Element breaking rules in computational models for brittle fracture

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Abstract
The performance of spring-network and finite-element methods for fracture is studied with respect to their ability to model crack propagation in an isotropic, two-dimensional, linearly elastic, and ideally brittle material. Element breaking rules based on critical energy or stress, coupled with a length scale characteristic of the mesh, result in Griffith scaling of fracture strength with crack length. For finite-element methods, the scaling works for surprisingly small cracks: two to three element lengths. Regular meshes of springs or finite elements are highly anisotropic with respect to crack propagation. Random meshes obviate this problem. However, for spring networks they introduce significant randomness in the distribution of forces, and for both methods they introduce some randomness in the strength-crack size scaling. For finite-element methods, element breaking based on energy can lead to unexpected crack propagation modes; rules based on maximum principal stress in an element are more robust. These breaking rules lead to an artificially low stress for crack nucleation so that different breaking rules are required for elements at the tip of a propagating flaw and those away from it.