3D robust iterative coupling of Stokes, Darcy and solid mechanics for low permeability media undergoing finite strains

Stokes, Darcy and solid mechanics coupling is a matter of interest in many domains of engineering such as soil mechanics, bio-mechanics, and composites. The aim of this paper is to present a robust iterative method to deal with this coupling for low permeability media within the framework of industr...

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Bibliographic Details
Published in:Finite elements in analysis and design 2015-02, Vol.94, p.1-15
Main Authors: Dereims, A., Drapier, S., Bergheau, J.-M., de Luca, P.
Format: Article
Language:English
Subjects:
Composites
Computational fluid dynamics
Fluid flow
Fluid–solid interaction
Formulations
Iterative coupling
Joining
Manufactured Exact Solution Method
Mathematical analysis
P1+/P1
Permeability
Solid mechanics
Stokes law (fluid mechanics)
Stokes–Darcy coupled problem
Three dimensional
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Summary:Stokes, Darcy and solid mechanics coupling is a matter of interest in many domains of engineering such as soil mechanics, bio-mechanics, and composites. The aim of this paper is to present a robust iterative method to deal with this coupling for low permeability media within the framework of industrial simulation, and especially for composite manufacturing processes. Stokes and Darcy problems are solved using a mixed velocity–pressure finite element using a mini-element formulation, and coupled together by the so-called Beavers–Joseph–Saffman conditions through their interface. This fluid formulation is then coupled to a non-linear solid mechanics formulation in finite deformations using Terzaghi׳s law at the pore level, and an explicit dependence of permeability with respect to porosity that is exactly computed from the solid mechanics kinematics. Then, those formulations are validated with test-cases and by the Method of the Manufactured Exact Solution (MMES) (Knupp and Salari, 2003[1]). Finally, a 3D curved transient example of application is presented. •Robust method to couple iteratively Stokes, Darcy and solid mechanics.•Application to industrial composite manufacturing (finite deformations, thin pure fluid layer, low permeability down to 10−15m2 and complex shapes).•Solution for key issues for Stokes Darcy coupling with low permeability (mass conservation).•Iterative fluid/solid coupling method based on Terzaghi principle and explicit permeability computation through solid mechanics volume changes.
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2014.09.003