ON THE MEAN ROTATION TENSORS

In this paper, we criticize a serious essential defect of the famous C auchy's measure of mean rotation of a deformable body formulated by Zh eng and Hwang (1988, Chinese Sci. Bull. 33, 1705-1707; (English transl ation, 1989) 34, 897-901; 1992, ASME J. Appl. Mech. 59, 505-510). A nu mber of mean rotation tensors are proposed, which are prime generaliza tions of Cauchy's mean rotation and avoid the defect of the latter. In this frame, several new significant geometrical meanings of the finit e rotation tensor Q in the polar decomposition of the deformation grad ient F are revealed. The so-called large rotation tensor R(w), as a qu ite natural generalization of the infinitesimal rotation tensor (W = F - F(T))/2, is introduced and is a very good approxmation of Q in the case of small or moderate strain accompanied by large rotation. A shor t discussion on the rates of mean rotation, the role of Q in constitut ive equations, and the effect of choosing a reference configuration is provided. Finally, we investigate the global measures of mean rotatio n and the global kinetic equations of a finite deforming body.