3D Crack growth simulation - Kolk, Karsten; Kuhn, Günther (Proceedings of the 2nd European Conference on Computational Mechanics, 2001)
UnivIS-Import:2015-04-16:Pub.2001.tech.FT.FT-TM.3dcrac

Acceleration of 3D crack propagation simulation by the utilization of fast BEM-techniques - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Engineering Analysis With Boundary Elements, 2009)
For the acceleration of the 3D simulation of fatigue crack propagation fast BEM techniques are combined in the present paper. The so-called dual BEM is utilized to separate the coincident crack surfaces. In the present context, the relevant boundary integral equations are evaluated in the framework of a collocation procedure. For the reduction of the numerical complexity of the stress analysis fast BEM techniques are applied. The domain is decomposed in order to obtain a band-structured system matrix. The crack is modeled in terms of the dual discontinuity method. Therewith, the relevant boundary of the domain is reduced by one crack surface. Finally, the adaptive cross approximation, an algebraic matrix compression technique, is utilized to compress the system matrix. The efficiency of this procedure is shown on complex industrial applications. © 2009 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.bem
Keywords: 3D dual BEM; Adaptive cross approximation (ACA); Domain decomposition; Dual discontinuity method (DDM)

Advanced simulation of 3D fatigue crack growth by a predictor-corrector procedure considering 3D singularities - Kolk, Karsten; Kuhn, Günther (Proceedings of the 11th International Conference of Fracture, 2005)
An advanced incremental algorithm for the simulation of 3D fatigue crack growth in the framework of linear elastic fracture mechanics is addressed to this paper. The simulation is based on an accurate stress analysis, which is performed by the 3D dual boundary element method (Dual BEM). The utilized fracture mechanics parameters are the stress intensity factors (SIFs) and the so-called T-stresses. They are extracted from the numerical crack near-field by an optimized extrapolation and regression algorithm providing very precise values of both parameters. To answer the still open question concerning a reliable 3D crack growth criterion a predictor-corrector procedure is implemented. This concept is capable of mode-I and three-dimensional mixed-mode conditions. As part of the proposed scheme, 3D corner singularities are considered. They appear especially at the intersection of the crack front and the free surface. Based on these known asymptotic exponents, it is advantageous that the crack front angle is adjusted at such intersection points ensuring a valid square-root singularity and therefore a bounded energy release rate. As a result, the shape of the numerical crack front matches experimentally observed crack fronts locally. After applying a certain number of corrector steps assuming a constant distribution of the energy release rate along the whole crack front a global matching occurs. Finally, a sophisticated re-meshing algorithm updates the numerical model automatically for the next increment.
UnivIS-Import:2015-04-16:Pub.2005.tech.FT.FT-TM.advanc

A Predictor - Corrector Procedure for the Determination of the Shape of 3D Crack Fronts - Kolk, Karsten; Kuhn, Günther (Proceedings of the Fifth World Congress on Computational Mechanics, 2002)
UnivIS-Import:2015-04-16:Pub.2002.tech.FT.FT-TM.apredi
Keywords: 3D crack growth; Dual BEM; stress intensity factor; 3D singularities

Efficient crack growth analyzes by combining fast methods for BEM - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Proceedings of the 77th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.effici

Fast 3D crack growth analyses by the combination of fast BEM techniques - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Proceedings of the 17th International Conference on Computer Methods in Mechanics, 2007)
UnivIS-Import:2015-04-16:Pub.2007.tech.FT.FT-TM.fast3d

Investigation of 3D crack propagation problems via fast BEM formulations - Kuhn, Günther; Weber, Wilhelm; Kolk, Karsten (Computational Mechanics, 2005)
The simulation of 3D fatigue crack growth is investigated and in combination with suitable experiments it is aimed to identify a reliable crack growth criterion. To perform the crack growth simulation as effectively as possible the boundary element method (BEM) in terms of the 3D Dual BEM is utilized. The relevant boundary integral equations are evaluated in the framework of a collocation procedure. To compress the system matrix and to speed-up the solution procedure the adaptive cross approximation (ACA) method is applied. It is an algebraic technique acting purely on the system matrix itself. The efficiency of this procedure with respect to crack problems will be shown on both a standard fracture specimen and an industrial application. © Springer-Verlag 2005.
UnivIS-Import:2015-03-09:Pub.2005.tech.FT.FT-TM.invest
Keywords: 3D Crack growth; 3D Dual BEM; ACA; Low-rank approximation

On the solution of the 3D crack surface contact problem using the boundary element method - Weber, Wilhelm; Kolk, Karsten; Willner, Kai; Kuhn, Günther (Key Engineering Materials, 2011)
The efficient solution of the 3D crack surface contact problem utilizing the boundary element method (BEM) is presented. The dual discontinuity method (DDM), a special formulation of the BEM, is applied. This method deals directly with the relative displacements and the discontinuities of the tractions at the crack. For the normal behavior a unilateral contact is assumed and for the description of the tangential behavior Coulomb's frictional law is utilized. The hard contact formulation is regularized by the application of the penalty method. An incremental iterative procedure based on a radial return mapping algorithm is applied for the solution of this non-linear problem. Based on the stress field the fracture mechanical parameters are determined by an extrapolation method for all increments of a characteristic load cycle. By the analysis of this load cycle the cyclic fracture mechanics values are obtained. Due to the non-linear nature of crack growth the simulation is implemented in the framework of a predictor-corrector scheme. For the investigation of the influence of the crack surface roughness on the behavior of cracks two numerical examples are presented. © 2011 Trans Tech Publications.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.onthes
Keywords: Crack surface contact; Dual boundary element method; Dual discontinuity method; Fatigue crack propagation