Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions |
| |
| Affiliation: | 1. Institut für Mechanik, Fachbereich 10, Universität Essen, 45117 Essen, Universitätsstr. 15, Germany;2. Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Schloßgartenstr. 7, Germany;1. Institute of Biomechanics, Graz University of Technology, Austria;2. Department of Surgery, Division of Transplantation Surgery, Medical University of Graz, Austria;3. Division of Cardiothoracic and Vascular Surgery, Klinikum Klagenfurt am Wörthersee, Austria;4. Department of Cardiology, Medical University of Graz, Austria;5. Institute of Pathology, Medical University of Graz, Austria;6. Institute of Molecular Biosciences, BioTechMed-Graz, University of Graz, Austria;1. Ruhr-University Bochum, D-44801 Bochum, Germany;2. Institute for Metal and Lightweight Structures, University of Duisburg-Essen, 45117 Essen, Germany;1. State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing, 100029, China;2. College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing, 100029, China;3. Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing, 100029, China |
| |
| Abstract: | In this paper we propose a formulation of polyconvex anisotropic hyperelasticity at finite strains. The main goal is the representation of the governing constitutive equations within the framework of the invariant theory which automatically fulfill the polyconvexity condition in the sense of Ball in order to guarantee the existence of minimizers. Based on the introduction of additional argument tensors, the so-called structural tensors, the free energies and the anisotropic stress response functions are represented by scalar-valued and tensor-valued isotropic tensor functions, respectively. In order to obtain various free energies to model specific problems which permit the matching of data stemming from experiments, we assume an additive structure. A variety of isotropic and anisotropic functions for transversely isotropic material behaviour are derived, where each individual term fulfills a priori the polyconvexity condition. The tensor generators for the stresses and moduli are evaluated in detail and some representative numerical examples are presented. Furthermore, we propose an extension to orthotropic symmetry. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
