MICROSTRUCTURE DESIGN OPTIMIZATION OF MATERIALS WITH SPECIFIC ELASTIC PROPERTIES

In this paper, the formulation of the design optimization problem of materials with specific elastic properties is investigated. A shape optimization method is used to determine the microstructure shape of composite materials composed of two phases (a material phase and a void phase) in order to design composite materials with specific elastic properties, such as with zero Poisson's ratio. Microstructure topology is limited to honeycombed skeleton structure in a unit cell as this is the most easily manufactured. The optimal goal is to minimize the square of the differences between the components of effective elastic tensor and the desired (given) values of these components. The effective behavior of composite materials is evaluated by use of a finite element based numerical homogenization procedure. As an example, the design of materials with zero Poisson's ratio shows the procedure.