Anisotropic Nonlocal Kernel Functions for Close-Packed Crystals Derived from Quantum-Mechanical Simulations

Classical continuum elasticity theories fail to capture the size-dependent elastic fields near nanoscale defects due to their inability to account for long-range interatomic forces. Eringen's nonlocal elasticity theory provides a remedy through the introduction of kernel functions that incorporate such interactions. However, most prior studies rely on oversimplified isotropic kernels, which neglect the anisotropy and symmetry of crystalline solids. In this work, a unified framework for deriving anisotropic nonlocal kernel functions based on ab initio Density Functional Perturbation Theory (DFPT) calculations is developed. Specifically, three distinct kernel functions are obtained for face-centered cubic (fcc) crystals (Al, Cu, Ni, Pd, Ag), and five distinct kernels are established for hexagonal close-packed (hcp) crystals (Mg, Cd, Ti, Zn). These kernel functions are extracted from nonlocal dispersion relations and matched with phonon frequencies obtained from DFPT. The proposed approach provides a general methodology for incorporating crystal symmetry into nonlocal elasticity. By eliminating the singular stress behavior inherent in classical elasticity, the framework delivers physically realistic stress distributions and enables accurate multiscale modeling of defect mechanics in crystalline solids.

Keywords:

Anisotropic , Nonlocal Kernel Functions , Close-Packed Crystals , Quantum-Mechanical Simulations , Elasticity , Crystal Symmetry , Density Functional Perturbation Theory , Nanoscale Defects