Performance of time-stepping schemes for discrete models in fracture dynamic analysis

In this work we present a critical evaluation of different time integration schemes within the setting of non-linear dynamic analysis of brittle fracture problem represented by a discrete model. The discrete model of this kind consists of Voronoi cells representing the grains of a heterogeneous structure, which are interconnected by cohesive forces modelled by beam-like links capable of taking properly into account both brittle dynamic fracture and large displacement of a still connected pack of grains that might split from the structure. The brittle behaviour of cohesive links requires that the dynamic analysis of such a model be treated with care, and the best possible integration scheme be selected. Four different schemes are explored and compared in application to a dynamic traction test, including Newmark explicit and implicit schemes, HHT- scheme and energy-decaying scheme