A poroplastic model of structural reorganisation in porous media of biomechanical interest. (English) Zbl 1348.74097

Grillo, Alfio; Prohl, Raphael; Wittum, Gabriel

Contin. Mech. Thermodyn. 28, No. 1-2, 579-601 (2016); erratum ibid. 28, No. 3, 919-920 (2016).

Summary: We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of “plastic” distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

MSC:

74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74L15	Biomechanical solid mechanics
76S05	Flows in porous media; filtration; seepage
92C10	Biomechanics

Keywords:

mixture theories; porous media; poroplasticity; remodelling; soft tissues

Software:

UG4; pcl; libDiscretization; libAlgebra; libGrid

References:

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