Structures, Composites, and Inhomogeneous Bodies

This project is focused on the mathematical modeling of materials and mechanical systems. The work aims to advance the mathematical underpinnings of several systems that have applications at the leading edge of technological development. Part of the project concerns seismic isolators, mechanical structures tailored to protect structures from the destructive shearing and vertical motions of earthquakes.

The goal of this part of the work is to guide the design of isolators with improved performance under large displacements. Other parts of the project concern composite materials and metamaterials. Composite materials are important in applications throughout modern technology and manufacturing.

Metamaterials, which are engineered composite materials where dissimilar materials are combined to produce a structure with properties unlike those of the components, can have properties not found in naturally occurring materials and among other uses can serve important functions in guiding waves. The goals of these parts of the project are to guide the design of dynamic metamaterials and to enhance understanding of the mathematical underpinnings for composite materials, as well as understanding inherent limits on their properties and behavior.

Parts of this work have potential application to medical imaging and other noninvasive testing. The project includes the interdisciplinary training of a postdoctoral research associate.

The research consists of five parts: (1) work on earthquake isolators utilizes mechanisms of plate-hinge linkages to develop a new conceptional approach to the construction of structural units that insulate a building from horizontal or vertical movement of the ground during seismic events; (2) design of space-time metamaterial microstructures in which energy is locally conserved, eliminating the need of current space-time microstructures to couple with outside systems, or employ supplementary pumping waves, to generate or absorb energy as demanded; (3) search for fundamental understanding of exact relations and links in the theory of composites, which could help in the discovery of new relations applicable to media where the local tensor field of material moduli take values on a manifold that is not rotationally invariant; (4) obtaining estimates of the range of possible behaviors in the time domain for viscoelastic two-phase composites or bodies, which could help in design of materials with desired temporal responses and in estimation of the volume fractions occupied by the phases; and (5) work on determining the range that the complex dielectric tensor can take in an anisotropic composite of two anisotropic phases, which could facilitate design of structures that absorb a maximum amount of electromagnetic energy or that guide electric and electric displacement fields in desired ways.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.