The study of equivalent material parameters in a hyperelastic model |
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| Institution: | 1. Department of Industrial Engineering, University of Padova, 35131 Padova, Italy;2. Centre for Mechanics of Biological Materials, University of Padova, 35131 Padova, Italy;3. Department of Mathematics, University of Padova, 35121 Padova, Italy;1. International Center for Applied Mechanics, SV Laboratory, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;2. Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA;3. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;4. School of Chemical Engineering, Northwest University, Xi’an 710069, China;1. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China;2. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China;1. PIMM Laboratory, UMR 8006 CNRS – Arts et Métiers ParisTech, 151 Bd de l’Hôpital, 75013 Paris, France;2. LTM – ICB Laboratory, UMR 6303 CNRS – Université de Bourgogne, 12 rue de la fonderie, 71200 Le Creusot, France |
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| Abstract: | We study a hyperelastic model of some biological soft tissues with emphasis on the problem of its matching with the material parameters acquired by experimental mechanical tests. First, we study the polyconvexity property of the hyperelastic model. Then, we explore the notion of equivalent sets of material parameters. We perform a numerical study of the regions of equivalent material parameters characterizing the curves predicted by the hyperelastic model that are close, within a prefixed tolerance, to those given by the experimental data. In the numerical study we use the quadratic variation and the Hausdorff distance. The study suggests that a qualitative knowledge of shape and volume of the regions of equivalent material parameters can provide both a criterion for the optimal match between the model with the experimental data and an indication on the reducibility of the number of parameters used in the model. |
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| Keywords: | Hyperelasticity Constitutive parameters Polyconvexity Tissue modeling |
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