The Macroscopic Response of Materials

本研究将研究均质和非均质材料的宏观响应。对于均匀材料，它将获得尖锐的测试，以确定在两个不同频率间隔上的电学或粘弹性响应的实际测量是否兼容。对于非均匀材料，它将在频域和时间域上约束材料的介电和粘弹性响应。此外，首席研究人员将确定在线性和非线性复合材料中可以或不可以出现什么宏观应力应变组合，并将确定具有极端应力应变组合的微观结构。这在人们希望将压力从一个区域转移到另一个区域的应用中将是重要的。这一研究将进一步揭示复合材料有效弹性系数之间的微观结构独立关系。它还将获得某些迭代数值格式的收敛速度的显著加快，这些迭代数值格式已被开发用于计算线性和非线性复合材料的性质。更好地理解材料的宏观响应具有核心的技术重要性。从了解工程材料的宏观响应(对国防、自动化和航空航天工业至关重要)，到了解多晶体和多孔岩石的宏观响应(与地震预报和石油工业有关)，到了解海冰的宏观响应(对气候模拟很重要)，到了解生物材料(如组织、骨骼、贝壳和肌腱)的宏观响应，这一重要性跨越了方方面面。由该奖项资助的研究将以促进新材料开发的方式增进我们的理解，提供测试实验测量可靠性的程序，并加快数值计算。

This research will investigate the macroscopic response of both homogeneous and heterogeneous materials. For homogeneous materials it will obtain sharp tests as to whether actual measurements of the electrical or viscoelastic response over two different frequency intervals are compatible. For heterogeneous materials it will bound the dielectric and viscoelastic response of materials both in the frequency domain and in the time domain. In addition the principal investigator will determine what macroscopic stress strain combinations can or cannot occur in both linear and non-linear composites and will identify microstructures which have extremal stress-strain combinations. These are expected to be important in applications where one wants to channel stress from one area to another. The research will shed further light on exact microstructure independent relations amongst the effective moduli of composites. It will also obtain dramatic accelerations of the convergence rate of certain iterative numerical schemes which have been developed to compute the properties of both linear and non-linear 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). The research funded with thisaward will enhance our understanding in ways that will facilitate the development of new materials, provide procedures for testing the reliability of experimental measurements, and accelerate numerical computations.