Data-driven inverse design of growth-based Voronoi meta-materials

Abstract

Metamaterials derive their properties from microstructure rather than from bulk material properties. This opens property spaces that are difficult, or impossible, to access with traditional methods. However, exploring this vast design space remains challenging because classical techniques can be computationally inefficient. Recent years has seen many successful applications of data-driven methods to this problem. Data-driven models can be used to bypass expensive Finite Element (FE) simulations and experiments by exploiting large datasets. This requires the parameterization of microstructures such that they can be mapped to properties. The forward problem, in which properties of are determined from design parameters, is typically well-posed, which allows straightforward application of machine learning methods. The inverse problem, in which design parameters are identified to match specific properties, is ill-posed because multiple sets of design parameters can produce similar properties. The Voronoi growth method induced by star-shape metrics provides a way to explore a large geometrical design space using simple parameterization. It is used to generate 2D unit cells of void and material pixels with non-trivial topologies. The growth process enforces connected geometry while also allowing for smooth transition between different designs. Using homogenization techniques, we generate a large dataset of design parameters and stiffness properties. Machine learning techniques are first used to model the forward problem. By combining the trained forward model with the inverse model, the inverse problem is rendered well-posed. Both the forward and (deterministic) inverse model show excellent agreement between target and predicted values. The method is generalized beyond the design space by targeting properties of non-growth based structures. We investigate methods to create a stochastic inverse model, that can produce multiple designs to match target properties. Verification is done by comparing tensile tests of 3D printed samples to FE simulations.