Mechanical metamaterials derive their properties from the combination of a base material and a designed mesostructure, making them ideal candidates for inverse design, i.e., identifying a specific metamaterial with target mechanical properties [1]. In this contribution, we present a neural network (NN)-based framework for inverse design of architected materials and demonstrate it for the specific task of reproducing a full stiffness tensor, focusing on mesostructure design for a fixed base material.

We apply this framework to two classes of architected materials: triply periodic minimal surfaces (TPMS) and spinodoid metamaterials [2]. TPMS metamaterials are mathematically defined by combinations of trigonometric functions and feature zero mean surface curvature with three-dimensional periodicity. Despite the diversity of TPMS unit cell types, the absence of a unified descriptor space limits their straightforward tuning for target mechanical properties. In contrast, spinodoid metamaterials, inspired by spinodal topologies found in nature, offer a broad design space with complex topologies governed by only a few descriptors [2]. Their tunable anisotropy, non-periodicity, and robustness to symmetry-breaking defects make them particularly well-suited for inverse design applications [2].

Using the NN-based inverse design framework, we examine the elastic properties that can be achieved by these two metamaterial types for the defined design task. This comparison highlights their capabilities and limitations in reproducing target stiffness tensors, providing insights into how mesostructural design can be leveraged to tailor the mechanical behaviour of architected materials.

REFERENCES
[1] Raßloff, A., Seibert, P., Kalina, K. A., & Kästner, M., Inverse design of spinodoid structures using Bayesian optimization, Computational Mechanics, (2025).
[2] Kumar, S., Tan, S., Zheng, L. & Kochmann, D. M., Inverse-designed spinodoid metamaterials, npj Comput. Mater. 6, 73 (2020).