We derive the second-order variation in the local static stress intensity factor of a tensile crack with a curved front. We then discuss the relevance of this result to the stability analysis of such fronts, and propose an equation of motion of planar crack fronts in heterogeneous media that contains two main ingredients--irreversibility of the propagation of the crack front and nonlinear effects.
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Adda-Bedia et al. (2006) studied this question.
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