基于Hill原理的非相关联流动法则的机理研究

为了克服经典塑性力学中与摩擦相关的n阶齐次屈服函数的耗散功与应力状态无关,以及砂性材料的耗散功为零,后者与塑性发生时耗散功必须大于零的热力学第二定律相违背的缺陷,将真实空间的Hill最大耗散功原理推广到耗散空间的Hill最大耗散功原理.根据摩擦引起的能量耗散与真实空间正应力（或球应力）相关的机制,在耗散空间的屈服准则中引入与真实空间正应力（或球应力）相关的函数项,从而使塑性发生时材料的耗散功大于零.由于耗散空间中的屈服准则与真实应力相关,真实空间的屈服准则与塑性应变之间必须服从非相关联流动法则.

Mechanism of non-associated flow rule based on Hill’s principle

nth homogeneous yield criteria related to friction effect is independent of true stress in classical plasticity and even equal to zero for sand materials. The latter does not conform to the second law of thermodynamics, which demonstrates that the dissipative work must be bigger than zero during the appearance of plastic behavior. Hill’s principle of maximum dissipative work was generalized from true stress space to dissipative stress space. According to the mechanism that the energy dissipation resulted from friction is related to normal stress (or spherical stress) of true stress, a partial function related to true stress was added into the yield function of dissipative space in order that the dissipative work is bigger than zero during the appearance of plastic behavior. Because the yield criterion of dissipative space was relative to the true stress, the relation between the yield criteria of true space and plastic strain conformed to non-associated flow rule.