使用主值空间表示的各向同性塑性本构方程

THE ISOTROPIC PLASTIC CONSTITUTIVE EQUATIONS REPRESENTED IN THE PRINCIPAL SPACE

针对各向同性材料,在内变量为标量的假定下,应用张量函数表示定理给出了其塑性应变增量的不变性表示,它的3个不可约基张量取决于应力张量、相互正交且共主轴.建立3个基张量构成的张量子空间与三维主值空间的对应关系,将共主轴的张量采用笛卡尔坐标系中的矢量描述,矢量在不同坐标系下的分量均为张量的一组不可约不变量.定义塑性应变增量对应的矢量为内变量增量,使用张量函数表示理论得到,内变量演化方程除取决于应力对应的矢量和内变量本身外,还取决于应力增量在张量子空间中的投影,该投影就是应力对应矢量的增量,因此,本构方程归结为确定主值空间中矢量之间的关系.最后表明,三维主值空间与张量子空间中的流动法则是等价的.

Based on the representation theorem and the assumption that the internal variables are scalars,the general formulation of the plastic strain increment for the isotropic materials is presented in the paper. Three tensor function bases of the general formulation depend on the stresses,are mutually orthogonal and with co-principal axes. The relations between the tensor subspace defined by three tensor function bases and three dimensional principal space are established. Then, the co-principal axis tensors are described by vectors in Cartesian coordinate systems in principal space, whose components consist of irreducible invariants of the tenors. The vector associated to the plastic strain increment in principal space is defined as the internal variables. Using the tensor function representation theorem, we obtain that the evolution of the internal variables depends on the projection of the stress increment on the tensor subspace, which is the components of the increment of the vector associated to the stress tensor. Besides,the evolution also depends on the invariants of the stress and the internal variables themselves, both of which are described by the associated vectors. Therefore,the constitutive equations are revealed to be a simple relationship among vectors in the principal space. Finally,the flow rule is equivalent in the tensor subspace and in the principal space.