A multi-cracked particle method for complex fracture problems in 2D

Abstract

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Adaptive configurational force‐based propagation for brittle and fatigue crack analysis

“…The final numerical example is the tearing of a cantilever beam containing a tree crack with 8 crack tips, which is used to demonstrate that the proposed algorithm is able to deal with numerous fractures propagating at different rates. This problem is similar to that analyzed by Bird et al, 39 Ai and Augarde, 78 and Ai 76 but there are some key differences in terms of the applied boundary conditions. The geometry of the problem is shown in Figure 17A, where L = 20 m, H = 4 m, a = 1 m, b = 0.5 m, and 𝜃 = 𝜋∕4 (note that the crack has been enlarged within the beam for clarity).…”

“…It is worth highlighting that other researchers have analyzed the same crack geometry but with spurious results as their applied loading causes some cracks to close and overlap as they do not enforce contact conditions on the crack faces. 76,78 In order to analyses this problem it is necessary to include Paris' law 79 so that the various cracks propagate at a rate consistent with the stress intensity at each of the crack tips. The Paris law crack growth rate is defined as where a is the crack length, N is the number of load/stress cycles, and C and m are the Paris law material constants set to 1 and 2 respectively.…”

A state-of-the-art review of crack branching

“…To solve the spurious cracking problems which appear in the original CPM [75], Ai and Augarde [99] improved the crack path curvature modelling through bilinear segments with consideration of cracking angle changes at particles, which allows crack kinks inside a particle. The model was further improved by the so-called "multi-cracked particle method" [100],…”

Thermoelastic fracture modelling in 2D by an adaptive cracking particle method without enrichment functions

“…This will be shown to work satisfactorily later in the paper. The CPM was originally presented by Rabczuk and Belytschko (2004) [35] and has since been applied to model 3D cracks [36][37][38], dynamic fracture [39], ductile fracture [40], shear bands [41,42] and multiple cracks [43]. Here the CPM is applied to thermoelastic fracture problems, where only the adiabatic crack is studied since there is little difference in the visibility criterion process for checking connectivities of particles between the adiabatic and isothermal situations.…”