## Performance of time-stepping schemes for discrete models in fracture dynamic analysis.(English)Zbl 1112.74065

Summary: We present a critical evaluation of different time integration schemes within the setting of nonlinear 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 must be performed with care, and the best possible integration scheme must be selected. Four different schemes are explored and compared in application to a dynamic traction test, including Newmark explicit and implicit schemes, HHT-$$\alpha$$ scheme and energy-decaying scheme.

### MSC:

 74S20 Finite difference methods applied to problems in solid mechanics 74R10 Brittle fracture

### Keywords:

Voronoi cells; Newmark schemes; energy-decaying scheme
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### References:

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