端到端优化多材料3D打印，实现结构与材料分布协同设计。
Towards end-to-end optimization in multimaterial 3D printing
- 用实验数据提取显式本构关系，结合有限元实现高效反向传播。
- 在软体抓手应用中实现各向异性接触响应的连续材料优化。
- 适合需要高精度多材料结构设计的研究者和工程师。
多材料3D打印可制造功能梯度部件，但同时优化空间材料分布与结构拓扑面临高维设计空间和复杂本构建模的挑战。本文提出一种端到端计算框架，结合稀疏化物理增强神经网络与基于有限元的拓扑优化。通过实验数据提取显式、成分感知的超弹性本构定律，利用FEniCSx实现伴随状态法的精确符号微分，有效规避了神经网络本构模型的应用瓶颈。该方法应用于软体抓手机器人，实现了高度各向异性接触响应的连续材料优化，并在非失效拉伸约束下同步优化宏观拓扑与材料分布。该方法可替代繁琐的试错原型，为先进多材料增材制造建立可解释、稳健的机器学习设计基元。
原文摘要 · Abstract (English)
Multimaterial 3D printing enables the fabrication of functionally graded components, but optimizing their spatial material distribution alongside structural topology remains a formidable challenge due to high-dimensional design spaces and complex constitutive modeling. This paper presents an end-to-end computational framework integrating sparsified physics-augmented neural networks with finite-element-based topology optimization. By extracting closed-form, composition-aware hyperelastic constitutive laws from experimental data, this approach facilitates exact symbolic differentiation via the adjoint state method implemented with FEniCSx, efficiently circumventing the bottlenecks of applying neural network constitutive models. This pipeline is deployed on soft robotic gripper applications, demonstrating continuous composition optimization for highly anisotropic contact responses, and the concurrent optimization of macroscopic topology and material distribution under non-failure stretch constraints. This methodology could replace laborious empirical prototyping, establishing interpretable machine-learning models as practical, robust design primitives for advanced multimaterial additive manufacturing.
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