Geometric Indexes of Atomic Configurations and Microscopic Expressions for Elastic Constants of Solids.

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  • 原子の配列状態を示す指標の導入とそれを用いた固体の弾性定数テンソルの微視的表現
  • ゲンシ ノ ハイレツ ジョウタイ オ シメス シヒョウ ノ ドウニュウ ト ソレ オ モチイタ コタイ ノ ダンセイ テイスウ テンソル ノ ビシテキ ヒョウゲン

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Elastic constants are usually obtained experimentally, since it has some problems to predict elastic constants of materials analytically from atomistic viewpoint.In the previous papers, the authors proposed a method for expressing internal forces from motions of atoms, and the conservation laws for solids are introduced microscopically.In the present paper, constitutive equations and elastic constants not only for stresses but also for higher-order stresses are derived by dividing the kinematical quantities of atoms into the macroscopic deformation and thermal motion.In the process of derivation, a concept of a hierarchical Reynolds decomposition is infroduced.It is an expansion in power series which can be divided into an average value and a deviation in each hierachy.The hierarchical deviation terms are expressed by characteristic tensors which can be called P-tensors.The P-tensors are the indexes of atomic configurations and are used effectively for the expression of the elastic constants.

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