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 引用本文: 陈明祥. 各向同性率无关材料本构关系的不变性表示[J]. 力学学报, 2008, 40(5): 629-635.
Invariant tensor function representations of constitutive equations for the isotropic and rate independent materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 629-635.
 Citation: Invariant tensor function representations of constitutive equations for the isotropic and rate independent materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(5): 629-635.

## Invariant tensor function representations of constitutive equations for the isotropic and rate independent materials

• 摘要: 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.

Abstract: This paper combines the internal variable theory and thetensor function representation theory to establish the constitutiveequations of the deformation theory and the increment theory for theisotropic and rate independent materials. In the equations, there are threecomplete and irreducible base tensors, that is, the stress tensor of thezero order, the first order and the second order power, to show that theprincipal axes of plastic strain and its increment are coincident with thoseof the stresses. With the orthogonalization of the base tensors, thegeometrical explanation of the constitutive equations is obtained in theprincipal stress space. Furthermore, the coefficients in the constitutiveequations of deformation theory (or increment theory) can be derived withthree invariants of stresses and plastic strain ( or plastic strainincrements). Meanwhile, the present constitutive equations may reduce toclassical deformation theory (or plastic potential theory), and beconsistent to the singular yield surface theory.

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