Mechanical Metamaterial Optimization via Automatic Differentiation

Optimizing metamaterials for specific mechanical tasks is challenging. Traditional optimization approaches, such as topological optimization, primarily address the linear response of these materials, limiting their effectiveness for applications requiring complex nonlinear responses. Furthermore, Finite Element Method (FEM) simulations are computationally intensive and often fail to handle self-contact interactions, which are prevalent in metamaterials. By using Automatic Differentiation (AD) directly on the metamaterial simulations, we can easily compute sensitivities of nonlinear tasks, such as energy dissipation or stress distribution. Also, by using a surrogate model of linked polygons, we accelerate simulation processes and enable self-contact interactions. Our results suggest that this approach could significantly influence the development of next-generation automotive crash boxes and other energy-absorbing components. This framework, adaptable to various physical simulations, offers a robust tool for advancing optimization in metamaterial design and beyond.