Coarse-graining atomistic dynamics of fracture by finite element method: formulation, parallelization and applications

The accurate prediction of material behaviors is one of the most important fields in both science and engineering communities. Understanding the mechanisms of material behaviors sometimes needs us to study the material over a wide span of length scales. In this work we present a new methodology which is able to coarse-grain the atomistic dynamics of fracture by finite element method. First, based on the Atomistic Field Theory (AFT) (Chen and Lee 2005, Chen et al. 2006, Chen 2009), a finite elements method with built in atomistic information is presented. Then a high efficiency parallel code for large scale computation is described. This code was written in FORTRAN language and uses the standard parallel programming environment message passing interface (MPI). The performance of the parallel code was tested on the supercomputer Trestle of SDSC (San Diego Supercomputer Center). Through the comparison of the coarse-grained (CG) simulation results with the molecular dynamics (MD) simulation results, it is found that the new CG method is able to predict the crack tip stress, dynamic crack propagation and even crack branching, with results similar to that of the atomic-level molecular dynamics simulations. Finally, both 2D (2 dimensional) and 3D (3 dimensional) dynamic fracture problems were computed through the CG method. In 2D dynamic fracture simulations, the relationship between stress waves and crack propagations was studied. It is found that the stress waves reflected back from the boundary can trigger the dynamic crack branching. In 3D simulations, the dynamic fractures under different loading were simulated. The largest 3D model is composed of over 0.1 million elements which are equivalent to over 0.1 billion atoms. To show the performance of the parallel code in dealing with large number of processors, the crack surface evolution in this model was simulated using 512 processors. All of simulations conducted in this study show the robustness of the parallel code in dealing with dynamic fracture problems. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)

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