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

Costanzo, Francesco; Miller, Scott T.

doi:10.1016/j.cma.2017.05.006

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

Journal Article · Mon May 22 00:00:00 EDT 2017 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2017.05.006· OSTI ID:1429778

Costanzo, Francesco ^[1]; Miller, Scott T. ^[2]

Pennsylvania State Univ., University Park, PA (United States). Center for Neural Engineering
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Simulation Group

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: AC04-94AL85000; CMMI-1537008

OSTI ID:: 1429778

Alternate ID(s):: OSTI ID: 1550052

Report Number(s):: SAND2017-4971J; 653205

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 323; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

References (33)

A Paravascular Pathway Facilitates CSF Flow Through the Brain Parenchyma and the Clearance of Interstitial Solutes, Including Amyloid Iliff, J. J.; Wang, M.; Liao, Y. Science Translational Medicine, Vol. 4, Issue 147 https://doi.org/10.1126/scitranslmed.3003748	journal	August 2012
Brain-wide pathway for waste clearance captured by contrast-enhanced MRI Iliff, Jeffrey J.; Lee, Hedok; Yu, Mei Journal of Clinical Investigation, Vol. 123, Issue 3 https://doi.org/10.1172/JCI67677	journal	February 2013
Cerebral Arterial Pulsation Drives Paravascular CSF-Interstitial Fluid Exchange in the Murine Brain Iliff, J. J.; Wang, M.; Zeppenfeld, D. M. Journal of Neuroscience, Vol. 33, Issue 46 https://doi.org/10.1523/JNEUROSCI.1592-13.2013	journal	November 2013
Is There a Cerebral Lymphatic System? Iliff, Jeffrey J.; Nedergaard, Maiken Stroke, Vol. 44, Issue 6_suppl_1 https://doi.org/10.1161/STROKEAHA.112.678698	journal	June 2013
Diffusion properties of the brain in health and disease Syková, Eva Neurochemistry International, Vol. 45, Issue 4 https://doi.org/10.1016/j.neuint.2003.11.009	journal	September 2004
Diffusion in Brain Extracellular Space Syková, Eva; Nicholson, Charles Physiological Reviews, Vol. 88, Issue 4 https://doi.org/10.1152/physrev.00027.2007	journal	October 2008
The diffusion parameters of the extracellular space are altered in focal cortical dysplasias Vargova, L.; Homola, A.; Cicanic, M. Neuroscience Letters, Vol. 499, Issue 1 https://doi.org/10.1016/j.neulet.2011.05.023	journal	July 2011
A Novel Three-Phase Model of Brain Tissue Microstructure Gevertz, Jana L.; Torquato, Salvatore PLoS Computational Biology, Vol. 4, Issue 8 https://doi.org/10.1371/journal.pcbi.1000152	journal	August 2008
Nanomaterials design and tests for neural tissue engineering Saracino, Gloria A. A.; Cigognini, Daniela; Silva, Diego Chem. Soc. Rev., Vol. 42, Issue 1 https://doi.org/10.1039/C2CS35065C	journal	January 2013
Development of biodegradable crosslinked urethane-doped polyester elastomers Dey, Jagannath; Xu, Hao; Shen, Jinhui Biomaterials, Vol. 29, Issue 35 https://doi.org/10.1016/j.biomaterials.2008.08.020	journal	December 2008
Crosslinked urethane doped polyester biphasic scaffolds: Potential for in vivo vascular tissue engineering Dey, Jagannath; Xu, Hao; Nguyen, Kytai Truong Journal of Biomedical Materials Research Part A, Vol. 95A, Issue 2 https://doi.org/10.1002/jbm.a.32846	journal	July 2010
Active Dilation of Penetrating Arterioles Restores Red Blood Cell Flux to Penumbral Neocortex after Focal Stroke Shih, Andy Y.; Friedman, Beth; Drew, Patrick K. Journal of Cerebral Blood Flow & Metabolism, Vol. 29, Issue 4 https://doi.org/10.1038/jcbfm.2008.166	journal	January 2009
A Polished and Reinforced Thinned-skull Window for Long-term Imaging of the Mouse Brain Shih, Andy Y.; Mateo, Celine; Drew, Patrick J. Journal of Visualized Experiments, Issue 61 https://doi.org/10.3791/3742	journal	January 2012
Two-Photon Microscopy as a Tool to Study Blood Flow and Neurovascular Coupling in the Rodent Brain Shih, Andy Y.; Driscoll, Jonathan D.; Drew, Patrick J. Journal of Cerebral Blood Flow & Metabolism, Vol. 32, Issue 7 https://doi.org/10.1038/jcbfm.2011.196	journal	February 2012
Incompressible porous media models by use of the theory of mixtures Bowen, Ray M. International Journal of Engineering Science, Vol. 18, Issue 9 https://doi.org/10.1016/0020-7225(80)90114-7	journal	January 1980
Compressible porous media models by use of the theory of mixtures Bowen, Ray M. International Journal of Engineering Science, Vol. 20, Issue 6 https://doi.org/10.1016/0020-7225(82)90082-9	journal	January 1982
A systematic approximation for the equations governing convection–diffusion in a porous medium Rajagopal, K. R.; Saccomandi, G.; Vergori, L. Nonlinear Analysis: Real World Applications, Vol. 11, Issue 4 https://doi.org/10.1016/j.nonrwa.2009.07.010	journal	August 2010
Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions Armero, F. Computer Methods in Applied Mechanics and Engineering, Vol. 171, Issue 3-4 https://doi.org/10.1016/S0045-7825(98)00211-4	journal	April 1999
A stabilized mixed finite element method for Darcy flow Masud, Arif; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 39-40 https://doi.org/10.1016/S0045-7825(02)00371-7	journal	August 2002
A stabilized mixed finite element method for Darcy–Stokes flow Masud, Arif International Journal for Numerical Methods in Fluids, Vol. 54, Issue 6-8 https://doi.org/10.1002/fld.1508	journal	January 2007
An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions Donea, J.; Giuliani, S.; Halleux, J. P. Computer Methods in Applied Mechanics and Engineering, Vol. 33, Issue 1-3 https://doi.org/10.1016/0045-7825(82)90128-1	journal	September 1982
Lagrangian-Eulerian finite element formulation for incompressible viscous flows Hughes, Thomas J. R.; Liu, Wing Kam; Zimmermann, Thomas K. Computer Methods in Applied Mechanics and Engineering, Vol. 29, Issue 3 https://doi.org/10.1016/0045-7825(81)90049-9	journal	December 1981
Representation of Moving Wavefronts of Whisker Deflection in Rat Somatosensory Cortex Drew, Patrick J.; Feldman, Daniel E. Journal of Neurophysiology, Vol. 98, Issue 3 https://doi.org/10.1152/jn.00056.2007	journal	September 2007
Chronic optical access through a polished and reinforced thinned skull Drew, Patrick J.; Shih, Andy Y.; Driscoll, Jonathan D. Nature Methods, Vol. 7, Issue 12 https://doi.org/10.1038/nmeth.1530	journal	October 2010
Boundary conditions at fluid-permeable interfaces in porous media: A variational approach dell’Isola, F.; Madeo, A.; Seppecher, P. International Journal of Solids and Structures, Vol. 46, Issue 17 https://doi.org/10.1016/j.ijsolstr.2009.04.008	journal	August 2009
Variational implementation of immersed finite element methods Heltai, Luca; Costanzo, Francesco Computer Methods in Applied Mechanics and Engineering, Vol. 229-232 https://doi.org/10.1016/j.cma.2012.04.001	journal	July 2012
Finite Element Multigrid Methods Brenner, Susanne C.; Scott, L. Ridgway The Mathematical Theory of Finite Element Methods https://doi.org/10.1007/978-1-4757-3658-8_7	book	January 2002
Variational Formulations and Finite Element Methods Brezzi, Franco; Fortin, Michel Springer Series in Computational Mathematics https://doi.org/10.1007/978-1-4612-3172-1_1	book	January 1991
Stabilized finite element method for incompressible flows with high Reynolds number Hachem, E.; Rivaux, B.; Kloczko, T. Journal of Computational Physics, Vol. 229, Issue 23 https://doi.org/10.1016/j.jcp.2010.07.030	journal	November 2010
Code Verification by the Method of Manufactured Solutions Salari, Kambiz; Knupp, Patrick https://doi.org/10.2172/759450	report	June 2000
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089020	journal	September 2005
On Large-Scale Diagonalization Techniques for the Anderson Model of Localization Schenk, Olaf; Bollhöfer, Matthias; Römer, Rudolf A. SIAM Review, Vol. 50, Issue 1 https://doi.org/10.1137/070707002	journal	January 2008
Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization Schenk, Olaf; Wächter, Andreas; Hagemann, Michael Computational Optimization and Applications, Vol. 36, Issue 2-3 https://doi.org/10.1007/s10589-006-9003-y	journal	February 2007

