论塑性旋率本构方程的必要性

在有限变形弹塑性理论中,本构方程通常是以率型形式给出的。因此,应变率的分解将是一个十分基本的问题。在当前,较为流行的是基于中间构形的应变率分解,而这其中最有影响的有 Lee,E.H.等人的工作和 Dafalias 等人的工作。然而,本文的研究表明,至少在某些特殊情况下,我们可以得到与微观子结构定向旋率的有关表达式。这就使给出塑性旋率本构方程变得不必要了。显然,本文的结果既不同于 Dafalias 的工作,也不同于 E.H.Lee等人的工作。前者需要通过塑性旋率的本构方程来确定微观子结构定向的旋率,而后者则需要作出附加的隐含假设来避免给出塑性旋率的本构方程。可以相信,本文工作将可能为有限弹塑性变形的本构理论提供一种新的途径。

ON THE NECESSITY OF THE CONSTITUTIVE EQUATIONS FOR THE PLASTIC SPIN

In the theory of finite elasto-plasticity, the constitutive relation is usually in the form of rate type. Hence the decomposition of strain rate based on the concept of intermediate configuration has become very popular, and among others, works developed by E. H. Lee et al. and Y. F. Dafalias et al. may be considered to be the most influential. Nevertheless, it is shown in this paper that, at least for some special cases, certain relation that the substruc-tural spin should satisfy can be derived. Thus, it becomes unnecessary to give the constitutive equation for the plastic spin. Clearly, the present theory is different from that either by Dafalias or by E. H. Lee. In order to determine the substructural spin, the former has to give the constitutive equaiton for the plastic spin, and the latter has to make certain implied assumptions on the decomposition of strain rate. It is believed that the present result may be used to pro-vide a new approach in the constitutive theory of finite plasticity.