Crack propagation in elastic solids using the truss-like discrete element method

Abstract

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.

Crack propagation with adaptive grid refinement in 2D peridynamics

“…17 Comparison of the crack tip propagation speed estimated with the implemented models, 1,580 m/s is the maximum speed measured experimentally by Bowden et al (1967) from the pre-existing cracks, and a secondary fracture that is generated at the side of the plate opposite to the impacted side. A similar morphology was observed as well in references (Belytschko et al 2003;Kosteski et al 2012), as shown in Fig. 20a, b.…”

“…16 Comparison of the crack shape at time t = 50µs: a uniform coarse grid (grid size level 0), b uniform refined grid (grid size level 1), c adaptive grid Table 4 Parameter values of the crack for the implemented models Table 7. The problem is symmetric so that symmetry conditions could be used to speed up the numerical solution (Belytschko et al 2003;Kosteski et al 2012), however, our model represents the entire plate. The properties of the material are E = 190 GPa, ρ = 8,000 kg/m 3 and G 0 = 22,170 J/m 2 , plane strain conditions are assumed so that Poisson's ratio is υ = 0.25.…”

“…The case under examination has been considered by various authors: Rashid (1998) used the FEM based method called Arbitrary Local Mesh Replacement, Tabiei and Wu (2003) used the explicit FEM code Kosteski et al (2012) used the TrussLike Discrete Element Method. A rectangular plate with a lateral pre-crack and a circular hole, as shown in Fig.…”

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

“…Other alternative numerical methodologies have been addressed with some success, e.g. peridynamics [10,32], discrete methodologies such as lattice models [13] and mesh-free methodologies [1], to mention a few.…”

A hyperelastic-bilinear potential for lattice model with fracture energy conservation

“…With decreasing lattice size, the energy dissipated for crack creation approaches zero, which contradicts the reality. To address this problem, some scholars [17,[23][24][25][26] have related the bond stress-strain relationship to the macro fracture energy based on the conception of crack band [27] while others [23,28] have developed a bond rupture criterion with the consideration of fracture energy. In contrast to the incorporation of fracture energy, it has been reported that the mesh size dependency also can be relieved through consideration of statistical distributions of lattice beam strengths in [29,30].…”