Mathematical Sciences: Nonlinear Dynamics in Continuum Mechanics

数学科学：连续介质力学中的非线性动力学

• 批准号: 9209049
• 负责人: Athanasios Tzavaras
• 金额: $ 6万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209049&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Dynamics; Continuum

The objective of this research is to understand the dynamic response of continuous media via the study of singularities for the governing partial differential equations of motion. Three topics are proposed: (i) Formation of shear bands at high strain rates; (ii) Study of self-similar viscous limits and of radial solutions for hyperbolic systems of conservation laws; (iii) Hydrodynamic limits for discrete velocity models in the case of Riemann data. Shear bands are regions of intensely localized strain that appear during high speed deformations of metals and often precede rupture. For that reason their study is critical for the design of improved materials in situations of high speed plastic flow. The theoretical understanding of structures such as shock waves or shear bands is critical for designing improved algorithms in technological applications where such phenomena are dominant, for instance in ballistic penetration of metals and in various manufacturing processes involving metals.

这项研究的目的是了解动态 连续介质的响应，通过研究奇点， 运动的偏微分方程 三 提出了以下课题：（1）高应变下剪切带的形成 （二）自相似粘性极限和径向粘性极限的研究 双曲守恒律方程组的解;（iii） 离散速度模型的水动力极限 Riemann数据 剪切带是强烈局部应变的区域， 出现在金属的高速变形过程中， 破裂 因此，他们的研究对设计至关重要 在高速塑性流动的情况下， 对冲击波等结构的理论认识 或剪切带是设计改进算法的关键， 这种现象占主导地位的技术应用， 例如金属的弹道穿透和各种 涉及金属的制造工艺。