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

Abstract

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.

Micromechanics of wing crack propagation for different flaw properties

“…Experimentally, it is difficult to generate closed flaws with controlled properties [9], but some results suggest similar crack propagation patterns from open or closed flaws [9,6,4]. Closed flaws were simulated in DEM in 2D [32] and in 3D [33], with, however, contradictory conclusions regarding the numerical requirements for wing crack simulations. This will be discussed in section 5.2, considering different approaches to model closed flaws.…”

Meso-mechanical analysis of deformation characteristics for dynamically triggered slip in a granular medium

“…We notice that the choice here of linear elastic springs was motivated by computational simplicity and evidence from previous studies that this type of elastic bond already allows for capturing the most relevant mechanical features of both regular and irregular lattices of bonded particles, including fracture phenomenology [33][34][35][36]. In Equation (1), K r ¼ 2.9775 Á 10 7 is the radial compressional/tensional spring stiffness.…”

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

“…In DLSM, only tensile and shear springs are incorporated. However, Wang and Mora conducted the simulation on the same geometry (refer to Figure C) and concluded that the correct path cannot be reproduced without considering particle rotation in their Lattice Solid Model, which resulted in the situation that the cracks “grow slowly and discontinuously, and several en echelon cracks appear” . The correct path can only be reproduced when normal, shear stiffness, bending stiffness, and single particle rotation are all included in their models.…”

“…(B) DLSM simulation. (C) LSM simulation without particle rotation from Wang and Mora [Colour figure can be viewed at wileyonlinelibrary.com]…”