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

Steven Yang; Michal Levin; Govinda Anantha Padmanabha; Miriam Borshevsky; Ohad Cohen; D. Thomas Seidl; Reese E. Jones; Nikolaos Bouklas; Noy Cohen

arXiv · 2507.02991

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

Steven Yang·Michal Levin·Govinda Anantha Padmanabha·Miriam Borshevsky·Ohad Cohen·D. Thomas Seidl·Reese E. Jones·Nikolaos Bouklas·Noy Cohen

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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 $L_0$ 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.

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Steven Yang, Michal Levin, Govinda Anantha Padmanabha, Miriam Borshevsky, Ohad Cohen, D. Thomas Seidl, Reese E. Jones, Nikolaos Bouklas, Noy Cohen. 2025-07-01. Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials. https://arxiv.org/abs/2507.02991

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