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Mit Extended Finite Elements und Moleküldynamik
: Lenzen, C.
:
Volltext urn:nbn:de:0011n647543 (2.1 MByte PDF) MD5 Fingerprint: ea8cb3f3280fb0d53c9c7cf821164069 Erstellt am: 10.1.2008 
 Bonn, 2007, 141 S. Bonn, Univ., Dipl.Arb., 2007 

 Deutsch 
 Diplomarbeit, Elektronische Publikation 
 Fraunhofer SCAI () 
Abstract
Cracks are of paramount importance in applied science whenever material failure occurs. On the one hand prediction and detection of defects are of major interest, on the other hand further understanding of crack propagation is needed. The mechanisms at the crack front are gouverned by atomistic length and time scales, limiting the possibilities for experimental research in this area severly. Computer simulations provide an appealing alternative: Exspecially with molecular dynamics (MD) experimental results have been reproduced and conclusions about possible physical mechanisms were drawn (Zhou et al. (1997); Abraham (2003)). A drawback is the large amount of computational time needed. Consequently the demand in coupled simulation techniques is rising (e.g. Tang et al.
(2006); F.F.Abraham et al. (1998); Kohlhoff et al. (1991); RafiiTabar et al. (1998)), as a correct physical response of the surrounding material is crucial for realistic simulations.
A slowly propagating crack can be approximated by solving a sequence of static problems in connection with a rule to extend the crack between the steps. A range of works is following this idea (Mergheim and Steinmann (2006); Zhang and Ge (2005); Jirasek and Patzak (2001); Jirasek (2000); Nazarow and SpecoviusNeugebauer (2005); Krawczuk et al. (2001); Strouboulis et al. (2000)). The majority of coninuum based method uses a Finite Element discretisation. \'\'Classical\'\' Finite Elements can only resolve cracks coinceding with element boundaries, as quadrature rules assume the ansatz functions to be continuous on elements. The Extended Finite Element Method (XFEM) meets this problem in a simple and efficient manner (Chahine et al. (2006a); Dolbow (1999); Chahine et al. (2006b); Laborde et al. (2005); Karihaloo and Xiao (2003); Dolbow et al. (2001)).
The crack surface is approximated by augmenting the standard basis with at the crack surface truncated basis functions. Compared to older methods the stability of the generated basis together with the quality of the crack approximation are convincing advantages. However, to the knowledge of the author no effort has been made in modelling a fast propagation crack by means of uncoupled continua.
Aim of this work is the adaption of the Bridging Domain Method (Xiao and Belytschko (2004); Anciaux et al. (2006)) to the coupling of an Extended Finite Element and a molecular dynamics model. The crack front is simulated solely by molecular dynamics, while the bigger part of the simulation domain is modelled by elastodynamics. A transition zone, the Bridging Domain, allows to couple the models by constraints. This way high frequency waves otherwise reflected at the MD domain boundary are implicitely removed. Hence a physically incorrect energy accumulation in the MD region is avoided. This concept has been successful applied to standard Finite Element discretisations of the continuum. Firstly we will use XFEM for an efficient approximation of the crack surface. Secondly a far more detailed analysis of the coupling than in the given works shall be presented. We focus on a justification in not viewing the method as a heuristic, possible further developments and open questions. An implementation will be given future work can be based on. The correctness of the program and the quality of the method will be analysed based on numerical examples.