Bifurcating initiation and evolution of periodic micro-defects

The following two phenomena observed in torsional shear experiments are strudied in this paper: (1) micro-defects are periodically initiated under uniform loading; and (2) the alternative evolution of periodic micro-defects occurs when they uniformly grow to some extent. Micro-defects are modeled as concentrated strain and suitable boundary value problems are posed for these initiation and evolution processes. With the aid of the equivalent inclusion method, the existence of bifurcated solutions is presented in a transparent manner, and the stability of these solutions are examined. It is shown that such unstable bifurcated solutions correspond to the phenomena observed in the experiments. Variational problems corresponding to the boundary value problems are formulated and the bifurcation and stability analyses used for the boundary value problems are presented in a more general manner.