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三、内蕴时间塑性理论的一些基本概念和本构方程 本节首先分别从经典塑性理论与内时理论的基本观点出发,对Drucker在其奠基性论文[46]中用过的一维力学模型的塑性响应特性进行分析比较,以便用简洁的方式阐述内时理论的某些最基本的概念,并说明经典模型可作为内时模型的一种理想化情况而得到。接着评述广义时间在固体力学中引入的概况和笔者最近提出的耗散型材料本构方程的形式不变性定律。然后根据这一定律首先得到了Valanis(1971)提出的小变形小变温下内时弹塑性本构方程的显式。接着研究了塑性应变偏张量的欧几里得模作为内时测度定义时的内时本构方程的特性,特别是讨论了它与经典塑性理论之间的关系。然后引入了含弱奇异性的内时本构方程。最后讨论了Valanis与笔者最近提出的新型弹塑性内时本构方程。
3. Some basic concepts and constitutive equations of the intrinsic time plasticity theory In this section, we begin with the basic viewpoints of the classical plasticity theory and the inner-time theory, and use the one-dimensional mechanical model that Drucker used in his foundational thesis [46]. The plastic response characteristics are analyzed and compared in order to explain some of the most basic concepts of the inner-time theory in a concise manner, and to illustrate that the classical model can be obtained as an ideal situation of the inner-time model. Then it reviews the general introduction of the generalized time in solid mechanics and the author’s recently proposed law of form invariance of dissipative material constitutive equations. Then according to this law, we first obtained the explicit formula of the elastoplastic constitutive equation under small deformation and small temperature change proposed by Valanis (1971). Then we study the Euclidean mode of the plastic strain bias as the characteristic of the inner-time constitutive equation when the inner-time measure is defined, especially the relationship between it and the classical plasticity theory. Then the inner-time constitutive equation with weak singularity is introduced. Finally, Valanis and the author recently proposed a new elastoplastic endogenous constitutive equation.