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<p>In this contribution, we propose a hyperelastic isotropic material model whose stress–strain response is non-linear even at infinitesimal deformations and cannot thus be linearized. As a result, the superposition principle does not apply and the generalized Hooke law is not valid even at small strains. A further unusual feature of this material model is that Poisson’s ratio can be greater than <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{0.5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn mathvariant="bold">0.5</mn> </mrow> </math></EquationSource> </InlineEquation> in full agreement with the laws of thermodynamics. In particular, for the proposed strain energy function, a value of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varvec{\nu =0.644}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">ν</mi> <mo mathvariant="bold">=</mo> <mn mathvariant="bold">0.644</mn> </mrow> </math></EquationSource> </InlineEquation> is reached. The model response appears to be plausible in various deformation states such as uniaxial tension/compression, simple shear, and pure dilation.</p>

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A hyperelastic isotropic model with Poisson’s ratio greater than one half

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  • 发表日期：

    2026年4月10日

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  • Mikhail Itskov

摘要

In this contribution, we propose a hyperelastic isotropic material model whose stress–strain response is non-linear even at infinitesimal deformations and cannot thus be linearized. As a result, the superposition principle does not apply and the generalized Hooke law is not valid even at small strains. A further unusual feature of this material model is that Poisson’s ratio can be greater than \(\varvec{0.5}\) 0.5 in full agreement with the laws of thermodynamics. In particular, for the proposed strain energy function, a value of \(\varvec{\nu =0.644}\) ν = 0.644 is reached. The model response appears to be plausible in various deformation states such as uniaxial tension/compression, simple shear, and pure dilation.