9403866 Lipton We address the design of composite materials and their application to optimal design of structures. Here we investigate the macroscopic properties for perfectly and imperfectly bonded composites as well as optimal transport properties for multi-phase emulsions and foams. On a theoretical level this work involves basic research in homogenization theory, perturbation theory, and gamma convergence of nonlinear functionals. The ultimate goal is the creation of efficient numerical methods for optimal design of structures built from composite materials. In this proposal we treat several topics involving the use of composites in optimal structural design. Composite materials and their transport properties are central to the design of structures ranging from the aeroelastic tayloring of airplane wings to optimal design of emulsions. The design approach put forth here focuses on finding the best composite material properties necessary for optimal structural performance. This program has immediate application to diverse areas ranging from design of fuel efficient transportation systems to the modeling of transport properties of biological materials.
