Energy minimizing multi-crack growth in linear elastic fracture using the extended finite element method
Danas Sutula  1@  , Stephane Bordas  1, 2@  , Pierre Kerfriden  1@  
1 : Cardiff University School of Engineering  (Cardiff ENGIN)
The Parade, CF243AA, Cardiff, UK -  United Kingdom
2 : Université du Luxembourg  (  -  Website
Université du Luxembourg 6 rue Richard Coudenhove-Kalergi L-1359 Luxembourg -  Luxembourg

We investigate multiple fracture evolution under quasi-static conditions in an isotropic linear elastic solid based on the principle of minimum total energy, i.e. the sum of the potential and the fracture surface energies. The technique, which has been implemented within the extended finite element method, enables minimization of the total energy of the mechanical system with respect to all crack increment directions. This is achieved by finding the orientations of the discrete crack-tip extensions that yield vanishing rotational energy release rates about their roots. Comparisons of the classic maximum hoop-stress criterion with the energy minimization approach via a multitude of numerical studies shows that both criteria converge to the same fracture path albeit from different directions. Thus, it is found that the converged fracture path solution lies in between those obtained by each criterion for coarser meshes. Upon further investigation of the energy minimization approach within the discrete framework, it is found that fracture increments favor the direction of a vanishing mode-II deformation in the post-incremented crack-tip orientation. Contrasting this solution with the maximum-hoop stress criterion, which is based on the vanishing mode-II deformation of the incipient crack-tip extension, it is possible to propose a modified crack growth direction criterion that assumes the average direction between those obtained by the aforementioned criteria. The numerical results show significant improvements in accuracy and convergence rates of the fracture paths, as found from over 10 numerical examples.

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