A topology optimisation of composite elastic metamaterial slabs based on the manipulation of far-field behaviours

We propose a numerical method for a topology optimisation of composite elastic metamaterial slabs. We aim to realise some anomalous functionalities such as perfect absorption, wave-mode conversion, and negative refraction by designing the shape and topology of (visco-)elastic inclusions. Instead of manipulating effective material constants, we propose to utilise the far-field characteristics of scattered waves. This allows us to achieve novel functionalities for waves in not only low- but also high-frequency ranges. The design sensitivity corresponding to the far-field characteristics is rigorously derived using the adjoint variable method and incorporated into a level-set–based topology optimisation algorithm. The design sensitivity is computed by the boundary element method with periodic Green’s function instead of the standard finite element method to rigorously deal with the radiation of scattered waves without absorbing boundaries. We show some numerical examples to demonstrate the effectiveness of the proposed method.