A comparative study on finite element methods for dynamic fracture

Abstract

The performance of finite element methods for dynamic crack propagation in brittle materials is studied. Three methods are considered: the extended finite element method (XFEM), element deletion method and interelement crack method. The extended finite element method is a method for arbitrary crack propagation without remeshing. In element deletion methods, elements that meet a fracture criterion are deleted. In interelement crack methods, the crack is limited to element edges; the separation of these edges is governed by a cohesive law. We show that XFEM and interelement method show similar crack speeds and crack paths. However, both fail to predict a benchmark experiment without adjustment of the energy release rate. The element deletion method performs very poorly for the refinements studied, and is unable to predict crack branching.

Discontinuous Cell Method (DCM) for the simulation of cohesive fracture and fragmentation of continuous media

“…A pre-notched rectangular panel is subjected to a uniform traction applied as a step function on the two edges parallel to the notch. This experiment has been simulated computationally by other authors [42,43], and related experimental results were reported by different researchers [44,45]. Ramulu and Kobayashi [44] observed experimentally that a major crack starts to propagate from the notch tip to the right, which branches into two cracks at a certain point during the experiment, see Figure 22 for the sketch of the experimental result.…”

“…A pre-notched rectangular panel is subjected to a uniform traction applied as a step function on the two edges parallel to the notch. This experiment has been simulated computationally by other authors [42,43], and related experimental results were reported by di↵erent shear strains develop leading to high principal tensile strains and crack initiation at the left side of the notch tip.…”

Dynamic fracture analysis by explicit solid dynamics and implicit crack propagation

“…This therefore makes eXtended Finite Element Method (XFEM) a more sensible choice than other approaches by bypassing the need re-mesh. To examine the applicability of the quasi-explicit CZM approach proposed here for dynamic macro-crack propagation it is compared to the following previously discussed approaches [22,23] The main difference of the approach used in this work compared to previous CZM approaches is that XFEM enrichment is used to insert a crack along a pre-defined path with a phenomenological cohesive law, meaning that the crack definition is no longer purely along element boundaries. It is anticipated that the new approach will provide further insight into the nature of modelling dynamic fracture.…”

“…The size of the geometry was considered such that the dissipated energy from the fast fracture event did not have enough time to reflect back to interact with the propagating crack before it arrested meaning the crack was purely driven by the rate-dependent fracture energy. When modelling this experiment using the quasiexplicit CZM approach, the initial material properties were chosen to be the ones used previously such that: E = 3.24 GPa, Mass Density ρ = 1190 kg/m 3 , with the Rayleigh Wave speed considered to be c r = 930 ms -1 [15,23]. The initial parameters for the cohesive law were also selected to be those used previously by Song et al and The contor stress plots for the initial notch and final crack are shown in Fig.…”

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

“…However, they show some limitations mainly related with the objectivity, computational cost and the overall ability to predict experimental tests [36]. Different alternatives have been adopted to model crack nucleation and propagation in a dynamic setting.…”