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

2025-07-01

AI Summary

This study addresses the challenge of modeling composition-dependent and nonlinear, rate-sensitive mechanical behavior of digital materials in multi-material 3D printing (polyjet). Methodologically, we propose a physics-enhanced machine learning framework that integrates partially input-convex neural networks (pICNNs) with L₀ sparsification to construct an interpretable, thermodynamically consistent hyperelastic strain-energy potential. Concurrently, a multilayer perceptron (MLP) predicts quasi-linear viscoelastic parameters, enabling coupled nonlinear hyperelastic–viscoelastic modeling. All components strictly embed fundamental physical constraints—including material frame indifference, convexity of the elastic potential, and thermodynamic consistency—thereby significantly improving generalization and extrapolation reliability. Validated against uniaxial tensile and torsional experiments, the model achieves high predictive accuracy for unseen material compositions. Results demonstrate strong scalability and engineering applicability in multi-material additive manufacturing.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Modeling composition-dependent mechanical behavior of 3D printed digital materials
• Developing physics-augmented neural networks for nonlinear rate-dependent responses
• Ensuring interpretability and accuracy in constitutive model discovery

Innovation

• Physics-augmented neural network for material modeling
• Partially input convex neural network for hyperelasticity
• Multilayer perceptron predicts viscoelastic relaxation parameters