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Title: Discontinuous Galerkin methods for elasticity and crack propagation problems
Author: Arranz Carreño, Aurelio
ISNI:       0000 0004 2726 441X
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
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A new set of numerical methods for predictive modelling of quasistatic and dynamic crack propagation in brittle materials for aerospace applications based upon the Symmetric Interior Penalty Galerkin Method (SIPG) and the Nonsymmetric Interior Penalty Galerkin Method (NIPG) is proposed. This new approach to solving problems in Computational Fracture Mechanics belongs to the family of Discontinuous Galerkin Finite Element Meth- ods (DGFEMs) and draws on the qualities of both the classical Finite Element Methods (FEMs) and Finite Volume Methods (FVMs) in order to overcome the shortcomings and limitations which both methods exhibit when trying to address the transition from contin- uum to discontinuum during material fracture. This thesis focuses mainly on the numerical linear algebra aspects associated with the two above DGFEM methods when applied to crack propagation problems. A new precondi- tioning technique for the iterative solution of linear systems of equations is introduced and its qualities are presented by means of numerical examples. A coupling technique with pre- conditioners for conforming approximations is also introduced. Several improvements and extensions to the original technique are presented to make crack propagation simulations with the SIPG viable. Results for both quasistatic and dynamic fracture propagation are presented. Practical aspects ofthe implementation are also discussed, revealing the important issues that still have to be addressed and that constitute paths for further research.
Supervisor: Petrinic, Nic ; Suli, Endre Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available