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Discrete kernel functions for fcc crystals within eringen’s nonlocal theory of elasticity

Shodja, H. M ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1007/s10659-020-09806-4
  3. Publisher: Springer Science and Business Media B.V , 2021
  4. Abstract:
  5. The dilemma with the deficiencies of the nonlocal kernel functions as the building blocks of the Eringen’s nonlocal theory has been of concern. The aim of the current work is to provide a remedy for the calculation of the components of the nonlocal moduli tensor pertinent to face center cubic (fcc) crystals accounting for their true symmetry group. To this end, three new distinct nonlocal kernel functions which are the discrete atomistic Green’s functions in the stress space are obtained through the nonlocal dispersion relations associated with the longitudinal and shear waves in fcc crystals combined with the corresponding ones calculated via ab initio based on density functional perturbation theory (DFPT). In other words, based on nonlocal continuum and quantum mechanical considerations different kernel functions pertinent to each component of the elastic moduli tensor are calculated for the first time. Moreover, the nonzero components of the classical elastic moduli as well as the equilibrium lattice parameter associated with Al, Cu, Ni, Pd, and Ag fcc crystals have been computed using ab initio density functional theory (DFT) and compared with the available experimental data. In order to show the importance of the anisotropy of the kernel functions, the nonlocal stress field of a screw dislocation inside an infinitely extended fcc medium has been calculated; the solutions for two cases where the dislocation line is along the [001] and [101] directions are compared. Within this theory the unrealistic singular behavior of the classical stresses at the dislocation core is eliminated. © 2020, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature
  6. Keywords:
  7. Calculations ; Crystal symmetry ; Crystals ; Density functional theory ; Elastic moduli ; Elasticity ; Perturbation techniques ; Quantum theory ; Shear flow ; Shear waves ; Tensors ; Ab initio density functional theories (DFT) ; Density functional perturbation theory ; Dislocation core ; Dislocation lines ; Dispersion relations ; Nonlocal continuums ; Quantum mechanical ; Singular behavior ; Lattice theory
  8. Source: Journal of Elasticity ; Volume 143, Issue 1 , 2021 ; 03743535 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s10659-020-09806-4?noAccess=true