Data-Driven Nonlinear Deformation Design of 3D-Printable Shells

TL;DR

This work introduces a tandem neural network (TNN) that jointly enables forward prediction and inverse design of generalized cylindrical shells (GCS) for nonlinear elastoplastic and hyperelastic compression. Trained on a large experimental dataset of over $12{,}000$ shells, the TNN uses a forward network to map designs to force-displacement curves and an inverse network to propose printable designs achieving target curves, with losses that balance performance accuracy and printability via a tunable parameter $oldsymbol{\alpha}$. The approach delivers accurate predictions of nonlinear behavior, offers physically validated inverse designs, and demonstrates practical applications in impact absorption and material emulation, outperforming alternative methods in handling elastoplastic regimes. The study highlights practical advantages of data-driven design for additive manufacturing, while outlining future directions in nonlinear compression, conditioning, and transfer learning to broaden applicability.

Abstract

Designing and fabricating structures with specific mechanical properties requires understanding the intricate relationship between design parameters and performance. Understanding the design-performance relationship becomes increasingly complicated for nonlinear deformations. Though successful at modeling elastic deformations, simulation-based techniques struggle to model large elastoplastic deformations exhibiting plasticity and densification. We propose a neural network trained on experimental data to learn the design-performance relationship between 3D-printable shells and their compressive force-displacement behavior. Trained on thousands of physical experiments, our network aids in both forward and inverse design to generate shells exhibiting desired elastoplastic and hyperelastic deformations. We validate a subset of generated designs through fabrication and testing. Furthermore, we demonstrate the network's inverse design efficacy in generating custom shells for several applications.

Figures (8)

• Figure 1: Overview. (a) We explore using a tandem neural network (TNN) for the forward and inverse design of generalized cylindrical shells (GCS). (b) GCS are fabricated with fused deposition modeling (FDM) 3D printers. (c) GCS geometry emerges from parameters that control a series of operations applied to cylindrical shells. The result of these operations is a diverse family of structures. (d) Compression tests applied to GCS yield force-displacement curvesSnapp2024. Fabricated with PLA, this GCS exhibits elastoplastic deformation. Highlighted metrics are the linear elastic region used to calculate stiffness (orange line), work performed (red area under curve), and maximum displacement (green value).
• Figure 2: One-to-many performance to design relationship. Two GCS with distinctly different geometry share nearly identical force-displacement behavior, a common problem in inverse design.
• Figure 3: TNN architecture. (a) The forward design network ($\mathcal{F}$) maps GCS designs to corresponding force-displacement curves. (b) The inverse design network ($\mathcal{I}$) maps force-displacement curves back to GCS designs.
• Figure 4: Forward design results. Eight randomly selected results from the test set. The GCS designs (blue) serve as input to $\mathcal{F}$, which predicts force-displacement curves (orange). For reference, we show the actual experimental force-displacement curves from the test set (blue). $\mathcal{F}$ can predict nonlinear deformation behavior for elastoplastic (b, c, e) and hyperelastic (a, d, f, g, h) GCS.
• Figure 5: GCS printability. The percentage of GCS generated by $\mathcal{I}$ that passes all printability checks when trained with different $\alpha$ values. The error bars depict 95% confidence intervals.