The macroscopic response of composites

DMS Award AbstractAward #： 0108626 PI： 米尔顿，格雷姆机构： 犹他州大学项目： 应用数学项目经理：Catherine Mavriplis职务：复合材料的宏观响应本提案旨在研究材料的宏观响应，重点关注四个主题。第一个主题涉及在两相复合材料中的蠕变，假定人们知道组成相的行为。问题是要获得可能发生的蠕变范围的界限，并确定具有最大和最小蠕变的微观结构。第二个主题涉及均匀或非均匀材料的复介电常数，它决定了材料如何反射，透射和吸收辐射。给定在一定频率范围内的复介电常数的测量值，问题是要明确地说明材料在测量范围之外的频率间隔上的响应。第三个主题，这代表了以前的工作的延续，是探索的平均应变值的范围可以采取在复合材料，这是受到一个固定的平均应力，作为微观结构是不同的。我们的目标是限制这个范围，并确定最佳的结构，产生应变的范围内的容许值的边界。这样的结构应该是有用的“应力导向器”，用于将应力引导到所需的位置。什么样的微观结构使最好的可能的流体静力压缩剪切转换器的具体问题将进行调查。第四个主题是探索一类相当奇特的微观结构的性质，称为偏微分微观结构。这些可能是解决某些优化设计问题的最佳微结构。更好地理解材料的宏观响应具有重要的技术意义。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相关），了解海冰的宏观响应（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。这一建议将提高我们的理解，将（1）促进新材料的开发，这些新材料具有通过调整微观结构而获得的不寻常的性能;（2）提供对复合材料响应的限制，这对于评估这种材料在预期应用中的安全性是必不可少的;以及（3）预测材料对已测量响应的频率之外的辐射的响应的某些方面，如果该材料是生物材料，并且如果人们想知道辐射在其影响已知的频率之外是否有害，则这可能是重要的。

DMS Award AbstractAward #: 0108626PI: Milton, GraemeInstitution: University of Utah Program: Applied MathematicsProgram Manager: Catherine MavriplisTitle: The macroscopic response of compositesThis proposal aims to investigate the macroscopic response of materials, focusing on four topics. The first topic concerns creep in a two phase composite given that one knows the behavior of the constituent phases. The problem is to obtain bounds on the range of creep that might occur, and to identify microstructures having the maximum and minimum creep. The second topic concerns the complex dielectric constant of homogeneous or heterogeneous materials which governs how a material reflects, transmits and absorbs radiation. Given measurements of the complex dielectric constant over a range of frequencies, the problem is to say something definite about the response of the material over an interval of frequencies outside the measured range. The third topic, which represents a continuation of previous work, is to explore the range of values the average strain can take in a composite which is subject to a fixed average stress, as the microstructure is varied. The objective is to bound this range, and to identify optimal structures that generate strains at the boundary of the range of admissible values. Such structures should be useful as ``stress guides'' for channeling stress to desired locations. The particular question of what microstructures make the best possible hydrostatic compression to shear converters will be investigated. The fourth topic is to explore the properties of a rather exotic class of microstructures, called partial differential microstructures. These may turn out to be the best microstructures for solving certain optimal design problems. 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 defense, automotive, 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 modeling), to understanding the macroscopic response of biological materials (such as tissues, bones, shells and tendons). This proposal will enhance our understanding in ways that will (1) facilitate the development of new materials having unusual properties that are achieved by tailoring the microstructure; (2) provide limits on the response of composite materials, that could be essential for assessing the safety of such materials in desired applications; and (3) predict certain aspects of the response of materials to radiation outside frequencies where the response has been measured, which could be important if the material is biological and if one wants to know if radiation could be harmful outside frequencies where its effects are known.Date: May 30, 2001