Large strain analysis of soft biological membranes

Formulation and finite element analysis

verfasst von: Gerhard A. Holzapfel, Robert Eberlein, Peter Wriggers, Hans W. Weizsäcker
Abstract: This paper presents a general formulation of thin incompressible membranes and investigates the behavior of soft biotissues using the finite element method. In particular the underlying hyperelastic model is chosen to examine the highly non-linear constitutive relation of blood vessels which are considered to be perfectly elastic, homogeneous and (nearly) incompressible. First, the stress-deformation relation and the elastic tangent moduli are derived in a very general material setting which is subsequently specified for blood vessels in terms of Green-Lagrangian strains. Based on the principle of virtual work the finite element equations are provided and briefly discussed. Consistent linearization of the weak form of equilibrium and the external pressure term ensures a quadratic convergence rate of the iterative solution procedure. On the computational side of this work an effort was undertaken to show a novel approach on the investigation of soft tissue biomechanics. Representative numerical analyses of problems in vascular mechanics are discussed that show isochoric finite deformations (large rotations and large strains). In particular, a numerical simulation of the interaction between an inflated balloon catheter and a plaque deposit on the wall of a blood vessel is presented.
Externe Organisation(en): Stanford University
Technische Universität Graz
Technische Universität Darmstadt
Universität Graz
Typ: Artikel
Journal: Computer Methods in Applied Mechanics and Engineering
Band: 132
Seiten: 45-61
Anzahl der Seiten: 17
ISSN: 0045-7825
Publikationsdatum: 15.05.1996
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik
Elektronische Version(en): https://doi.org/10.1016/0045-7825(96)00999-1 (Zugang: Unbekannt)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{52f2dc01e12f486e934d8e2a9c1da95e,
title = "Large strain analysis of soft biological membranes: Formulation and finite element analysis",
abstract = "This paper presents a general formulation of thin incompressible membranes and investigates the behavior of soft biotissues using the finite element method. In particular the underlying hyperelastic model is chosen to examine the highly non-linear constitutive relation of blood vessels which are considered to be perfectly elastic, homogeneous and (nearly) incompressible. First, the stress-deformation relation and the elastic tangent moduli are derived in a very general material setting which is subsequently specified for blood vessels in terms of Green-Lagrangian strains. Based on the principle of virtual work the finite element equations are provided and briefly discussed. Consistent linearization of the weak form of equilibrium and the external pressure term ensures a quadratic convergence rate of the iterative solution procedure. On the computational side of this work an effort was undertaken to show a novel approach on the investigation of soft tissue biomechanics. Representative numerical analyses of problems in vascular mechanics are discussed that show isochoric finite deformations (large rotations and large strains). In particular, a numerical simulation of the interaction between an inflated balloon catheter and a plaque deposit on the wall of a blood vessel is presented.",
author = "Holzapfel, {Gerhard A.} and Robert Eberlein and Peter Wriggers and Weizs{\"a}cker, {Hans W.}",
note = "Funding information: Support for this researchw as partly provided by the Austrian Fonds zur {\textquoteleft}Forderung der wissenschaft-lichen Forschung (FWF){\textquoteright} under Grants No. J0721-TEC and J0962-TEC to G.A.H. and by the {\textquoteleft}DeutscheF orschungsgesellscha(fDt FG){\textquoteright} with Project No. Wr 19/7-l to R.E. This support is gratefully acknowledged.W e also thank Dr. Thomas D. Kampp from the University of Southern California-School of Medicine, Los Angeles, to fit the experimentald ata of the blood vessel.",
year = "1996",
month = may,
day = "15",
doi = "10.1016/0045-7825(96)00999-1",
language = "English",
volume = "132",
pages = "45--61",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "1-2",
}