Cited By (3)

Functional hyperemia drives fluid exchange in the paravascular space Kedarasetti, Ravi Teja; Turner, Kevin L.; Echagarruga, Christina https://doi.org/10.1101/838813	posted_content	November 2019
Functional hyperemia drives fluid exchange in the paravascular space Kedarasetti, Ravi; Turner, Kevin L.; Echagarruga, Christina https://doi.org/10.21203/rs.3.rs-22610/v1	preprint	August 2020
Functional hyperemia drives fluid exchange in the paravascular space Kedarasetti, Ravi; Turner, Kevin L.; Echagarruga, Christina https://doi.org/10.21203/rs.3.rs-22610/v3	preprint	August 2020

Similar Records

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: General theory and application to fluid interfaces

Journal Article · Mon Jan 13 00:00:00 EST 2020 · Journal of Computational Physics · OSTI ID:1429778

Sahu, Amaresh; Omar, Yannick A. D.; Sauer, Roger A.; +1 more

An arbitrary lagrangian-eulerian finite element approach to non-steady state fluid flows. Application to mould filling

Conference · Sun Dec 31 00:00:00 EST 1995 · OSTI ID:1429778

Gaston, L; Glut, B; Bellet, M; +1 more

Multi-dimensional arbitrary Lagrangian-Eulerian method for dynamic fluid-structure interaction

Conference · Fri Jan 01 00:00:00 EST 1982 · Am. Soc. Mech. Eng., Pressure Vessels Piping Div., (Tech. Rep.) PVP; (United States) · OSTI ID:1429778

Wang, C Y; Zeuch, W R

Related Subjects

97 MATHEMATICS AND COMPUTING
finite element method
theory of mixtures
poroelasticity
ALE formulation

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

Citation Formats

References (33)

Cited By (3)

Similar Records

Related Subjects