Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries - Archive ouverte HAL Access content directly
Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2022

Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries

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Abstract

Computational analysis of the nonlinear mechanical properties of anisotropic hyperelastic materials aims at a better understanding of its physiology and pathophysiology under different loading conditions. This has an important role in biomechanics, surgical, clinical diagnostic and design of medical devices. This study investigates the modeling of arterial tissues made of a four-fiber family by using an anisotropic hyperelastic model. This model is based on the theory of polynomial invariant and was implemented in the university finite element code FER. The convex property of the strain energy function is investigated as well as the positive definite nature of the tangent stiffness matrix used within the framework of a finite element analysis. This allows us to guarantee the invertibility of the linearized problem and the uniqueness of the solution computed at each step of the Newton–Raphson scheme used to solve nonlinear problems.
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Dates and versions

hal-03739575 , version 1 (27-07-2022)

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Cite

Renye Cai, Libang Hu, Frédéric Holweck, François Peyraut, Zhi-Qiang Feng. Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries. Computer Methods in Applied Mechanics and Engineering, 2022, 399, pp.115294. ⟨10.1016/j.cma.2022.115294⟩. ⟨hal-03739575⟩
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