Variant design generation and machine learning aided deformation prediction for auxetic metamaterials

Abstract

Auxetic metamaterials have been applied in many domains due to their unique auxetic behavior, tunable local kinematics, and morphological intelligence. However, the classic auxetic designs normally cannot be directly applied due to their defects. How to modify the existing classic design to achieve diverse but also valid variant designs remains a challenging problem. One common approach is to use predefined parameters and fine-tune these parameters. Yet, this approach limits the design space and highly relies on expert knowledge. In this paper, we proposed a variant design generation method based on a path-finding algorithm to achieve pixel-level design freedom. Meanwhile, to support the evaluation of designs in such a large design space, we developed a multi-scale geometry-informed Graph U-net. More specifically, we proposed MeshPool—a predefined clustering-based pooling technique, and distortion loss—a geometry-informed loss function inspired by finite element analysis (FEA). A variant design family for re-entrant structures is generated as a case study to validate the variant design generation method. And the Graph U-net is developed to predict complex nonlinear deformation with simple linear FEA results. The results from the case study demonstrated that the proposed variant design generation method covered the properties space of re-entrant structures and the developed Graph U-net achieved accurate prediction with a nodal displacement mean absolute error (MAE) of around 0.0169 mm under an average nodal displacement of 0.5058 mm. More importantly, we demonstrated the graph neural network’s unique capability of learning gradient information compared with convolutional neural network in a benchmark on strain and stress.