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岩土材料一些常用的与摩擦有关的经典屈服准则,如Mohr-Coulomb屈服准则、俞茂宏广义双剪应力屈服准则、Lade-Duncan屈服准则、Matsuoka-Nakai屈服准则和沈珠江三剪应力屈服准则等,都属于n阶欧拉齐次函数。把上述屈服准则从真实空间推广到耗散空间后发现,当耗散空间中的n阶齐次屈服函数与真实应力无关时,根据耗散空间的Drucker塑性公设获得的耗散功与应力状态无关;对于砂性材料其值甚至为零,与塑性发生时熵增大于零的热力学第二定律相违背。为了克服上述缺陷,必须在耗散空间的n阶齐次屈服函数中引入与真实应力有关的函数项,然而,由此获得的真实空间屈服准则与塑性应变增量之间必须服从非相关联流动法则。由于服从相关联流动法则时耗散空间屈服准则表达式与真实空间的完全相同,故在真实空间中服从n阶齐次屈服准则的岩土摩擦材料也不适宜采用相关联流动法则。
Some commonly used friction-related classical yield criterion of geomaterials, such as Mohr-Coulomb yield criterion, Yu Maohong generalized double shear stress yield criterion, Lade-Duncan yield criterion, Matsuoka-Nakai yield criterion and Shenzhujiang triple shear stress yield criterion , All belong to n-order Euclidean times function. When the above yield criterion is extended from the real space to the dissipative space, it is found that the dissipative work and stress state obtained from the Drucker plasticity of the dissipative space have nothing to do with the nth-order homogeneous yield function in dissipative space and the true stress ; Even for sand materials the value is even zero, contrary to the second law of thermodynamics where entropy increases to zero when plasticity occurs. In order to overcome the above shortcomings, it is necessary to introduce the function term related to true stress into the n-th order homogeneous yield function in dissipative space. However, the real space yield criterion obtained from this must obey the non-correlated flow law. Since the expression of yielding criterion in dissipative space is exactly the same as real space when obeying the associated flow law, the geomaterials subject to n-order homogeneous yield criterion in true space are not suitable for the associated flow law.