メゾ力学のための非局所化弾性定数の検討 : 第1報, ミクロ・マクロ連結手法からの定式化

概要

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Nonlocal elastic constants associated with the higher-order strain gradients 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. The key objective of this work is to describe elastic behavior on the mesoscopic scale. First the equation of motion (EOM) in the cosserat theory is derived in the most general form with the arguments of the deformation gradient tensor and its material derivative as well. Second the EOM in the lattice dynamics with the harmonic approximation is formulated by introducing the continuous atomic displacement field. Then the nonlocal elastic constants, including the ordinary fourth-order tensor, are expressed in terms of both the atomic positions in a relaxed (stable) configuration and the force constants which are the second derivative of the interatomic potential employed, with respect to position.
一般社団法人日本機械学会の論文
1996-09-25