Elastic compliances of non-flat cracks

Cracks of non-flat geometries are common in materials science applications. Their effect on the overall elastic properties is addressed. Applications of Rice’s [Rice, J.R., 1975. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In: Argon, A. (Ed.), Constitutive Equations in Plasticity, MIT Press, pp. 23–75.] theorem that, in particular, relates stress intensity factors to crack compliances, are discussed and illustrated by a 2-D example of a circular arc crack. Then we conduct computational studies of several non-flat patterns and suggest a simple approximation for compliances of non-flat cracks. Implications for anisotropy due to non-random orientation distributions of cracks of non-flat geometries are discussed.