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A hybrid atomistic-continuum finite element modelling of locally disordered crystalline structure

Paweł Dłużewski 2Piotr Traczykowski 2Grzegorz Jurczak 2Marcin Maździarz 2S Nagao 3Roman Nowak 3Krzysztof J. Kurzydlowski 1

1. Warsaw University of Technology, Faculty of Materials Science and Engineering (InMat), Wołoska 141, Warszawa 02-507, Poland
2. Polish Academy of Sciences, Institute of Fundamental Technological Research (IPPT PAN), Świętokrzyska 21, Warszawa 00-049, Poland
3. Nordic Hysitron Laboratory, Dept. Materials Sci. & Engg., Helsinki University of Technology (TKK/HUT), Vuorimiehentie 2A, Helsinki FIN-02015, Finland


Problem of locally disordered atomic structure is solved by using a hybrid formulation in which nonlinear elastic finite elements are linked with discrete atomic interaction elements. The continuum approach uses nonlinear hyperelasticity based upon the generalized strain while the atomistic approach employs the Tight-Binding Second-Moment Approximation potential to create new type of elements. The molecular interactions yielding from constitutive models of TB SMA were turned into interactions between nodes to solve a boundary value problem by means of finite element solver. Atomistic psudoelements are noting more than two-node atomic interaction. The application is used to deal with the problem of edge dislocation and its dissociation into two Schockley's dislocation in Cu crystals.

Three examples are shown. In the first, the whole considered crystal region has been discretized and solved by means of the nonlinear elastic FEs. In the second example, the same FE region has been discretized by means of the molecular lattice and solved by molecular dynamics and statics. Finally, in the third example the regions around the dislocations' cores have been replaced by discretized atomic structure and linked on the boundary with corresponding nodes of continuum FEs. In this way, a single boundary value problem with two different types of discretization of the crystal structure has been solved in this example. A transition on the continuum/atomic interface is assured by taking into account a crystallographic data in the finite element mesh preparation. In this example the regions of dislocation cores were modelled using molecular interaction mesh while the ordered lattice was discretized by FEs. The obtained MD-FE model has been applied to simulate the nanoindentation test on nanocrystalline copper in order to conclude on the singularities observed in P-h curves.


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Presentation: oral at E-MRS Fall Meeting 2005, Symposium F, by Paweł Dłużewski
See On-line Journal of E-MRS Fall Meeting 2005

Submitted: 2005-05-30 14:39
Revised:   2009-06-07 00:44