How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

Mihai, Loredana Angela ORCID: https://orcid.org/0000-0003-0863-3729 and Goriely, Alain 2017. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2207) , 0607. 10.1098/rspa.2017.0607

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Abstract

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus, and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue, and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Royal Society
ISSN:	1364-5021
Date of First Compliant Deposit:	3 November 2017
Date of Acceptance:	3 November 2017
Last Modified:	04 May 2023 23:07
URI:	https://orca.cardiff.ac.uk/id/eprint/106200

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