Growth instabilities in mechanical breakdown

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Abstract
A linear stability analysis of a circular crack growing in an elastic medium in two dimensions is presented. Two boundary conditions at the outer boundary are considered, namely, a constant strain and a constant pressure. Size effects are included by assuming a finite distance between the inner and the outer boundaries. If the outer boundary is placed at infinity, the result for the ratio between the instantaneous rates of growth of the perturbation and that of the circular crack is twice that obtained for growth in fields governed by the Laplace equation (diffusion or electrostatic fields) no matter which of the two boundary conditions is imposed. This result is in line with the smaller fractal dimensions obtained in the case of mechanical breakdown.

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