Deep Learning for Topology Optimization of Triply Periodic Minimal Surface Based Gyroid-Like Structures

Abstract

Triply periodic minimal surfaces (TPMS) are non-intersecting complex geometrical surfaces that can be used in unit cell design of cellular structures. TPMS possess attractive properties like large surface area to volume ratio and mathematically controlled geometry which find them applications in catalytic converters, cocontinuous composites, thermal and permeability management, to name a few. The advent of additive manufacturing eased the manufacture of these structures which were previously challenging with traditional methods of manufacturing. Design of TPMS unit-cell based materials involves topology optimization to achieve the desired physical properties depending on the specific application of the structure. Topology optimization, in turn, involves the objective function evaluations for each iteration till converging to an optimal design and this may pose a computational burden when the function evaluations are time consuming finite element or computational fluid simulations. This can be alleviated by employing machine learning based methods for the optimization process. Deep learning using convolutional neural networks (CNN) have effectively been used for prediction of optimal topologies required for desired properties thus eliminating any objective function evaluations. In this paper, we explore the use of 3D CNN models for topology optimization of a TPMS based unit cell. The Solid Isotropic Material Penalization density method in topology optimization is employed on energy based homogenized unit cell properties. The unit cell that is obtained satisfying a desired mechanical property along with their topology parameters is then learnt to build a CNN model which can then be used to predict the optimal unit cell design for any topology parameters. The class of TPMS used in this work is Gyroids. The CNN model is tested for errors in prediction using mean square error metric and dice coefficient of the 2D slices of unit cell. The results indicate that the model can predict the ground truth accurately with few data points. This showed a promising approach in the area of TPMS based unit cell design using CNN.