Nonlocal Elastic Constants of Inhomoegeneous Structure by Linking Approach of Generalized Continuum to Atomistic Model

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Nonlocal elastic constants associated with strain gradient terms in the Cosserat theory are linked to atomic-level properties, in particular to coefficients that arise in lattice dynamics equations when atomic displacements are expressed in terms of a continuous displacement field. Therefore, the nonlocal elastic constants, including the ordinary tensor with rank of four, are expressed in terms of both relaxd lattice configuration and force constants which are the second derivative of an interatomic potential with respect to an atom position. Molecular statics and molecular dynamics simulations of the less symmetric surface and the high SIGMA-value grain boundary structures are performed using a Finnis-Sinclair type many-body potential. Then, the nonlocal properties are estimated by the derived relations for homogeneous centrosymmetric bulk region and inhomogenous part. It is found that the inhomogeneity enlarges the nonlocality the materials intrinsically have. The characteristic length defined by the 4th and 6th-order constants is less than a lattice spacing for most of the cubic lattice structures.