各向同性率无关材料本构关系的不变性表示

在内变量理论的框架下，针对各向同性率无关材料，使用张量函数表示理论建立了塑性应变全量及增量本构关系的最一般的张量不变性表示. 它们均由3个完备不可约的基张量组合构成，这3个基张量分别是应力的零次幂、一次幂和二次幂. 因此得出，塑性应变、塑性应变增量与应力三者共主轴. 通过对基张量的正交化，给出了本构关系式在主应力空间中的几何解释. 进一步，全量(或增量)本构关系中3个组合因子被表达为应力、塑性应变(或塑性应变增量)的不变量的函数. 当塑性应变(或塑性应变增量)的3个不变量之间满足一定关系时，所给出的本构关系将退化为经典的形变理论(或塑性势理论).最后，还讨论它与奇异屈服面理论的关系，当满足一定条件时，两者是一致的. 

INVARIANT TENSOR FUNCTION REPRESENTATIONS OF CONSTITUTIVE EQUATIONS FOR THE ISOTROPIC AND RATE INDEPENDENT MATERIALS

This paper combines the internal variable theory and the tensor function representation theory to establish the constitutive equations of the deformation theory and the increment theory for the isotropic and rate independent materials. In the equations, there are three complete and irreducible base tensors, that is, the stress tensor of the zero order, the first order and the second order power, to show that the principal axes of plastic strain and its increment are coincident with those of the stresses. With the orthogonalization of the base tensors, the geometrical explanation of the constitutive equations is obtained in the principal stress space. Furthermore, the coefficients in the constitutive equations of deformation theory (or increment theory) can be derived with three invariants of stresses and plastic strain ( or plastic strain increments). Meanwhile, the present constitutive equations may reduce to classical deformation theory (or plastic potential theory), and be consistent to the singular yield surface theory.