在螺杆位移非线性力学中的几何挫折
Shunsuke Kobayashi1, Ryuichi Tarumi1
1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan.
Royal Society open science
|December 5, 2024
概括
本研究模型使用微分几何学来模拟螺丝失位,解决应力奇点. 几何挫折,而不是奇点,产生应力场,里奇曲率决定应力对称性.
科学领域:
- 材料科学 材料科学 材料科学
- 固体力学 固体力学是什么
- 数学物理学的数学物理.
背景情况:
- 应力奇点和线性近似使理解脱位应力场变得复杂.
- 失位是影响材料性能的基本晶体缺陷.
研究的目的:
- 用微分几何学来开发用于螺杆位移的新型数学模型.
- 以数值分析压力场围绕失位的产生机制.
- 研究材料中应力和曲率之间的关系.
主要方法:
- 利用微分几何和变量微积分来进行数学建模.
- 采用里曼 - 卡顿多元体与 метри和亲系连接来描述位移动力学.
- 应用霍奇二元论和赫尔姆霍尔茨分解来塑性功能构造.
- 进行了弹性应力场的数值分析.
主要成果:
- 开发的模型有效地消除了沿脱位线的应力奇点.
- 数字结果与伏尔特拉的理论在脱离离位核之外的理论非常一致.
- 几何挫折被确定为脱位压力场的主要来源.
- 证明了里奇曲线控制着应力场的对称性.
结论:
- 这项研究提供了一个强大的数学框架来分析失位.
- 证实了应力和曲率之间的二元性,证实了长期以来的假设.
- 提供了对晶体材料压力生成的基本机制的新见解.
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