Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials

2025/07/01 by Yang, Steven, Levin, Michal, Padmanabha, Govinda Anantha +6 · 1 citation
#Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2507.02991

Abstract

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. This work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply L₀ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

Citations

• Inverse design of anisotropic microstructures using physics-augmented neural networks
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• Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics
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• Towards mechanical characterization of soft digital materials for\n multimaterial 3D-printing
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• Input Convex Neural Networks
• Adam: A Method for Stochastic Optimization

Cited by

• COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates

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