广义八面体理论研究综述

Review on generalized octahedral theory

在真三轴应力状态下,根据不同材料的破坏(屈服)面特征,依次采用三组破坏面对正六面单元体进行截取,则可得到一系列八面单元体(特别是岩土),亦即广义八面体,并进而可派生出其他相应的单元体,而已知的等倾八面体和双剪理论中的正交八面体则是其中的2类特征过渡单元体,由此构成了一个广义八面体单元体系.而不同单元体上的应力,则可通过双剪应力、静水应力和应力Lode参数建立起内在联系,并可据此对应力状态进行划分.在这一理论体系中,若首先考虑中间主应力和静水应力效应的情况,则可探究材料的多轴强度模型及其演变规律;其次,可根据材料的弹塑性理论,探究材料的强度、变形的本构关系;第三,可通过对建立在偏平面上的屈服方程,探索其演化规律.由此可初步建立起广义八面体理论体系的架构.进一步可在此基础上开展更为广泛的包括材料的弹-塑-粘、损伤、疲劳和蠕变等性征的内在规律,从而建立起较为完善的广义八面体理论体系.

According to failure （or yield） characteristics of materials, a serials of octahedral element bodies, which is generalized octhedron is cut orderly from cubic element by three groups of failure planes under true triaxial stress state . Further, by which other corresponding element bodies can be derived, in which well known isoclinal octahedron and orthogonal octahedron are two important characteristic element bodies, thus a generalized octahedral element system is formed. Although stresses are different on the different element bodies which can be established a link among double shear stress and hydrostatic stress and stress Lode parameter, then stress state can be divided by the interrelations. In the theory system, if the effections of hydrostatic stress and mean principal stress are considered firstly, then muhiaxial strength models and laws of evolution of the models may be achieved. Secondly, constitutive relations of strength and deformation can be proposed by elastoplasticity theory. Thirdly, evolution laws of yield equations made on the π. -plane may also be given. By the above study, a generalized octhedral theory may be founded initially. Further, more broadly study on inner - law of elasticity - plasticity - viscous, damage, fatigue and creep of materials, etc. , and a more perfect theory system of generalized octhedron may be founded.