Mathematical Sciences: Microstructure and its Influence on Composite Material Properties

数学科学：微观结构及其对复合材料性能的影响

• 批准号: 9501025
• 负责人: Graeme Milton
• 金额: $ 13.2万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501025&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microstructure; its; Influence

DMS-9501025 Milton This proposal aims to investigate microstructures which have novel or extremal elastic behavior, develop new variational principles as a tool for analysis, derive bounds on the complex shear modulus of viscoelastic composites, obtain exact relations between plane elasticity anti-plane elasticity and piezoelectricity, seek a more general link between coupled equations and uncoupled equations, and numerically solve coupled field problems through the use of integral equation methods. Composite and polycrystalline materials are ubiquitous in nature and amongst engineered materials. Their technological importance stretches from applications in earthquake prediction (many rocks are polycrystalline),in the oil industry (rocks containing oil), the aerospace industry (lightweight composites), to understanding sea ice, a composite of brine and ice (important to climate modelling), colloids (a composite of suspended particles in a fluid),to shape memory materials (a composite of different variants of a metallic phase), to hydrophones (composites of piezoelectric materials), to biological applications (bones, shells, tendons are all examples of composite structures). This proposal will enhance our knowledge of composite and polycrystalline materials in ways that will facillitate the development of new materials, and improve procedures for estimating the properties of composites.

DMS-9501025米尔顿 该建议旨在研究具有新颖或极端弹性行为的微结构，发展新的变分原理作为分析工具，推导粘弹性复合材料复剪切模量的界限，获得平面弹性-反平面弹性和压电性之间的精确关系，寻求耦合方程和非耦合方程之间更一般的联系，并通过使用积分方程方法数值求解耦合场问题。 复合材料和多晶材料在自然界和工程材料中普遍存在。它们的技术重要性从地震预测的应用（许多岩石是多晶的），在石油工业中（含石油的岩石），航空航天工业（轻质复合材料），以了解海冰，盐水和冰的复合材料（对气候建模很重要）、胶体（流体中悬浮颗粒的复合物），形状记忆材料（金属相的不同变体的复合物），到水听器（压电材料的复合材料），生物应用（骨骼、外壳、肌腱都是复合结构的例子）。这一建议将提高我们的复合材料和多晶材料的知识，将促进新材料的开发，并改善程序估计复合材料的性能。