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  • 1
    Publication Date: 2014-04-26
    Description: This study introduces a numerical tool to generate virtual diffraction peaks from known elastic displacement or strain fields arising in the presence of discrete straight or curved dislocations in continuous media. The tool allows for the generation of diffraction peaks according to three methods: the displacement-based Fourier method of Warren, the Stokes–Wilson approximate method and a new average-strain-based Fourier method. The trade-off between the accuracy and the demand for computational power of the three methods is discussed. The work is applied to the cases of single-crystal microstructures containing (i) straight dislocations, (ii) low-angle symmetric tilt grain boundaries, (iii) a restrictedly random distribution of dislocations and (iv) complex microstructures generated by discrete dislocation dynamics, to illustrate the differences and domains of validity of the aforementioned methods. Dissimilar diffraction profiles reveal that peak broadening from dislocated crystals has additional contributions coming from strain gradients – a feature that is rejected in the Stokes–Wilson approximation. The problem of dealing with multi-valued displacement fields faced in the displacement-based Fourier method is overcome by the new average-strain-based Fourier method.
    Print ISSN: 0021-8898
    Electronic ISSN: 1600-5767
    Topics: Geosciences , Physics
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  • 2
    Publication Date: 2021-10-29
    Description: FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by H. Moulinec and P. Suquet for the homogenization of composites. From that moment on many dierent approaches have been proposed for a more accurate and efficient resolution of the non- linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to many other problems including continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems as fracture or multiphysical problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier-Galerkin and displacement-based methods. The paper will present then the most relevant applications of the method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture. It will also include an insight into synergies with experiments or its extension towards dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.
    Print ISSN: 0965-0393
    Electronic ISSN: 1361-651X
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Institute of Physics
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