岩土塑性理论中功表达的近似性

Approximation of work calculation in theory of geotechnical plasticity

对广义剪应力、广义剪应变的表达式作了说明,在给出其增量表达的同时,指出了在计算二者增量时可能产生的误解。在此基础上,分析比较由平均主应力、体积应变增量、广义剪应力、广义剪应变增量表述的功的增量以及由三向主应力与三向主应变增量表述的功的增量得出:两种表述在一般情况下并不一致。但在某些特殊情况下,例如等应力Lode角加载并满足应力全量Lode角与应变增量Lode角相等时,二者的表述一致。岩土塑性理论中塑性功增量存在与功的增量相同的问题,然而对于实际岩土材料,应力全量与塑性应变增量等Lode角的假定在一般情况下是不能满足的。因此在岩土塑性理论中,对于一般情况下的等应力Lode加载情况,用平均主应力、塑性体积应变增量、广义剪应力、塑性广义剪应变增量表述的塑性功增量也只是一种近似。

The expressions of generalized shear stress and generalized shear strain are introduced. After analyzing the two expressions, mistakes in calculating the increment of generalized shear stress and generalized shear strain are pointed out, and then the right calculations are given. Based on this, two expressions of work increment that one is described by mean stress, volumetric strain increment, generalized shear stress and generalized shear strain increment and the other is described by three-dimensional stresses and three-dimensional strain increments are compared. The conclusion is that the two expressions are not always consistent except in some particular conditions. An example of the particular conditions is that loading in constant Lode angle and also the Lode angle of the three-dimensional stresses is equal to that of the three-dimensional strain increments. The same inconsistency still exists in applications of plastic work increment, while unfortunately the equation of Lode angle of the threedimensional stresses and the threedimensional strain increments is not always satisfied for practical geomaterials. So in the theory of geotechnical plasticity, for the condition of loading in constant Lode angle, the plastic work increment expressed by mean stress, plastic volumetric strain increment, generalized shear stress and generalized plastic shear strain increment is just a kind of approximation.