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Analysis of the compressible, isotropic, neo-Hookean hyperelastic model

  • The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.

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Document Type:Article
Author:Attila KossaORCiD, Megan T. ValentineORCiD, Robert M. McMeekingORCiD
Parent Title (English):Meccanica
First Page:217
Last Page:232
Year of first Publication:2023
Release Date:2023/02/17
Tag:Compressibility; Constitutive model; Hyperelasticity; Material modeling; Neo-Hookean
Impact:02.538 (2021)
Funding Information:Hungarian National Research, Development and Innovation Office (NKFI FK 142457) National Research, Development, and Innovation Fund of Hungary under Grant TKP2021-EGA-02. MRSEC Program of the National Science Foundation through Grant No. DMR-1720256 (IRG-3).
DDC classes:500 Naturwissenschaften und Mathematik / 530 Physik
Open Access:Open Access
Signature:INM 2023/018
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International