A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

Abstract

Please cite this article as: Nejati, M., Paluszny, A., Zimmerman, R.W., A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes, International Journal of Solids and Structures (2015), doi: http://dx.doi.org/10. 1016/j.ijsolstr.2015.05.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes Abstract A novel domain integral approach is introduced for the accurate computation of pointwise Jintegral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2 − 3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics

“…This inaccuracy may not influence the SIF computation when energy methods such as the J-integral are employed. This is because these methods rely on an integration over a domain, which reduces the influence of local numerical inaccuracies on the SIF computation (Nejati et al, 2015). However, the SIF values may be considerably influenced by the local numerical inaccuracies when local displacements are used in a displacement correlation scheme.…”

“…A displacement correlation (DC) scheme is also proposed to compute very good approximations of the SIFs from unstructured meshes. The authors have recently developed a domain integral approach which computes SIFs with an average error of about 1% (Nejati et al, 2015). The results from both DC and domain integral methods provide considerable evidence on the reliability, efficiency and accuracy of the unstructured meshes by tetrahedral elements for analyzing cracked bodies.…”

Modelling of primary fragmentation in block caving mines using a finite-element based fracture mechanics approach

“…However, as the density of fractures increases, the complexity of the generation of such a structured mesh also increases. A virtual integration technique avoids the need of a structured mesh by using an artificial 'virtual' mesh to integrate around the tips, using a 'virtual' cylinder (Cervenka and Saouma 1997;Paluszny and Zimmerman 2011) or a 'virtual' disk (Nejati et al 2015b). When aided by isoparametric quadratic elements (Daimon and Okada 2014) and with the quarter-point optimisation (Nejati et al 2015a), this technique allows swift and accurate computation of stress intensity factors on unstructured tetrahedral meshes.…”

“…When aided by isoparametric quadratic elements (Daimon and Okada 2014) and with the quarter-point optimisation (Nejati et al 2015a), this technique allows swift and accurate computation of stress intensity factors on unstructured tetrahedral meshes. The integration yields high quality solutions when the integration domain radius approximates the mesh size around the fracture (Nejati et al 2015b). Thus, the use of quarter-point quadratic tetrahedra around the fracture front in combination with the virtual technique allows the use of coarse, unstructured tetrahedral meshes for growth computations.…”

“…Thus, the use of quarter-point quadratic tetrahedra around the fracture front in combination with the virtual technique allows the use of coarse, unstructured tetrahedral meshes for growth computations. In this work, the disk virtual integration technique is used to compute the interaction integral [see details and equations in Nejati et al (2015b)], which allows the independent computation of K I , K II , and K III along the fracture tips.…”