应变空间塑性余位势理论的力学基础研究

岩土材料的力学试验表明在应变空间中Iliushin塑性公设不适用于岩土材料，为了克服这一
理论缺陷，依照Caratheodory定理，建构了应变空间的广义塑性公设。根据广义塑性公设，证明了塑性余
位势函数在应变空间塑性区的存在性。研究表明，塑性余位势函数的物理含义是超余功增量为零面；
Iliushin塑性公设存在的条件是塑性余位势函数正定且可逆；在应变空间塑性区必须采用分部塑性应力而
不能采用总塑性应变来建构屈服面方程和塑性余位势函数，否则与热力学第二定理相矛盾。最后给出了考
虑塑性应力相互耦合的应变空间弹塑性模量的普遍表达式。

Fundamental and mechanical study of plastic complementary potential theory in strain space

Geomaterial experiment showed that the Iliushin's postulate is not available for geomaterial in strain space. In order to rectify this academic flaw, a new plastic postulate in strain space was provided based on the Caratheodory's theorem. The plastic complementary potential function was proved to exist in the plastic region of strain space by virtue of the new plastic postulation. The mechanical meaning of plastic complementary potential is that the plastic excess incremental complementary work is zero, and the sufficient and necessary condition of Iliushin's postulate is that the change along the plastic complementary potential surface is reversible and the plastic complementary potential surface is positive normalization. It is necessary to emphasize that the yielding function and the plastic complementary potential surface must be expressed by terms of the fractional plastic stress rather than the whole plastic stress in order not to inflict with the second law of thermodynamics. The generalized expression of elastic-plastic modulus in view of the coupling fractional plastic stress was finally derived in strain space.