Towards end-to-end optimization in multimaterial 3D printing

Xue-Ling Luo; Steven Yang; Jingye Tan; Robert F. Shepherd; Noy Cohen; Nikolaos Bouklas

physics.comp-phJul 14, 2026

Towards end-to-end optimization in multimaterial 3D printing

Authors: Xue-Ling Luo, Steven Yang, Jingye Tan, Robert F. Shepherd, Noy Cohen, Nikolaos Bouklas

Organizations: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA · Department of Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA, USA · Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa, Israel · Pasteur Labs, Brooklyn, NY, USA

Abstract

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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Sep 3, 2026 · cs.AIJ/K move · Enter open · S save

Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materials

Josué García-Ávila, Beijun Shen, Manuel K. Rausch, Mary C. Boyce+1

Department of Mechanical Engineering, Columbia University, New York City, USA · Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, USA · Department of Biomedical Engineering, University of Texas at Austin, Austin, USA · Department of Mechanical Engineering, University of Texas at Austin, Austin, USA

Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition-dependent, and rate-dependent dissipative behavior. Classical finite-strain viscoelastic models represent such behavior with closed-form strain energy functions for equilibrium and non-equilibrium stresses as well as evolution of internal variables, which may limit flexibility when a single constitutive model is expected to generalize across materials and loading rates. Here, we present a data-driven multi-material constitutive modeling framework that generalizes a formulation by Bergström and Boyce. The proposed framework retains the structure of the classical model, namely multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law directed along the normalized nonequilibrium deviatoric stress. For the equilibrium branch, the data-driven discovery framework either directly predicts closed-form model parameters as functions of composition or automatically constructs a polyconvex strain-energy function using neural ordinary differential equations (NODEs). The nonequilibrium branch kinetics are learned similarly, either by directly identifying closed-form parameters across compositions or by using appropriately constrained artificial neural networks. Using multi-rate uniaxial compression data across multiple material compositions, we show that the proposed formulation captures rate-dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.

6-Dof Viscoelastic Mechanism

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Abstract

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