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Title: An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory

In this paper, a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–Eulerian (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.
Authors:
 [1] ;  [2]
  1. Pennsylvania State Univ., University Park, PA (United States). Center for Neural Engineering
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Simulation Group
Publication Date:
Report Number(s):
SAND2017-4971J
Journal ID: ISSN 0045-7825; 653205
Grant/Contract Number:
AC04-94AL85000; CMMI-1537008
Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 323; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; finite element method; theory of mixtures; poroelasticity; ALE formulation
OSTI Identifier:
1429778

Costanzo, Francesco, and Miller, Scott T. An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory. United States: N. p., Web. doi:10.1016/j.cma.2017.05.006.
Costanzo, Francesco, & Miller, Scott T. An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory. United States. doi:10.1016/j.cma.2017.05.006.
Costanzo, Francesco, and Miller, Scott T. 2017. "An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory". United States. doi:10.1016/j.cma.2017.05.006. https://www.osti.gov/servlets/purl/1429778.
@article{osti_1429778,
title = {An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory},
author = {Costanzo, Francesco and Miller, Scott T.},
abstractNote = {In this paper, a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–Eulerian (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.},
doi = {10.1016/j.cma.2017.05.006},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = 323,
place = {United States},
year = {2017},
month = {5}
}