Large strain analysis of soft biological membranes: Formulation and finite element analysis
type: Item
instance of: scholarly article
title: Large strain analysis of soft biological membranes: Formulation and finite element analysis
zbMATH Open document ID: 0890.73051
DOI: 10.1016/0045-7825(96)00999-1
author: Robert Eberlein
author: P. Wriggers
author: Hans W. Weizsäcker
author: Gerhard A. Holzapfel
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1998-07-01T00:00:00Z
review text: This paper presents a general formulation of thin incompressible membranes and investigates the behavior of soft biotissues using the finite element method. In particular, a hyperelastic model is chosen to examine the highly nonlinear 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. Finally, we present a numerical simulation of the interaction between an inflated balloon catheter and a plaque deposit on the wall of a blood vessel.
Mathematics Subject Classification ID: 74L15
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 92C10
zbMATH DE Number: 1081947
zbMATH Keywords: vascular mechanics
zbMATH Keywords: incompressible membranes
zbMATH Keywords: hyperelastic model
zbMATH Keywords: stress-deformation relation
zbMATH Keywords: elastic tangent moduli
zbMATH Keywords: Green-Lagrangian strains
zbMATH Keywords: principle of virtual work
zbMATH Keywords: linearization
zbMATH Keywords: quadratic convergence
zbMATH Keywords: iterative solution
zbMATH Keywords: inflated balloon catheter
zbMATH Keywords: plaque deposit
zbMATH Keywords: blood vessel
MaRDI profile type: Publication
full work available at URL: 0045-7825(96)00999-1
OpenAlex ID: W2005955302
cites work: Large elastic deformations of isotropic materials IV. further developments of the general theory
cites work: Q4001844
cites work: Q4023641
cites work: Q3327849
cites work: Displacement dependent pressure loads in nonlinear finite element analyses
cites work: Pressure Loaded Structures under Large Deformations
cites work: A note on finite-element implementation of pressure boundary loading
cites work: Consistent linearization in mechanics of solids and structures
cites work: Remarks on rate constitutive equations for finite deformation problems: Computational implications
cites work: A fully non‐linear axisymmetrical quasi‐kirchhoff‐type shell element for rubber‐like materials
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description: scientific article; zbMATH DE number 1081947