Presentation
Construction of kernel for nonlocal elasticity from one-dimensional dispersion data in reciprocal space
54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
(2013)
Abstract
Kernels for non-local elasticity are frequently obtained from phonon dispersion relations. The dispersion relations are generally available in the form of one-dimensional (1D) curves in reciprocal space for different high-symmetry directions of the Brillouin zone, however, 3D kernels for three-dimensional (3D) solids are needed. To the best of knowledge of the authors, there is no systematic procedure to obtain material specific nonlocal kernels (for integral Type nonlocality) from the dispersion data. The present paper proposes strategies to build the 3D kernels from the dispersion data. Our particular focus is on isotropic media that is interesting due to the inherent quasi-1D nature of the axisymmetric kernel. We have obtained these kernels using Fourier-Bessel transforms, yielding axisymmetric kernel profiles in both reciprocal and real spaces.
Disciplines
Publication Date
2013
Location
Boston, Massachesetts
DOI
10.2514/6.2013-1508
Citation Information
Susanta Ghosh, Veera Sundararaghaven and Anthony M. Waas. "Construction of kernel for nonlocal elasticity from one-dimensional dispersion data in reciprocal space" 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2013) Available at: http://works.bepress.com/susanta-ghosh/3/