The Multipole Method (MPM) is used to simulate the many-body self-consistent problem of interacting elliptical micro-cracks and inclusions in single crystals. A criterion is employed to determine the crack propagation path based on the stress distribution; the evolution of individual micro-cracks and their interactions with existing cracks and inclusions is then predicted using what we coin the Discrete Crack Dynamics (DCD) method. DCD is fast (semi-analytical) and particularly suitable for the simulation of evolving low-speed crack networks in brittle or quasi-brittle materials. The method is validated against finite element analysis predictions and previously published experimental data.
Ebrahimi, M. T., Dini, D., Balint, D. S., Sutton, A. P., & Ozbayraktar, S. (2018). Discrete crack dynamics: A planar model of crack propagation and crack-inclusion interactions in brittle materials. International Journal of Solids and Structures, 152–153, 12–27. https://doi.org/10.1016/j.ijsolstr.2018.02.036