Micromechanics of Composites: Asymptotic Homogenization and Metamaterials

An issue of a high significance in micromechanics of composites is determination of effective properties depending on the spatial distribution, geometric characteristics and mechanical properties of the constituents. Various asymptotic approaches to the analysis of composites have reached their conclusion in the multi-scale asymptotic homogenization. The proof of the possibility of homogenizing the composite material of a regular structure is one of the principal results of this theory. Asymptotic homogenization method has also indicated a method of transition from the original problem for the inhomogeneous composite to a problem for a homogeneous material described by a set of the effective properties. This transition is accomplished through the solution of the unit cell local problems that allows determining the effective properties and distribution of displacements and stresses. The presentation will cover the basics of asymptotic homogenization. Simple examples will be used to illustrate the asymptotic homogenization technique. The general asymptotic homogenization models will be further introduced and applied to the analysis of composite materials and thin-walled composite structures of a practical importance, including wafer-reinforced shells, composite grids, sandwich shells and carbon nanotubes. Final part of presentation will address new developments in the analysis, design and fabrication of lightweight composite metamaterials and cellular structures.