Lagrange型有限变形弹塑性本构理论

Casey和Naghdi（1992）指出，塑性本构理论中引入的量如塑性应变和背应力张量等至少在理论上必须有明确的定义。从而使理论可进行实验验证。根据Dafalias（1988）和Chen（1999）背应力张量和塑性应变张量的定义，在Naghdi等的理论框架下建立了Lagrange型的有限变形弹塑性本构理论。讨论了Ilyushin公设导致的正交流动法则和对弹性响应泛函的限制条件。进一步讨论了由于使用上述背应力张量的定义对屈服函数形式的限制。

A Lagrangian Finite Plasticity Theory

As pointed out by Casey and Naghdi~([2]),the introduced internal variables,such as plastic strain and back stress in plasticity should be defined,at least theoretically,so that the theory can be testable.In the present paper based on the definitions of plastic strain and back stress in Dafalias~([4]) and Chen and Zhao~([8]),a Lagrangian finite plasticity theory is constructed in the theory framework by Naghdi et al.The normal flow rule is derived by the method in Fosdick and Volkmann~([9])using Ilyushin's postulate.With the help of Stoke's theorem,the restriction condition of elastic-response functional is obtained.From the definition of back stress,the given yield function completely determines the back stress.Accordingly in the present paper the restricted form of yield functions is discussed.