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

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.

An Improved Trabecular Bone Model Based on Voronoi Tessellation

“…The influence of the distribution of the seeds on the morphometrical parameters of the structures could be further studied (Zheng et al, 2020). As mentioned before, the distribution of the seeds will not only influence the distribution of cells, but also the geometry of the polyhedrons and the mechanical properties of the structure.…”

“…If the material properties change within the bone, e.g. due to local pathological differences, unit cells with different parameters can be used to accommodate for the corresponding properties (Zheng et al, 2020).…”