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An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling

  • Original Article
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Journal of Biorheology

Abstract

Recent experimental studies have highlighted the significant influence of axonal fibers on the nonlinear and anisotropic behavior of brain tissue. This study aims to implement these properties in a transversely isotropic visco-hyperelastic constitutive law for brain tissue. The second step consists in implementation of this law under finite-element (FE) code to improve brain FE modeling by including brain tissue specificities proposed in the recent literature. Validation of the model is shown by comparison of numerical simulation of unconfined compression with experimental tests from the literature. This study represents a step toward more realistic brain FE modeling.

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Abbreviations

F :

Deformation gradient tensor

J :

Jacobian of the deformation (determinant of F)

C :

Right Cauchy–Green deformation tensor

W :

Strain energy function

I i :

(i = 1, 2, 3, 4, 5) invariants of C

K :

Bulk modulus

G :

Shear modulus

λ i :

(i = 1, 2, 3) principle stretches of F

S :

Second Piola–Kirchhoff stress tensor

σ :

Cauchy stress

N :

Nominal stress tensor

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Authors and Affiliations

  1. University of Strasbourg, IMFS-CNRS, 2 rue Boussingault, 67000, Strasbourg, France

    Simon Chatelin, Caroline Deck & Rémy Willinger

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  1. Simon Chatelin
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  2. Caroline Deck
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  3. Rémy Willinger
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Correspondence to Rémy Willinger.

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Chatelin, S., Deck, C. & Willinger, R. An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling. J Biorheol 27, 26–37 (2013). https://doi.org/10.1007/s12573-012-0055-6

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  • DOI: https://doi.org/10.1007/s12573-012-0055-6

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