Abstract
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.
Highlights
This paper presents an iterative method to strongly couple Stokes and Darcy flows, in low permeability media, with finite strain solid mechanics in order to deal with fluid seepage into and out from low permeability media undergoing finite strains
The proper implementation of the coupling algorithm was verified with the method of the manufactured exact solutions (MMESs) [1]
Concerning forthcoming developments, a full experimental validation is currently conducted with industrial partners in the frame of a FP7 funded project and a transient formulation is studied for the simulation of three-dimensional dynamic consolidation of the porous medium
Summary
This paper presents an iterative method to strongly couple Stokes and Darcy flows, in low permeability media, with finite strain solid mechanics in order to deal with fluid seepage into and out from low permeability media undergoing finite strains. It is applied here to complex manufacturing processes for composites in an industrial framework It represents an improved extension of the work presented by Celle in [2,3] to 3D and complex shapes with low permeability down to 10 À 15 m2, opening the possibility to deal with industrial cases. In this approach two main problems have to be tackled, first the coupling between Stokes (pure fluid) and Darcy (flow through low permeability porous medium) flows and second, the fluid/structure interaction. Special attention will be paid, in this paper, to validate the numerical development in this framework
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