Lode角对应力张量的导数的基本性质

为计及岩土类材料塑性力学行为的中主应力影响或应力路径相关性，通常将应力张量Lode角/Lode数引入屈服函数与塑性势函数。由此在计算塑性应变增量时必然涉及Lode角/Lode数对应力的导数张量（记为 ）。然而，应力张量主值有重根时 的计算存在困难。本文给出了 的主值计算方法及谱分解表达式并详细讨论了张量 的基本性质。

PROPERTIES OF THE DERIVATIVES OF LODE ANGLE WITH RESPECT TO STRESS

The Lode angle is often introduced into yield function or plastic potential function for accounting the complex mechanical behaviors, such as influences of intermediate principle stress and stress path on failure and deformation, of granular soil. Therefore, the derivative of Lode angle with respect to stress (denoted as ) must be involved for the calculation of plastic strain. Yet, the singularity of occurs at the stress states which correspond to the repeated principle stress, so it is difficulty to obtain the principle value of . A new method for calculation of principle value of are presented in the study，and some basic properties of are discussed in detail.