自旋张量的绝对表示及其在有限变形理论中的应用

ON THE INVARIANT REPRESENTATION OF SPIN AND ITS APPLICATION IN FINITE DEFORMATION THEORY

基于对一类线性张量方程的一般解法,导出了任一对称张量所对应的自旋张量的绝对表示。该结果可以很自然地用于研究左和右伸长张量的自旋并研讨在连续介质力学中常见到的各种转动率张量间的关系。一个重要的公式,即Hill意义下广义应变的共轭应力和Cauchy应力之间的关系,从功共轭原理建立了起来。尤其是详细讨论了对数应变的时间变率及相应的共轭应力。无疑,上述结果对有限变形条件下本构理论的研究是颇为重要的。

Based on the general solution of a kind of linear tensorial equations, the invariant representation of the spin of a symmetric tensor is obtained. This expression is used to study the spin of right and left stretch tensors and to discuss the relations between the different rotation rate of tensors encountered in finite deformation theory. According to the work conjugate principle, a representation of the stress conjugate to Hill's generalized strain is derived. As an important example, the rate of logarithmic strain and its conjugate stress are obtained in an invariant form. These formulas might play an important role in construction of the constitutive relations in finite deformation theory.