Description

Overall behavior of composite materials and metamaterials. The fundamentals of homogenization for elastic composites, variational principles and energy-based bounds, and dynamic homogenization concepts and techniques are introduced. Voigt and Reuss mixture rules are discussed and expanded to dilute distribution, self-consistent, Mori-Tanaka, and periodic approaches with examples from particulate, whisker, platelet, and fiber-reinforced composites. The effects of damage and cracks and the concept of metamaterial are discussed and examples are presented. The use of finite element calculations for static, nonlinear, and dynamic homogenization will be discussed and the application to non-mechanical and coupled problems are explored.