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

Abstract

SummaryA 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.