The Macroscopic Response of Materials

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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.