Keywords: porous medium, flow, large deformation, Biot model, Coulomb friction, nonsmooth equation.

In this paper we consider the flow of a large-deforming porous medium saturated by fluid; such a model is now being developed for its application in simulating the oil expression from plant seeds [1]. The expression is based on the friction-driven flow of the oil-containing squashed seeds with gradually increasing deformation caused by the conical shape of the channel. Such a process is realised in a rotating bladed conical shaft of the screw-press machine where the friction between the perforated stator part and the rotating medium is the propelling force.

In our model the material is represented by the fluid-saturated medium and the flow-convected configuration is used to describe the deformation. The computing algorithm is based on the linearization associated with one time step analysis for a given reference state of the material. The reference finite element mesh (RFEM) representing the flow problem configuration is fixed to the rotating channels (rotor configuration). After each time step the computed state is used to update the temporal material configuration, which is then projected to the rotor configuration, so that the next time step is initiated with the same RFEM as before, but carrying a new reference state.

We discuss several topics related to the mechanical and numerical aspects of the problem. The subproblem equations involve the material skeleton displacement increments and the fluid pore pressure as the primary variables; presence of the friction conditions makes even the subproblem nonlinear (variational inclusions) [2], attaining the form of a nonsmooth equation. Nevertheless their correct treatment is crucial for the physical relevance of the model. An implementation using our in-house developed finite element method code SfePy [3] is discussed. Numerical illustrations of the computer simulation are given and some numerical aspects are reported.

1

E. Rohan, R. Cimrman, J. Ocenášek, "On modeling process of expression of the fluid saturated medium in screw compression machine", In Proceedings of Engineering Mechanics 2009, Svratka (CD-ROM), 2009.

2

J. Haslinger, M. Miettinen, P.D. Panagiotopoulos, "Finite element method for hemivariational inequalities: Theory, methods and applications", Series: Nonconvex Optimization and Its Applications, 35, Kluwer Academic Publishers, Springer, 1999.

3

R. Cimrman, et al., "Simple Finite Elements in Python", http://sfepy.kme.zcu.cz, http://sfepy.org, 2010.

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