用物理增强神经网络,自动发现3D打印复合材料的力学规律。
Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials
- 结合物理约束与神经网络,学习材料成分与力学性能的关系。
- 在拉伸和扭转测试中,对5种配方、3种速率下均实现高精度预测。
- 适合材料设计、智能制造领域,可加速新复合材料研发。
多材料3D打印,尤其是通过聚合物喷射技术,可在单次打印中以微米级混合不同光固化聚合物,制造出机械性能可调的数字材料。本文通过实验与计算相结合的方法,研究了3D打印数字材料的组分依赖性力学行为。实验对五种配方(软硬光聚合物组合)在三种应变率和扭转载荷率下进行单轴拉伸与扭转测试,结果表明其响应具有强非线性与速率依赖性,且受组分影响显著。为建模该行为,提出一种物理增强神经网络(PANN),采用部分输入凸神经网络(pICNN)学习组分依赖的超弹性应变能函数,并结合准线性黏弹性(QLV)模型描述时间依赖响应。pICNN确保应变不变量下的凸性,同时允许组分呈现非凸关系;引入$ L_0 $稀疏化提升可解释性。对于时间依赖性,使用多层感知机(MLP)从组分预测黏弹性松弛参数。所提模型在单轴拉伸与扭转下均准确捕捉非线性、速率依赖行为,对插值组分亦有高预测精度。该方法为多材料3D打印提供了一套可扩展的、组分感知的本构模型自动发现框架。
原文摘要 · Abstract (English)
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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