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Basic Equations of Solid Mechanics Based on Lattice Dynamics and Molecular Dynamics

基于晶格动力学和分子动力学的固体力学基本方程

基本信息

批准号：
12650094
负责人：
TAKAHASHI Kunihiro
金额：
$ 2.05万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

In conventional continuum mechanics, macroscopic state variables such as stress, strain, and temperature are defined at each macroscopic point, and only the macroscale is referenced. On the other hand, since these values are determined from the motions of atoms or molecules, a microscopic scale must be introduced to observe such internal motions from the microscopic standpoint.The domain in which this mesoscale is used to measure distance is called the mesodomain, i.e., it is sufficiently smaller than the macroscopic domain, yet sufficiently larger than the microscopic volume.This study proposes a method for expressing stresses from motions of atoms, and for deriving the conservation laws for solids microscopically. Constitutive equations and elastic constants not only for stresses but also for higher-order stresses are also derived microscopically. For the derivation of equations, a concept of a hierarchical Reynolds decomposition is introduced. The hierarchical deviation terms are ex … More pressed 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.The microscopic expressions described above are useful for obtaining the values of the macroscopic stress, higher-order stresses or constitutive equations from the results of molecular dynamics simulations. A three-dimensional simulation model with 10 x 10 x 10 Al atoms is introduced for calculations. Loads are applied to the atoms on the horizontal surface, changing proportionally with the gradient of 7.06 μN/m. The values of velocities of atoms calculated by molecular dynamics are substituted into the present microscopic expressions of stresses, higher-order stresses and constitutive equations. The numerical values and the theoretical values correspond well.Based on these results, a notion of one dimensional thermal polar materials are introduced. These materials can be said as thermal beams. A model of the thermal beam is proposed, and thermal cross-sectional constants for the model are obtained by FEM calculations. Less

在传统的连续介质力学中，宏观状态变量如应力、应变和温度在每个宏观点上定义，并且仅参考宏观尺度。另一方面，由于这些值是由原子或分子的运动确定的，因此必须引入微观尺度以从微观观点观察这种内部运动。本文提出了一种由原子运动表示应力的方法，并导出了固体微观守恒定律。本构方程和弹性常数不仅为应力，而且为高阶应力也来自微观。对于方程的推导，引入了分层雷诺分解的概念。分层偏差项为ex ...更多信息被称为P张量的特征张量所压制。P张量是原子构型的指标，可有效地用于弹性常数的表达，上述微观表达式可用于从分子动力学模拟结果中获得宏观应力、高阶应力或本构方程的值。采用10 × 10 × 10铝原子的三维模拟模型进行计算。载荷施加到水平表面上的原子上，与7.06 μN/m的梯度成比例地变化。将分子动力学计算的原子速度值代入现有的应力、高阶应力的微观表达式和本构方程中。在此基础上，提出了一维热极性材料的概念。这些材料可以说是热梁。提出了热梁模型，并通过有限元计算得到了热梁的热截面常数。少