一维非线性黏弹体和黏塑性体中的最优应变路径

ONE DIMENSIONAL OPTIMAL STRAIN PATHS OF THE NONLINEAR VISCOELASTICITY AND THE VISCOPLASTICITY

得出了一维非线性黏弹体和黏塑性体中最优应变路径方程，并揭示了它们的某些特性，如：（１）当非线性黏弹本构方程中的黏性部分与应变的关系具有上凸形式时，相应的最优应变路径具有下凸性质；（２）对于过应力和Ｂｏｄｎｅｒ－Ｐａｒｔｏｎ黏塑性体，它们的最优应变路径是塑性应变为线性形式，即塑性应变率为常数，而弹－黏塑性体的最优应变路径则不同。

In this paper, we presented the equations of the optimal strain paths for the nonlinear viscoelasticity and the viscoplasticity in one dimensional case. We also showed some character of the optimal paths,i.e(1)if the relation of the viscous part and the strain in the nonlinear viscoelastic constitutive equation is cave,the corresponding optimal strain path is cave;(2)the optimal paths of the overstress viscoplasticity and the Bodner-Parton one are that the plastic strain is linear and the plastic strain rate is constant,but the one of the elastic-viscoplasticity is different.