Noy Cohen

Xue-Ling Luo, Steven Yang, Jingye Tan et al.

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.

Steven Yang, Michal Levin, Govinda Anantha Padmanabha et al.

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.