FRACTURE UNDER COMPRESSION - THE DIRECTION OF INITIATION

The preferential orientation for the initiation of a crack is the one which gives the maximum strain energy reduction for a given crack leng th. This proposed criterion is a logical extension of the maximum ener gy release rate criterion. It makes no assumptions on the configuratio n, the homogeneity, the stress condition on the crack faces, or the ma terial response, consequently it is applicable to the usual engineerin g cases as well as to cases under compression and/or high confining pr essures such as obtain inside the Earth. Numerical results for brittle materials (rocks) agree with laboratory and field data, and show that the criterion is an improvement over the empirical and approximate Co ulomb-Mohr criterion which has been used for compressive fracture prob lems for more than 200 years. They also show that our method can be us ed in cases where it is not a priori evident whether the fracture will remain closed or will open. The mathematical formulation of the crite rion is approached by way of constrained optimization, and the solutio n is proven to exist uniquely. The numerical implementation is based o n a finite element scheme. An iterative method is employed to handle t he material and geometric non-linearities.