A projection method to extract biological membrane models from 3D material models

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• 作者：Farshad Roohbakhshan ; Thang X. Duong ; Roger A. Sauer ; ^{sauer@aices.rwth-aachen.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Anisotropic hyperelasticity ; Constitutive modeling ; Differential geometry ; Membrane theory ; Nonlinear finite elements ; Soft tissues
• 刊名：Journal of the Mechanical Behavior of Biomedical Materials
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：58
• 期：Complete
• 页码：90-104
• 全文大小：4553 K

文摘

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.