Large strain analysis of soft biological membranes

Formulation and finite element analysis

authored by: 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.
External Organisation(s): Stanford University
Graz University of Technology
Technische Universität Darmstadt
University of Graz
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 132
Pages: 45-61
No. of pages: 17
ISSN: 0045-7825
Publication date: 15.05.1996
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/0045-7825(96)00999-1 (Access: Unknown)

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",
}