含主应力轴旋转的广义塑性位势理论

Generalized Plastic Potential Theory Involving the Rotation of Principal Stress Axes

大量岩土实验与工程实践表明传统塑性位势理论无法合理反映岩土材料的基本变形机制。从塑性位势理论角度来看,当存在主应力轴旋转时,塑性应变增量与应力不共主轴,此时最一般情况下的塑性应变增量须用六个线性无关的塑性势函数来表述,从而提出含主应力轴旋转的广义塑性位势理论一般表达式。通过矩阵分析,将一般应力增量分解成共轴分量与旋转分量之和。在应力增量分解的基础上,提出含主应力轴旋转的广义塑性位势理论的分解表达式,它大大减小了求取塑性系数量的难度。论文也给出了塑性系数的确定方法及应力轴旋转的广义塑性位势理论与传统塑性位势理论的关系。

Numerous geotechnical experiments and engineering experiences show that the traditional plastic potential theory can not describe the basic mechanical behavior of geomaterials. While the principal stress axes rotation can not be ignored, the principal axes of plastic strain increment will now coincide with that of stress. Under such condition, the plastic strain increment in general case should be described by six linearly independent plastic potential functions, then the general formulation of generalized plastic potential theory involving principal stress axes rotation is presented. By means of matrix theory, arbitrary stress increment is decomposed into two parts: coaxial part and rotational parts. Based on the decomposition of stress increment, the decompostion formulation of the generalized plastic potential theory involving principal stress axes rotation is put forward and the difficulty of determination of plastic coefficients is reduced significantly. In the end, the determination methods of platic coefficients and the relation between the traditional plastic potential theory and the generalized plastic potential theory involving principal stress axes rotation are given.