We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve such bounds. These approaches allow us to get new and improved geometrical-parameter bounds on the elastic moduli of two-dimensional composites. Applications of the bounds for effective-medium geometries as well as random arrays of aligned fibers in a matrix are discussed.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering