R. Brighenti et alii, Frattura ed Integrità Strutturale, 34 (2015) 80-89; DOI: 10.3221/IGF-ESIS.34.08 88 A discrete approach can replace the traditional continuous modeling of solids, allowing to examine complex phenomena such as failure, fracture, contact and interaction with other bodies, by also taking into account large strain and dynamic effects. 0 0.0002 0.0004 0.0006 Time, t (s) -200 -150 -100 -50 0 50 100 Vertical reaction, R z (kN) ref. [27] Pres. res. v 0 (m/s) 2 4 6 8 No. 3366 particles No.5551 particles Figure 5 : (a) Elastic wave propagation and (b) failure pattern for the case 0 2 / v m s . (c) Time history of the reaction force at the beginning of the impact phenomenon for 0 2, 4, 6, 8 / v m s from the present model. (d) FE crack path reported in [26]. In the present study, a particle method – based on the description of the forces between discrete elements evaluated on the basis of a force potential – has been proposed. It has been emphasized that the formulation applies without changes to problems involving granular materials or solids interacting with granular materials. The above approach has been applied to the simulation of different problems dealing with the 3D fracture and failure of both granular materials and compact solids. The formulated discrete method shows a wide capability to deal with different complex mechanical problems by properly describing the evolution of the crack pattern under dynamic conditions. R EFERENCES [1] Cundall, P.A., Strack, O.D.L., A discrete numerical model for granular assemblies. Geotechnique, 29(1) (1979) 47–65. [2] Oñate, E., Particle-Based Methods: Fundamentals and Applications. Springer Science & Business Media, (2011). [3] Liu, B., Huang, Y., Jiang, H., Qu, S., Hwang, K.C., The atomic-scale finite element method. Comput. Methods Appl. Mech. Engng., 193 (2004) 1849–1864. [4] Krivtsov, A., Molecular dynamics simulation of impact fracture in polycrystalline materials, Meccanica, 38 (2003) 61- 70. [5] Onate, E., Idelson, S.R., Del Pin, F., Aubry, R., The particle finite element method. An overview. Int. J. Comput. Meth., 1 (2004) 267–307. (a) t = 4 4.2 10 s (b) t = 0.125 s (d) (c)

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