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

Cosserat理论中与应变梯度项相关的非局域弹性常数与原子能级性质有关，特别是当原子位移用连续位移场表示时，与晶格动力学方程中出现的系数有关。因此，非局域弹性常数，包括四阶的普通张量，用弛豫晶格构型和力常数来表示，力常数是原子间势对原子位置的二阶导数。对非对称表面和高Sigma值晶界结构的分子静力学和分子动力学模拟采用Finnis-Sclair多体势。然后，根据所导出的齐次中心对称体区和非均匀部分的非局域性质估计了非局域性质。结果表明，材料的非均匀性增大了材料固有的非局域性。对于大多数立方晶格结构，由四阶和六阶常数定义的特征长度小于晶格间距。

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.