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Numerical implementation of static Field Dislocation Mechanics theory for periodic media

Amit Acharya's picture

 R. Brenner   A. J. Beaudoin    P. Suquet    A. Acharya

(to appear in Philosophical Magazine)

This paper investigates the implementation of Field Dislocation Mechanics theory for media
with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are
considered as spatially periodic continuous fields). In this context, the uniqueness of the stress
and elastic distortion fields is established. This allows to propose an efficient numerical scheme
based on Fourier transform to compute the internal stress field, for a given spatial distribution
of dislocations and applied macroscopic stress. This numerical implementation is assessed by
comparison with analytical solutions for homogeneous as well as heterogeneous elastic media.
A particular insight is given to the critical case of stress-free dislocation microstructures which
represent equilibrium solutions of the Field Dislocation Mechanics theory.

http://faculty.ce.cmu.edu/acharya/files/2013/07/article-FDM-FFT.pdf

 

 

 

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