Three‐dimensional elastic analysis of cracks with the g2 constant displacement discontinuity method

Abstract

Summary A new triangular element was created that could be used for the improvement of the accuracy of the constant displacement discontinuity method (CDDM). This element is characterized by three degrees of freedom in the three‐dimensional space as in the classical CDDM approach. The element is based on strain gradient elasticity theory that accounts for the difference of the average value of stress with the local stress at surfaces with large curvature (eg, crack borders, corners, and notches) in elastic bodies. The new element is characterized by a strain gradient term in addition to the two Lamè constants that gives a more representative value of the stresses at the centroid of crack edge elements compared with the classical elasticity solution and thus an accurate stress intensity factor. In this approach, special crack border elements with square‐root radius dependent displacements and numerical integrations are avoided. The extra strain gradient term is calibrated once only on the analytical solution for the penny‐shaped crack. In a verification stage, the accuracy of the computational algorithm for the elliptic and rectangular crack problems is demonstrated. Then, the algorithm, which also accounts for crack closure in compression, is applied for the modeling of crack propagation and crack interaction in uniaxial tension and compression loading. It is illustrated that the numerical predictions are in accordance with experimental evidence pertaining to uniaxial compression of transparent precracked specimens in the lab.

An Experimental Investigation on the Foliation Strike-Angle Effect of Layered Hard Rock under Engineering Triaxial Stress Path

“…Nevertheless, significant attention has been devoted to investigating the mechanical properties of these rocks during loading and unloading [18]. Previous studies have highlighted that the deformation and failure behavior of layered rocks under loading and unloading conditions are noticeably influenced by the orientation of foliation [22][23][24]. However, a scarcity of research persists concerning the specific loading-unloading stress-path effect on layered rocks, particularly under true triaxial stress conditions.…”

“…The lack of true triaxial testing conditions has led to a predominant focus on the dip angle's influence in conventional triaxial studies concerning the anisotropy of layered rock formations. These studies specifically explore the foliation angle within the maximum and minimum principal stress planes [22][23][24]. However, what has been overlooked in these investigations is the influence of the foliation strike angle in space, which pertains to the angle within the intermediate and minimum principal stress planes.…”

An Anisotropic Damage Model of Quasi-Brittle Materials and Its Application to the Fracture Process Simulation

“…With the development of computer technology and numerical computation, numerical simulations have been gradually used to study failures. A range of methods and models have been proposed to simulate the initiation and propagation of cracks, such as the traditional finite element method [9][10][11][12][13], discrete element method [14][15][16][17][18], extended finite element method [19][20][21], boundary element method [22][23][24], displacement discontinuity method [25][26][27][28][29], etc. The most popular ones are the finite element method and discrete element method.…”