Homogenization of a Periodic Elastic Structure Saturated with a Maxwell Fluid

In this paper, we investigate the dynamics of an elastic porous medium saturated with a Maxwell fluid. The Maxwell fluid belongs to the class of viscoelastic fluids whose strain rate tensor is proportional to the sum of the stress tensor and its time derivative. The porous medium is governed by the...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2022, Vol.16 (3), p.572-588
Main Authors: Starovoitov, V. N., Starovoitova, B. N.
Format: Article
Language:English
Subjects:
Homogenization
Mathematical analysis
Mathematics
Mathematics and Statistics
Maxwell fluids
Porous media
Strain rate
Tensors
Viscoelastic fluids
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Summary:In this paper, we investigate the dynamics of an elastic porous medium saturated with a Maxwell fluid. The Maxwell fluid belongs to the class of viscoelastic fluids whose strain rate tensor is proportional to the sum of the stress tensor and its time derivative. The porous medium is governed by the linear elasticity equations. A homogenized model of the structure is derived by employing the two-scale convergence technique. The model describes a new material which possesses two kinds of memory. The first memory is inherited from the Maxwell fluid, and the second one is standard for the homogenization of nonstationary problems.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478922030206