title: A projection method to extract biological membrane models from 3D material models.
abstract: This paper presents a projection method for deriving membrane models from the corresponding three-dimensional material models. As a particular example the anisotropic Holzapfel-Gasser-Ogden model is considered. The projection procedure is based on the kinematical and constitutive assumptions of a general membrane theory, considering the membrane to be a general two-dimensional manifold. By assuming zero transverse stress, the Lagrange multiplier associated with the incompressibility constraint can be eliminated from the formulation. The resulting nonlinear model is discretized and linearized within the finite element method. Several numerical examples are shown, considering quadratic Lagrange and NURBS finite elements. These show that the proposed model is in very good agreement with analytical solutions and with full 3D finite element computations.
authors.affiliation: Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
authors.forename: Farshad
authors.initials: F
authors.lastname: Roohbakhshan
authors.affiliation: Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
authors.forename: Thang X
authors.initials: TX
authors.lastname: Duong
authors.affiliation: Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany. Electronic address: sauer@aices.rwth-aachen.de.
authors.forename: Roger A
authors.initials: RA
authors.lastname: Sauer
mesh_terms: D016880:Anisotropy; D002462:Cell Membrane / Q000502:physiology*; D003198:Computer Simulation; D020342:Finite Element Analysis; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013314:Stress, Mechanical
keywords: Anisotropic hyperelasticity; Constitutive modeling; Differential geometry; Membrane theory; Nonlinear finite elements; Soft tissues