A radial integration displacement discontinuity method with discontinuous isoparametric elements for 3D fracture simulations

Abstract

To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering problems where discontinuous surfaces such as cracks are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity values, respectively. Both of them belong to discontinuous elements, in which the geometry shape functions are different from the interpolation shape functions. The new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains hypersingular integrals which can be evaluated in the sense of Hadamard principal value. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Various numerical examples including stress intensity factor calculation are given to validate the accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the present isoparametric displacement discontinuity elements show better accuracy.