A simple polyconvex strain energy density with new invariants for modeling four-fiber family biomaterials

Autor: Renye Cai, Zhi-Qiang Feng, Frédéric Holweck, François Peyraut
Přispěvatelé: Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), School of Mechanics and Engineering [Chengdu], Southwest Jiaotong University (SWJTU), Laboratoire de Mécanique et d'Energétique d'Evry (LMEE), Université d'Évry-Val-d'Essonne (UEVE), Laboratoire Interdisciplinaire Carnot de Bourgogne ( LICB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), School of Mechanics and Engineering, Southwest Jiaotong University ( SWJTU ), Laboratoire de Mécanique et d'Energétique d'Evry ( LMEE ), Université d'Évry-Val-d'Essonne ( UEVE ), Laboratoire Interdisciplinaire Carnot de Bourgogne (LICB)
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Materials science
0206 medical engineering
02 engineering and technology
Strain energy
Linear form
General Materials Science
Biomechanics
Invariant (mathematics)
Anisotropy
business.industry
Applied Mathematics
Mechanical Engineering
Mathematical analysis
[SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph]
Strain energy density function
Structural engineering
021001 nanoscience & nanotechnology
Condensed Matter Physics
020601 biomedical engineering
Anisotropic hyperelasticity
Mathematical theory
Nonlinear system
Mechanics of Materials
Modeling and Simulation
Hyperelastic material
Theory of invariant polynomials
[ SPI.MECA.BIOM ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph]
0210 nano-technology
business
Zdroj: International Journal of Solids and Structures
International Journal of Solids and Structures, 2016, pp.(in Press). ⟨10.1016/j.ijsolstr.2017.03.007⟩
International Journal of Solids and Structures, Elsevier, 2016, pp.(in Press). 〈10.1016/j.ijsolstr.2017.03.007〉
International Journal of Solids and Structures, Elsevier, 2016, pp.(in Press). ⟨10.1016/j.ijsolstr.2017.03.007⟩
ISSN: 0020-7683
DOI: 10.1016/j.ijsolstr.2017.03.007⟩
Popis: International audience; We introduce in this paper a new hyperelastic model for the prediction of nonlinear mechanical properties of anisotropic hyperelastic materials under biaxial stretching. The proposed strain energy function (SEF) can be applied for understanding the nature of behavior laws for materials with four-fiber family structures, which has a large potential of applications, particularly in biomechanics, surgical and interventional therapies for peripheral artery disease (PAD). This SEF is built with a recent and new invariant system based on the mathematical theory of invariant polynomials. By recombining them in an appropriate manner, we demonstrate that it is possible to build a polyconvex integrity basis of invariants. Accuracy and reliability of the corresponding numerical model were validated by a comparison with experimental and numerical results extracted from Kamenskiy et al. (2014). 1 1We warmly thank Assistant Professor Kamenskiy to have kindly provided us the numerical data corresponding to the measurements included in These results concerned diseased superficial femoral (SFA), popliteal (PA) and tibial arteries (TA) from one patient under planar biaxial extension. For each kind of arteries tested with 5 combinations of different biaxial stretches, the predicted results of the proposed model and the experimental data are consistent. Our model includes 7 material parameters and their identification result in a single solution because of the linear form we have chosen for the SEF with respect to the material parameters.
Databáze: OpenAIRE
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