformation field. The constitutive response at the macroscopic level is obtained using variationally consistent homogenization (Larson et al. in Int J Numer Method Eng 81(13):1659–1686, 2010. doi: 10.1002/nme.2747). This approach allows to treat transient microscale problems on a representative volume element which has a finite size, i.e., the scales are not clearly separated. Full details of the implementation are provided. A series of numerical examples compares the homogenization results to single-scale formulations which fully resolve all microstructural features.


First-order homogenization Coupled problem Transient microscale 



The authors gratefully acknowledge the support by the German Research Foundation (DFG) under Grant STE 544/48.


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Chair of Applied MechanicsFriedrich–Alexander Universität Erlangen–NürnbergErlangenGermany

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