Material microstructure optimization for linear elastodynamic energy wave management

We describe a systematic approach to design material microstructures to achieve desired energy propagation in a two-phase composite plate. To generate a well-posed topology optimization problem we use the relaxation approach which requires homogenization theory to relate the macroscopic material properties to the microstructure, here a sequentially ranked laminate. We introduce an algorithm whereby the laminate layer volume fractions and orientations are optimized at each material point. To resolve numerical instabilities associated with the dynamic simulation and constrained optimization problem, we filter the laminate parameters. This also has the effect of generating smoothly varying microstructures which are easier to manufacture. To demonstrate our algorithm we design microstructure layouts for tailored energy propagation, i.e. energy focus, energy redirection, energy dispersion and energy spread.