Mathematical Sciences: Nonlinear Elasticity and the Calculusof Variations

数学科学：非线性弹性和变分演算

• 批准号: 9002679
• 负责人: Stefan Muller
• 金额: $ 3.9万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002679&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Elasticity; Calculusof

With this award the principal investigator will study models of nonlinear elasticity that describe the behavior of elastic materials at moderate to large deformations. In contrast to linear models nonlinear models usually require for their solution more sophisticated types of mathematical analysis. On the theoretical side the principal investigator will study the weak continuity of the Jacobian determinant and the choice of a space of admissible deformations. On the applied side he will study the stability of elastic composite materials such as foam rubber, and he will analyze solid-solid phase transitions in elastic crystals. A goodly number of everyday phenomena involving elastic materials can be explained using what is called linear elasticity theory. This linear theory concerns the behavior of elastic materials in response to small deformations. However when the deformations are moderate to large in size the linear theory must be replaced with a more complicated nonlinear theory. A nonlinear theory is also required if the material is a composite, such as foam rubber or fibre-reinforced rubber. With this award the principal investigator will use mathematical analysis to study models of nonlinear elastic materials.

凭借该奖项，首席研究员将研究非线性弹性模型，该模型描述弹性材料在中度至大变形下的行为。 与线性模型相比，非线性模型通常需要更复杂类型的数学分析来求解。 在理论方面，主要研究者将研究雅可比行列式的弱连续性和允许变形空间的选择。 在应用方面，他将研究泡沫橡胶等弹性复合材料的稳定性，并分析弹性晶体中的固-固相变。 许多涉及弹性材料的日常现象都可以用所谓的线性弹性理论来解释。 该线性理论涉及弹性材料响应小变形的行为。 然而，当变形大小为中等到大时，必须用更复杂的非线性理论代替线性理论。 如果材料是复合材料，例如泡沫橡胶或纤维增强橡胶，则还需要非线性理论。 获得该奖项后，首席研究员将使用数学分析来研究非线性弹性材料模型。