The Response of Composites and Quasiconvexity

复合材料的响应和拟凸性

• 批准号: 0411035
• 负责人: Graeme Milton
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0411035&HistoricalAwards=false
• 关键词: Response; Composites; Quasiconvexity

Proposal: DMS-041103PI: Graeme W. MiltonInstitution: University of UtahTitle: The Response of Composites and QuasiconvexityABSTRACTThis work will improve our understanding of creep in composite materials, through establishing bounds on the total creep and identifying microstructures that exhibit the maximum or minimum possible creep. It will also identify microstructures which are best for guiding stress in linear elasticity. These composites should be useful for distributing or concentrating the force in a structure. Additionally, microstructures will be identified with an anomalous Hall coefficient, which could potentially be useful in reducing stray electric fields in circuit design when there is a magnetic field present. In a second part of the work three fundamental problems will be studied: characterizing the surfaces in tensor space associated with sets of effective tensors of hierarchical laminate geometries; exploring the connection between rank-one convexity and quasiconvexity; and developing new tools for bounding the effective moduli of composites and for bounding the quasiconvexification of a function. These problems are important for making progress on the question of what responses of composites are or are not possible. Their solution could, in a wide variety of cases, make numerically tractable the search for the possible macroscopic responses of composites.A better understanding of the macroscopic response of materials is of central technological importance. This importance stretches across the board, from understanding the macroscopic response of engineered materials (of critical importance to the defence, automative, and aerospace industries), to understanding the macroscopic response of polycrystalline and porous rocks (relevant to earthquake prediction and to the oil industry), to understanding the macroscopic response of sea ice (important to climate modelling), to understanding the macroscopic response of biological materials (such as tissues, bones, shells and tendons). In the past many useful composites were obtained by trial and error, or by mimicking composites found in nature, or by using intuition. In this century we will have greater flexibility to produce designer composites tailor made to meet specific needs. Improving our understanding of the response of composites will facilitate the construction of these designer composites.

提案：DMS-041103 PI：Graeme W. Milton机构：犹他大学标题：复合材料的响应与准凸性本文通过建立复合材料蠕变的边界和识别表现出最大或最小可能蠕变的微观结构，将提高我们对复合材料蠕变的理解。它还将识别最适合于在线性弹性中引导应力的微观结构。 这些复合材料应该有助于在结构中分布或集中力。此外，微结构将被识别为具有异常霍尔系数，这可能有助于在存在磁场时减少电路设计中的杂散电场。在第二部分的工作三个基本问题将进行研究：表征张量空间中的表面与套有效张量的层次层压几何;探索之间的连接秩一凸性和quasiconvexity;和开发新的工具，用于绑定的有效模量的复合材料和绑定的quasiconvexification的功能。这些问题对于在复合材料的哪些响应是可能的或不可能的问题上取得进展是重要的。 他们的解决方案可以，在各种情况下，数值上易于处理的搜索可能的复合材料的宏观响应。更好地了解材料的宏观响应是核心的技术重要性。从了解工程材料的宏观响应，（对国防、汽车和航空航天工业至关重要），了解多晶和多孔岩石的宏观响应（与地震预测和石油工业有关），了解海冰的宏观反应（对气候建模很重要），了解生物材料（如组织、骨骼、贝壳和肌腱）的宏观反应。过去，许多有用的复合材料都是通过反复试验、模仿自然界中发现的复合材料或凭直觉获得的。在这个世纪，我们将有更大的灵活性来生产设计师为满足特定需求而量身定做的复合材料。提高我们对复合材料响应的理解将有助于这些设计复合材料的构建。