A variational approach for materially stable anisotropic hyperelasticity |
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| Institution: | 1. Institut für Mechanik, Fachbereich 10, Universität Duisburg-Essen, Standort Essen, Universitätsstr. 15, 45117 Essen, Germany;2. Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Schloßgartenstr. 7, Germany;3. Fachbereich Mechanik, Technische Universität Darmstadt, 64289 Darmstadt, Hochschulstr. 1, Germany;1. Institute of Applied Mechanics (CE), Chair I, University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany;2. Chair of Applied Mechanics, Department of Mechanical Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Egerlandstr. 5, 91058 Erlangen, Germany;3. Institute of Mechanics, Department of Civil Engineering, Faculty of Engineering, University of Duisburg–Essen, Universitätsstr. 15, 45141 Essen, Germany;1. School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA;2. Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA;3. Department of Clinical Sciences, Colorado State University, Fort Collins, CO, USA;1. Institut für Mechanik, Fachbereich für Ingenieurwissenschaften/Abtl. Bauwissenschaften, Universität Duisburg-Essen, 45117 Essen, Universitätsstr. 15, Germany;2. Institut für Mechanik und Flächentragwerke, TU Dresden, Nürnberger Str. 31A, 01187 Dresden, Germany;3. Dresden Center for Computational Materials Science, 01062 Dresden, Germany;4. Institut für Kontinuumsmechanik, Fakultät für Maschinenbau, Leibniz Universität Hannover, 30167 Hannover, Appelstr. 11, Germany |
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| Abstract: | In this work we propose an anisotropic stored energy function which satisfies a priori the Legendre–Hadamard condition, which is strongly related to the material stability of the constitutive equations. In the linearized case this condition implies positive wave speeds. The Legendre–Hadamard condition plays also an important role for the (local) existence of solutions in the neighborhood of stationary points. We apply the proposed hyperelastic energies to soft tissues and compare the formulation with existing models which have been used for the calculation of medial collateral ligament and arterial walls. In our numerical and analytical investigations we discuss the distribution of wave speeds for a sequence of deformation states containing some essential stress–strain characteristics of the compared models. |
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