The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on L. Kosteski (B) · I. Iturrioz Pos-Graduate Program in Mechanical Engineering different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out.

Purpose -The purpose of this paper is to further develop the truss-like discrete element method (DEM) in order to make it suitable to deal with damage and fracture problems. Design/methodology/approach -Finite and boundary elements are the best developed methods in the field of numerical fracture and damage mechanics. However, these methods are based on a continuum approach, and thus, the modelling of crack nucleation and propagation could be sometimes a cumbersome task. Besides, discrete methods possess the natural ability to introduce discontinuities in a very direct and intuitive way by simply breaking the link between their discrete components. Within this context, the present work extends the capabilities of a truss-like DEM via the introduction of three novel features: a tri-linear elasto-plastic constitutive law; a methodology for crack discretization and the computation of stress intensity factors; and a methodology for the computation of the stress field components from the unixial discrete-element results. Findings -Obtained results show the suitability and the performance of the proposed methodologies to solve static and dynamic crack problems (including crack propagation) in brittle and elasto-plastic materials. Computed results are in good agreement with experimental and numerical results reported in the bibliography. Research limitations/implications -This paper demonstrates the versatility of the truss-like DEM to deal with damage mechanics problems. The approach used in this work can be extended to the implementation of time-dependent damage mechanisms. Besides, the capabilities of the discrete approach could be exploited by coupling the truss-like DEM to finite and boundary element methods. Coupling strategies would allow using the DEM to model the regions of the problem where crack nucleation and propagation occurs, while finite or boundary elements are used to model the undamaged regions. Originality/value -The scope of the truss-like DEM has been extended. New procedures have been introduced to deal with elastoplastic-crack problems and to improve the post processing of the stress results. IntroductionDuring the 1960s an alternative set of computational methods that do not use a set of differential or integral equations to describe the problem were introduced. Depending on the individual element introduced, such as particles, agents or molecules, methods such as molecular dynamics, discrete element method (DEM), discontinuous deformation analysis, and similar were invented. In the process, computational mechanics of discontinua emerged, and its is now an integral part of cutting edge research in nanotechnology and industrial processes spanning over diverse fields as mining, milling, pharmaceuticals, powders, ceramics, composites, blasting, construction, etc. (Munjiza, 2009).The numerical simulation of fracture and damage problems is always an active research topic. Finite and boundary element methods (BEMs) are the best developed methods in this field (Anderson, 2005;Aliabadi and Rooke, 1991...

A B S T R A C T The prediction of the response of reinforced concrete structures subjected to projectiles impact still presents open questions. These include the rate dependence of material properties, the interaction between concrete and steel reinforcement and the simulation of fracture and fragmentation. Because the appearance of discontinuities in the target structure is difficult to account using a continuum approach, the application of discrete models was developed as an appealing alternative. A version of the discrete model in which nodal masses are linked by an array of uniaxial elements, herein called discrete element method, is used in this study. This method was implemented in the system Abaqus to take advantage of its numerical and post-processing capabilities. A reinforced concrete rectangular plate subjected to impact of a projectile is examined in detail. Comparisons between experimental and numerical results are shown with the aim of validating the proposed method.Keywords hard impact; numerical simulation; reinforced concrete plate; truss-like discrete element method. N O M E N C L A T U R E a = side length of plate A d = area of diagonal elements A d * = equivalent fracture areas of diagonal elements A l * = equivalent fracture areas of longitudinal elements A n = area of normal elements B = coefficient that depends on the boundary conditions and the vibration mode c = volume concentration of the second phase composite C = damping matrix c A = scaling parameter CV = coefficient of variation E = Young's Modulus f duc = function to account for steel-concrete interaction F → r t ð Þ = vector of internal forces acting on the nodal masses G f = specific fracture energy L = length of the element L r = distance to the surrounding steel reinforcement M = mass matrix → P t ð Þ = vector of external forces t = the thickness of plate t = time V = velocity → _ x = velocity vector of generalized nodal masses Correspondence: L. E. Kosteski.

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