Modeling Wing Crack Extension: Implications for the Ingredients of Discrete Element Model

In this study, we investigate what basic mechanisms a Discrete Element Model should have in order to reproduce the realistic wing crack extension, a widely observed phenomenon in uni-axial compression of brittle material with pre-existed crack. Using our Discrete Element Model—the Lattice Solid Model, we study how cracks propagate when different force-displacement laws are emplyed. Our results suggest that the basic features of crack propagation observed in laboratories cannot be reproduced under the following circumstances: 1) When only normal forces between two bonded particles exist and particle rotation is prohibited; 2) normal and shear stiffnesses are present and particle rotation is prohibited; 3) normal, shear stiffnesses and particle rotation are present and bending (rolling) stiffness is absent. Only when normal, shear and bending stiffness exist and particle rotation is permitted, is it possible to reproduce laboratory tests. We conclude that particle rotations and rolling resistance play a significant role and cannot be neglected while modeling such phenomenon. The effects of friction in the crack plane and confining pressure on extension of the cracks are also discussed.