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A note on the Mooney–Rivlin material model

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Abstract

In finite elasticity, the Mooney–Rivlin material model for the Cauchy stress tensor T in terms of the left Cauchy–Green strain tensor B is given by

$$T = -pI + s_1 B + s_2 B^{-1},$$

where p is the pressure and s 1, s 2 are two material constants. It is usually assumed that s 1 > 0 and s 2 ≤ 0, known as E-inequalities, based on the assumption that the free energy function be positive definite for any deformation. In this note, we shall relax this assumption and with a thermodynamic stability analysis, prove that s 2 need not be negative so that some typical behavior of materials under contraction can also be modeled.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21945-970, Brasil

    I-Shih Liu

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  1. I-Shih Liu
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Correspondence to I-Shih Liu.

Additional information

Communicated by Manuel Torrilhon.

Dedicated to Ingo Müller on the occasion of his 75th birthday.

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Liu, IS. A note on the Mooney–Rivlin material model. Continuum Mech. Thermodyn. 24, 583–590 (2012). https://doi.org/10.1007/s00161-011-0197-6

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  • DOI: https://doi.org/10.1007/s00161-011-0197-6

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