张量和张量率的投影算子

Projection operators of rank-two tensor and rate tensor

通过对张量谱分解方法的深入研究,提出了一种对于张量正、负分解在表达形式上统一的投影算子,并建议了一类投影算子的统一格式,指出Ortiz算子、Simo-Ju算子和新算子均为该统一格式的特例,澄清了已有研究在此问题上的混淆之处。对于上述三种投影算子及建议的统一格式,还给出了相应张量率惟一的投影算子,该算子同时是张量和相应张量率的公共投影算子。最后指出了投影算子的微观力学意义及各表达式可能的适用范围,并给出了投影算子在描述混凝土单边效应上的本构建模应用。

Upon the systematical research on the spectral decomposition of tensor, new expressions for the projection operators of rank-two tensor, uniform for both the positive one and the negative one, are proposed in this paper. Then the unified expressions for the projection operators are presented to include the Ortiz＇s ones, the Simo-Ju＇s ones and the proposed ones as its special cases, clarifying the existing ambiguities in the literature. The unique expressions for the projection operators of the corresponding rate tensor, which are the shared ones of both the rank-two tensor and its rate tensor, are provided as well. Finally the micromechanical meanings are pointed out, and the application in modeling the unilateral effect of concrete is illustrated.