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首页> 外文期刊>Acta Mechanica >Hencky's elasticity model and linear stress-strain relations in isotropic finite hyperelasticity
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Hencky's elasticity model and linear stress-strain relations in isotropic finite hyperelasticity

机译：各向同性有限超弹性中的Hencky弹性模型和线性应力-应变关系

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Hencky's elasticity model is an isotropic finite elasticity model assuming a linear relation between the Kirchhoff stress tensor and the Hencky or logarithmic strain tensor. It is a direct generalization of the classical Hooke's law for isotropic infinitesimal elasticity by replacing the Cauchy stress tensor and the infinitesmal strain tensor with the foregoing stress and strain tensors. A simple, straightforward proof is presented to show that Hencky's elasticity model is exactly a hyperelasticity model, derivable from a quadratic potential function of the Hencky strain tensor. Generally, Hill's isotropic linear hyperelastic relation between any given Doyle-Ericksen or Seth-Hill strain tenser and its work-conjugate stress tensor is studied, A straightforward, explicit expression of this general relation is derived in terms of the Kirchhoff stress and left Cauchy-Green strain tensors. Certain remarkable properties of Hencky's model are indicated from both theorectical and experimental points of view. [References: 27]
机译：Hencky的弹性模型是各向同性的有限弹性模型，它假设Kirchhoff应力张量和Hencky或对数应变张量之间存在线性关系。通过用上述应力和应变张量代替柯西应力张量和无穷应变张量，这是经典的Hooke定律的各向同性无穷小弹性的直接推广。提出了一个简单直接的证明，以表明Hencky的弹性模型恰好是超弹性模型，可以从Hencky应变张量的二次势函数得到。通常，研究任何给定的Doyle-Ericksen或Seth-Hill应变张量与其功共轭应力张量之间的Hill的各向同性线性超弹性关系。根据Kirchhoff应力和左Cauchy-绿色应变张量。从理论和实验的角度都表明了Hencky模型的某些显着特性。 [参考：27]

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