Programming Material Behaviour through Multiscale Optimization and Surrogate Models of Unit Cells
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Programmable metamaterials establish a new subset of metamaterials offering controllable and variable physical properties. As metamaterials, they are artificial materials and exhibit exotic and counter-intuitive material behavior, but are more specifically tailored for engineering purposes. Additionally, from industrial point of view, an automated and robust process chain is desired: From a parametrized unit cell to the final model of the programmable material, ready to be manufactured. In order to tackle the customization of material response, a computational optimization framework like topology or material optimization is proposed. Besides, our work relies on a multiscale and data-driven approach, allowing a broad range of application to large strains and different classes of unit cells and target functions. From a black box simulation model, we obtain a large amount of data for all considered loading and parametric scenarios at micro scale, sampled on a high dimensional grid. After that, the data set is significantly compressed and this reduced data representation enables an adequate interpolation and differentiation. For that purposes, we use low rank decomposition to compute multivariate material models allowing easy parametrizations of individually designed unit cells at macro scale. By means of this data-based constitutive surrogate model we can apply efficient gradient-based optimization, for which hardly accessible design gradients are necessary to find the optimal parameter distribution. Furthermore, we present numerical results with different unit cells and compare them to fully resolved simulations. One example of lab-scale production is shown and compared to simulation results.