A hybridized displacement discontinuity method for mixed mode I–II–III loading

Abstract

Abstract A new hybridized displacement discontinuity numerical method is presented. The existing code FROCK is modified to incorporate loading mode III, and thus have a fully coupled solution for mixed mode I–II–III loading. The new code can be applied to homogeneous elastic bodies with small scale yielding and to cracks where one of the dimensions is much larger than the other two. The code combines both displacement discontinuity (DD) and stress discontinuity (SD) elements. DD elements are characterized by a jump of the displacement field across the element, while SD elements show a stress jump. DDEs are very well suited to model cracks inside of a body, and SDEs for the boundaries of the body. A new set of DDEs and SDEs is developed which incorporate mode III loading. For open elements, loading modes I and II are coupled, but they are independent of mode III. For closed elements, friction may develop along the surface of the elements. Friction depends on the normal stress and on the shearing (mode II) and tearing (mode III) stresses, and thus the solution is fully coupled. Hence the problem is non-linear and iterations are needed to achieve convergence. The new code FROCK is verified by a number of comparisons with analytical solutions and with other numerical methods. A new analytical solution to obtain stress intensity factors for closed cracks in mode II–III is also presented and validated.