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.
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.
Josué García-Ávila, Beijun Shen, Manuel K. Rausch +2
Typically, heuristic/trial-based approaches are used to design soft pneumatic grippers (SPGs). This paper presents a systematic topology optimization framework for developing SPGs. The design-dependent nature of actuating load is modeled using Darcy's law with an added drainage term. A 2D soft arm unit is then optimized as a compliant mechanism under pneumatic loading. To ensure the design is robust and manufacturable, the problem is formulated as a min-max optimization, where output deformations of blueprint and eroded designs are considered. A volume constraint is imposed on the blueprint part, while a strain-energy constraint is enforced on the eroded part. The Method of Moving Asymptotes is employed to solve optimization problems. The optimized 2D part is extruded suitably to generate a 3D unit. Ten such 3D units are assembled to create a gripper arm. Both the optimized 2D unit and the corresponding gripper arm outperform their conventional rectangular designs under pneumatic loading, demonstrating the efficacy of the proposed approach. The arms are fabricated using the SLA printing technique. Numerical and experimental results are compared at different pneumatic loads. Four 3D-printed arms are integrated with a supporting structure to form the SPG. The gripping action of the SPG is demonstrated on objects with different weights, sizes, structures, stiffnesses, and shapes.
Thermo-mechanical compliant devices are commonly designed with small-strain linear elasticity and temperature-independent material properties, even though they might operate hundreds of kelvin above ambient where both assumptions are questionable. In this work, we quantify the effect and cost of each assumption in multi-material topology optimization of thermally actuated compliant devices. To this end, we introduce a physics-informed, simultaneous analysis-and-design framework with (i) a finite-strain quadratic-Hencky (logarithmic-strain) constitutive model whose isotropic thermal eigenstrain admits an exact additive split in log-strain space, and (ii) temperature-dependent conductivity, thermal expansion, and elastic moduli for a titanium--copper--steel material system. We optimize a thermal actuator and a thermal gripper at three design temperatures under both a baseline model and the full physics, subject to mass and manufacturability constraints. Every converged design is re-evaluated by verified nonlinear finite element solvers in the full factorial of constitutive law and property model. The comparison between the two factors reveals that the constitutive law is the decisive modeling choice: These devices work as linkages where linear kinematics mistakes rotation for compressive strain; its error therefore grows with the design temperature and concentrates on the very layouts that exploit rotation best. Because a linear optimizer also steers away from the rotation-rich mechanisms that would expose this bias, the model can deceptively appear trustworthy when validated against its own designs. Designing with the full physics yields consistently stronger and more temperature-robust devices at a modest increase in design-time cost.