Design of smart composite materials using topology optimization

The topology optimization method is used to find the distribution of material phases that extremizes an objective function (e.g., thermal expansion coefficient, piezoelectric coefficients etc) subject to constraints, such as elastic symmetry and volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using a numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming. We review the topology optimization procedure as a tool for smart materials design and discuss in detail two recent applications of it to design composites with extreme thermal expansion coefficients and piezocomposites with optimal hydrophone characteristics.