Dr. Safdar Abbas
Advisor / Co. Advisor
Dr. Fries / Prof. Schöberl
High Gradient XFEM for Fracture Mechanics
Safdar Abbas, M.Sc.
Aachen Institute for Advanced Study
in Computational Engineering Science (AICES)
Tel. (0241) 80 99140
Fax (0241) 80 628498
- since 11/2007 Postgraduate Position at Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen
- 10/2005 - 10/2007 Master Courses in Computational Science in Engineering (CSE), TU Braunschweig, Germany
- 03/1996 - 06/2000 Bachelor Degree in Civil Engineering, University of Engineering and Technology, Lahore, Pakistan
- 12/2001 - 08/2005 Work as a software testing engineer at Trivor Software Consultants, Islamabad, Pakistan (an offshore office of the Bentley Systems inc. USA)
High Gradient XFEM for Fracture Mechanics:
The extended finite element (XFEM) is a numerical method to simulate discontinuities and singularities. The XFEM has been mostly used in the field of fracture mechanics. Its application to fracture problems involve enriching the approximation space with appropriate enrichment functions. These enrichment functions include the a priori knowledge about the solution behavior into the approximation space. In the case of fracture mechanics, there are two solution characteristics that need to be included in the approximation space. The first is a discontinuity along the crack path. The second is the stress concentration in the near-tip region. For the discontinuity along the crack path, the approximation space is enriched by a step enrichment function. In the near-tip region, the enrichment function is based upon the asymptotic solution in that region. This dependence on the asymptotic solution makes the crack-tip enrichment function dependent on a particular fracture model. For someone who needs to concentrate on modeling issues, it becomes an additional task to create the appropriate enrichment function. Additionally in the case where fracture models with unknown analytical solutions are considered, it becomes often impossible to find the appropriate enrichment function. In this work, a model independent approach is proposed and investigated in order to find a set of model-independent enrichment functions that are valid independent of the fracture model.
- S. Abbas: "A Third Order Accurate Semi-Implicit Runge-Kutta Method for the Compressible Navier-Stokes Equations", M.Sc Thesis at the Institute of Aerodynamics and Flow Technology, DLR (German Aerospace Center), Braunschweig, October 2007.
Publications in Journals and Books
- Richard Dwight, Ursula Mayer and Safdar Abbas : High-Order Time-Accuracy using Approximate Jacobians for the Compressible Navier-Stokes Equations. Modern Techniques for Solving Partial Differential Equations, Koninklijke Vlaamse Academie van Belgie, 2008. Editors: Chris Lacor, Eli Turkel. ISBN 978-9-065-69041-8.
- S. Abbas, A. Alizada, T.P. Fries: The extended finite element method for high-gradient solutions, Proceedings of the ECCOMAS Thematic Conference on Extended Finite Element Methods (XFEM 2009) (T.P Fries, A. Zilian, Eds.), Aachen, Germany, Sep. 2009.
- S. Abbas, T.P. Fries: XFEM as an alternative for the classical h-refinement, 10th U.S. National Congress on Computational Mechanics, Columbus, Ohio, USA, July 2009.
- S. Abbas, A. Alizada, T.P. Fries: The extended finite element method for convection-dominated problems, 3rd GACM Colloquium on Computational Mechanics in Hannover, Germany, Sep. 2009.
- S. Abbas, T.P. Fries: High gradient enrichment functions for crack propagation in cohesive and cohesion-less cracks, IV European Conference on Computational Mechanics (ECCM), Paris, France, May 16-21, 2010.