大变形条件下材料本构关系研究

推导了轴向均匀大变形等截面杆的Lagrangian-Green应变张量和Eulerian应变张量以及分别与它们能量共轭的第二类Piola-Kirchhoff应力张量和Cauchy应力张量的表达式,给出了这2对能量共轭的应力应变张量的本构关系式。计算结果表明:当工程应变较小时,可以直接用常值弹性模量代替真实弹性模量进行计算;当工程应变较大时,必须对常值弹性模量进行修正。

Analysis on Constitutive Relations of Material under Large Deformation

The expressions of the Lagrangian-Green strain tensor and the Eulerian strain tensor and their work-conjugate stress tensors,namely,the second Piola-Kirchhoff stress tensor and Cauchy stress tensor,are derived for the beam under axial uniformly tension,and the constitutive relations of these two pairs of work-conjugate stress and strain measures are also presented.The calculated results show that: when the engineering strain is much smaller than unity,the constant elastic modulus can directly replace the true elastic modulus,when the engineering strain is comparable with unity,the constant elastic modulus needs to be modified.