Three-dimensional brittle fracture: configurational-force-driven crack propagation

Abstract

SUMMARY This paper presents a computational framework for quasi‐static brittle fracture in three‐dimensional solids. The paper sets out the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of configurational mechanics, consistent with Griffith's theory. Resolution of the propagating crack by the FEM is achieved by restricting cracks to element faces and adapting the mesh to align it with the predicted crack direction. A local mesh improvement procedure is developed to maximise mesh quality in order to improve both accuracy and solution robustness and to remove the influence of the initial mesh on the direction of propagating cracks. An arc‐length control technique is derived to enable the dissipative load path to be traced. A hierarchical hp‐refinement strategy is implemented in order to improve both the approximation of displacements and crack geometry. The performance of this modelling approach is demonstrated on two numerical examples that qualitatively illustrate its ability to predict complex crack paths. All problems are three‐dimensional, including a torsion problem that results in the accurate prediction of a doubly‐curved crack. Copyright © 2013 John Wiley & Sons, Ltd.

Validation simulations for the variational approach to fracture

“…However, as previously noticed in the literature [31,34,10,37], we also observed that the crack path is very sensitive to small changes in geometry and loading, or to changes in the regularization parameter . Figure 19 shows changes in the final fracture geometry (isovolume renderings of the fracture field 0.9 ≤ α ≤ 1.0) and the final deformed geometry for three different values of .…”

“…We finally focussed our attention on a fully three-dimensional problem initially presented in [24] and previously investigated in a number of articles [31,34,10,37]. The Brokenshire test consists of a specimen with a 45 • oblique notch subject to a torsional load (see Figure 17 for a schematic description of the domain geometry).…”

High-fidelity prediction of crack formation in 2D and 3D pullout tests

“…Later, Areias and Belytschko [21] and Duan et al [58] studied it using extended finite elements. Recently, Kaczmarczyk et al [59] solved the problem with a configurational mechanics method, consistent with Griffith's theory.…”

Stochastic modelling of crack propagation in materials with random properties using isometric mapping for dimensionality reduction of nonlinear data sets

“…Cohesive crack methodology has been widely used by many researchers for stochastic analyses of fracture propagation, eg, in which cohesive elements are inserted between element edges. If crack paths are unknown a priori, local r‐adaptivity and mesh‐realignment techniques are required to resolve mesh dependency issues . This can lead to high computational cost, particularly if Monte Carlo (MC) simulation approach is employed.…”

“…If crack paths are unknown a priori, local r-adaptivity and mesh-realignment techniques are required to resolve mesh dependency issues. 13 This can lead to high computational cost, particularly if Monte Carlo (MC) simulation approach is employed.…”