Mie-Grüneisen状态方程的物理力学释义

李晓杰; 闫鸿浩; 王小红; 孙明

doi:10.11858/gywlxb.2014.02.015

Mie-Grüneisen状态方程的物理力学释义

doi: 10.11858/gywlxb.2014.02.015

大连理工大学工业装备结构分析国家重点实验室，辽宁大连 116023

基金项目: 国家自然科学基金(10872044, 10902023, 11272081);教育部博士点基金(20090041110024)

详细信息

作者简介:
李晓杰(1963—), 男，教授，博士生导师，主要从事爆炸力学研究.E-mail:robinli@dlut.edu.cn

中图分类号: O521.22
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出版历程
- 收稿日期: 2011-12-21
- 修回日期: 2012-06-06

A Physical Mechanics Paraphrase on Mie-Grüneisen Equation of State

Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China

摘要

摘要: 通过建立一种简单的固体一维点阵定容热振动的物理力学模型，完全由力学方程推演出了Mie-Grüneisen形式的固体状态方程，并从力学本质上明确了热压力的物理意义是原子热振动时均值所造成的作用力偏载量。所得Grüneisen系数与频率的关系说明，真实三维晶体的Grüneisen系数与晶体结构相关。在简单立方晶体的情况下，获得了与Dugdale-MacDonald公式形式相同的Grüneisen系数-冷压微分关系式。研究结果证明，在状态方程构建方面，“物理力学”是一种非常有效的研究工具。
- 物理力学 /
- Mie-Grüneisen状态方程 /
- 原子热振动 /
- 点阵动力学
Abstract: A one-dimensional model of lattice physical mechanics was built up to study the atomic thermal vibration in a constant volume state.According to the lattice dynamics model, An equation of state of solids which is similar to the Mie-Grüneisen's, was deduced absolutely from vibration mechanics.The mechanical implication of thermal pressure was ascertained, that thermal pressure was the average value of thermal vibration force in time domain.The relationship between Grüneisen parameter and thermal vibration frequency shows that the Grüneisen parameter of a real solid corelates with its crystal structure.The differential expression between Grüneisen parameter derivated from a simple cubic crystal and cold pressure was obtained, which agrees with the D-M relation.
- physical mechanics /
- equation of state of Mie-Grüneisen /
- atom thermal motion /
- lattice dynamics

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图 1 晶体中一维点阵热运动示意图

Figure 1. Schematic diagram of one-dimensional lattice thermal motion in a crystal

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