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

广义连续体与原子模型的联系方法研究非齐次结构的非局部弹性常数

• 批准号: 08650111
• 负责人: SHIBUTANI Yoji
• 金额: $ 1.34万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650111/
• 关键词: Mesomechanics; Nonlocal elastic constants; Cossevat theory; Lattice dynamics; Molecular Dynamics

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.

Cosserat 理论中与应变梯度项相关的非局部弹性常数与原子级特性相关，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相关。因此，非局域弹性常数，包括四阶普通张量，都用松弛晶格构型和力常数来表示，力常数是原子间势相对于原子位置的二阶导数。使用 Finnis-Sinclair 型多体势对不太对称的表面和高 SIGMA 值晶界结构进行分子静力学和分子动力学模拟。然后，通过推导的均匀中心对称体区域和非均匀部分的关系来估计非局部性质。研究发现，不均匀性扩大了材料本质上具有的非局域性。由四阶和六阶常数定义的特征长度小于大多数立方晶格结构的晶格间距。

项目成果

Y.Shibutani: "Nonlocal Elastic Canstants of Centrosymmetric Hmogeneous Lattice Structure and In homogeneous One" JSME Int.J.(掲載予定).

Y.Shibutani：“中心对称均匀晶格结构和齐次结构的非局部弹性常数”JSME Int.J（待出版）。

渋谷陽二: "弾性定数の数理展開" 材料(日本材料学会誌). 46・3. 2-11 (1997)

涩谷洋二：“弹性常数的数学展开”材料（日本材料学会会刊）46・3（1997）。

Yoji Shibutani: "Definitions of elastic Constants" J.Soc.Mat.Sci.Japan. Vol.46, No.3. 218-227 (1997)

Yoji Shibutani：“弹性常数的定义”J.Soc.Mat.Sci.Japan。

Y.Shibutani, V.Vitek and J.L.Bassani: "Nonlocal Properties of Inhomogeneous Structures by Linking Approach of Generalized Continuum to Atomistic Model" Int.J.Mech.Sci.Vol.40, Nos.2-3. 129-137 (1998)

Y.Shibutani、V.Vitek 和 J.L.Bassani：“通过广义连续体与原子模型的链接方法研究非均匀结构的非局部性质”Int.J.Mech.Sci.Vol.40，Nos.2-3。

渋谷陽二: "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)" 日本機械学会論文集 A編. 62. 2054-2059 (1996)

Yoji Shibuya：“介观动力学非定域弹性常数的研究（第 1 次报告，微观-宏观耦合方法的公式）”日本机械工程师学会会刊，A 版 62。2054-2059（1996 年）。