THE DISCRETE ELEMENT METHOD FOR ANALYSIS OF FRAGMENTATION OF DISCONTINUA

Abstract

This paper is concerned with the determination of the transient stress and deformational state of plate‐like discontinua subject to flexural cracking. Such a phenomenon can be easily visualized as the type of fragmentation to floating sea ice impacted by an ice‐breaker or offshore platform. The discrete element method is used to solve the dynamic equilibrium equations for each distinct deformable body and the interaction between bodies. Each body may deform elastically and fracture into further pieces if a brittle failure criterion for flexure is exceeded. The discrete plate element is a hybrid thin‐plate (Kirchhoff) mode lumped at element boundaries with transverse shear deformation computed at element centroids. Errors in computed stresses near point loads and cracks by the current element warrant the use of an improved mixed mode plate element. A three‐dimensional application of the discrete element method is presented for the case of fragmentation of floating sea ice impacting an arctic offshore platform. A semi‐implicit solution scheme is introduced to overcome the stringent explicit time step stability conditions due to stiff members in the discrete element formulation.