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An RVE-based multiscale modeling method for constitutive relations

A multiscale method to define: viscosity and friction coefficients

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Abstract

This article reports an efficient method to characterize constitutive responses based on multiscale modeling for fluid flow in heterogeneous media based on the concept of representative volume element (RVE). Between different scales, it is considered as the basic principles for down-scaling information the conservation of velocity and of the strain rate tensor. Within this context, we formulate (i) the problem to be solved at the micro-scale, (ii) the up-scaling procedure which involves homogenization rules, and (iii) the generalized principle of multiscale virtual power. The complete theory for constitutive modeling is revisited and shown that when employing multiscale analysis among the suitable variational arguments we are able to obtain, in a straightforward manner, new constitutive behavior between kinematic motions and actions. Some examples of application of fluid flow in heterogeneous media with obstacles are presented to show the consequences of the proposed approach.

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Notes

  1. Without loss of generality these volumetric forces are the Lagrange multipliers.

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Acknowledgements

The authors would like to thank the resources provided by the Brazilians research councils FAPEMIG and CAPES.

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Authors and Affiliations

  1. Computational Modeling Graduate Program, Federal University of Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil

    Andrés R. Valdez, Bernardo M. Rocha & Iury Igreja

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  1. Andrés R. Valdez
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  2. Bernardo M. Rocha
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  3. Iury Igreja
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Correspondence to Andrés R. Valdez.

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Valdez, A.R., Rocha, B.M. & Igreja, I. An RVE-based multiscale modeling method for constitutive relations. Rheol Acta 56, 461–476 (2017). https://doi.org/10.1007/s00397-017-1006-3

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  • DOI: https://doi.org/10.1007/s00397-017-1006-3

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