A Relay-Zone Technique for Computing Dynamic Dislocations

S. Q. Tang (), W. K. Liu, E. G. Karpov and T. Y. Hou
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S. Q. Tang: Peking University, LTCS, Department of Mechanics and Aerospace Engineering
W. K. Liu: Northwestern University, Department of Mechanical Engineering
E. G. Karpov: Northwestern University, Department of Mechanical Engineering
T. Y. Hou: California Institute of Technology, Applied and Computational Mathematics

A chapter in Computational Mechanics, 2007, pp 228-228 from Springer

Abstract: Abstract We propose a multiscale method for simulating solids with moving dislocations. Away from atomistic subdomains where the atomistic dynamics are fully resolved, a dislocation is represented by a localized jump profile, superposed on a defect-free field. We assign a thin relay zone around an atomistic subdomain to detect the dislocation profile and its propagation speed at a selected relay time. The detection technique utilizes a lattice time history integral treatment. After the relay, an atomistic computation is performed only for the defect-free field. The method allows one to effectively absorb the fine scale fluctuations and the dynamic dislocations at the interface between the atomistic and continuum domains. In the surrounding region, a coarse grid computation is adequate. We illustrate the algorithm for a 1D Frenkel-Kontorova model at finite temperature. By comparison of the numerical results in the following figure, the reflection is absorbed by the proposed relay-zone technique.

Date: 2007
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DOI: 10.1007/978-3-540-75999-7_28

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