Bifurcating initiation and evolution of periodic micro-defects

The following two phenomena observed in torsional shear experiments are str udied in this paper: (1) micro-defects are periodically initiated under uni form loading; and (2) the alternative evolution of periodic micro-defects o ccurs when they uniformly grow to some extent. Micro-defects are modeled as concentrated strain and suitable boundary value problems are posed for the se initiation and evolution processes. With the aid of the equivalent inclu sion method, the existence of bifurcated solutions is presented in a transp arent manner, and the stability of these solutions are examined. It is show n that such unstable bifurcated solutions correspond to the phenomena obser ved in the experiments. Variational problems corresponding to the boundary value problems are formulated and the bifurcation and stability analyses us ed for the boundary value problems are presented in a more general manner. (C) 2000 Elsevier Science S.A. All rights reserved.