mlsanityData to 14 Oct 2026

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

arXiv 2507.02991 ↗First posted 1 Jul 2025cs.LG physics.comp-phcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 11 of its 58 references that are in the map. First posted on arXiv 1 Jul 2025.

Builds on

11 of 58 references.

References · 11

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Learning Sparse Neural Networks through L0 Regularizationcited by 583
  3. 2016Input Convex Neural Networkscited by 414
  4. 2023Neural networks meet hyperelasticity: A guide to enforcing physicscited by 46
  5. 2021Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equationscited by 29
  6. 2024Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variablescited by 17
  7. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  8. 2023Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteriacited by 14
  9. 2025Neural networks meet hyperelasticity: A monotonic approachcited by 8
  10. 2024Inverse design of anisotropic microstructures using physics-augmented neural networkscited by 7
  11. 2024Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networkscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)cited by 3
  2. 2025COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updatescited by 2
  3. 2026Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modelingcited by 0
  4. 2026Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materialscited by 0