率形式大变形弹塑性本构律中的超弹性条件

ON HYPERELASTIC CONDITION OF RATE-FORM ELASTICPLASTIC CONSTITUTIVE LAW AT FINITE DEFORMATION

本文证明了若取客观应力率为 Kirchhoff 应力的 Oldroyd 导数,对于 Lame 参数λ、μ为常数的情况,率形式弹性本构律的可积条件为 λ=0。这显然表明在大变形情况下率形式弹塑性本构律与超弹性条件这两者之间在一般情况下并不协调。文中还讨论了几种弹性本构律可以近似用于大变形描述的情况。

It is proved that if the objective stress rate is taken as the Oldroyd rate of the Kirchhoff stress tensor, the integrability condition of the rate-form elastic constitutive law is λ=0, provided that the Lame parameters λ and μ are. constants. This fact renders the rate-form elastic-plastic constitutive law incompatible with the hyperelastic framework in the regime of finite deformation. Several particular situations in which the rate-form elastic con-stitutive laws can be approximately applied to the case of finite deformation are discussed.