In the past decade, computational design methods based on formal optimization approaches have gained substantial popularity for solving engineering design problems. Traditional optimization approaches, such as boundary variation and sizing techniques, have been successfully applied to improve and refine designs that were initially found through engineering intuition and/or transfer of solutions for similar design problems. In contrast topology optimization is an optimization approach for finding conceptually novel, non-intuitive designs and does not require a close-to-optimal initial design. These features are in particular appealing for complex design problems in emerging technology areas, such as the design of active materials and micro-systems. For both applications, as for many others, the systems response is strongly nonlinear and dominated by the interaction of two or more coupled physical phenomena.