Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy

TL;DR

This paper introduces a multiscale topology optimization method for designing elastic bodies with tunable anisotropic properties using spinodoid microstructures and deep neural network surrogates for efficient homogenization.

Contribution

It develops a novel data-driven framework combining spinodoid microstructures, finite element analysis, and neural networks for efficient multiscale topology optimization.

Findings

Neural network surrogate models accurately predict effective elastic properties.

Seamless spatial grading of microstructures enables tunable anisotropy.

The approach reduces computational cost compared to classical homogenization methods.

Abstract

We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE$^2$-type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives - a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.