Lagrange型有限变形塑性本构理论

In the present paper, the Lagrangian finite plasticity theory is discussed based on the theory of materials with elastic range by the assumptions of the existence of a yield functional and a flow rule, to generalize the framework of A.E. Green, P.M. Naghdi and J. Casey (see Naghdi(1990), Brown et al (2003)), so that it can describe better the mechanical behaviors of anisotropic elastic-plastic materials and the strain induced anisotropy. Here the plastic strain, also called intermediate strain, is defined by the plastic stress, and the elastic response functional is assumed to be a functional of plastic strain history. As a result of this definition of intermediate strain, the elastic response functional has a special form, the normal flow rule of generally accepted Il’yushin’s Postulate is the evolution law for the plastic stress. If the plastic stress is also defined to describe the kinematical hardening, it is the kinematical hardening law. The definitions of strain, plastic strain and elastic strain are discussed from a geometric point of view. It is shown that Green-Naghdi elastic strain is the Lagrange elastic strain. The discussion of the consequences of Il’yushin’s Postulate has detailed, the necessary and sufficient condition is obtained. The rate-form of this theory is obtained. The material symmetry and strain induced anisotropy are also discussed in detail. Finally an example of isotropic elastic plastic materials is given. It has been shown that in general this model can satisfy the basic conditions such as Il’yushin postulate and uniqueness and existence of solution of flow rule for any plastic deformation.