scholarly journals A finite element formulation for modeling dynamic wetting on flexible substrates and in deformable porous media.

2004 ◽  
Author(s):  
Peter Randall Schunk ◽  
Richard A. Cairncross ◽  
S. Madasu
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Flexible Substrates ◽  
Dynamic Wetting ◽  
Deformable Porous Media

scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

scholarly journals Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Deformation ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Element Formulation ◽  
Momentum Exchange ◽  
Deformable Porous Media ◽  
Chemical Effects ◽  
Highly Nonlinear

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

A mixed least‐squares finite element formulation within the framework of the theory of porous media

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Alexander Schwarz ◽  
Solveigh Averweg ◽  
Joachim Bluhm ◽  
Jörg Schröder
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Least Squares ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Theory Of Porous Media
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