[Paper Review] Experiment-informed finite-strain inverse design of spinodal metamaterials

Prakash Thakolkaran, Michael A. Espinal+3 more|arXiv (Cornell University)|Dec 18, 2023

Topology Optimization in Engineering4 citations

TL;DR

This study presents an experiment-informed, physics-enhanced machine learning framework for inverse design of spinodal metamaterials with tailored finite-strain mechanical responses. By leveraging a small dataset of 107 experimentally measured stress-strain curves up to 40% strain, the method uses physics-based inductive biases through partial input convex neural networks (PICNNs) to model nonconvex energetic potentials, enabling accurate prediction and optimization of complex nonlinear behavior without relying on high-fidelity simulations.

ABSTRACT

Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials -- observed experimentally and in selected nonlinear simulations -- leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

Motivation & Objective

• To address the challenge of designing spinodal metamaterials with customized finite-strain mechanical properties when computational simulations are limited and experimental data is sparse.
• To bridge the gap between structure and property relations in spinodal metamaterials by directly integrating high-fidelity experimental data into a machine learning framework.
• To overcome the quality-quantity duality in machine learning for metamaterials by embedding physics-based inductive biases that compensate for limited data.
• To enable inverse design of spinodal architectures that achieve target stress-strain responses, including extreme deformation behaviors such as energy absorption up to 40% strain.
• To provide a physically interpretable framework that captures instability-driven pattern formation via nonconvex energetic potentials inspired by phase transformation modeling.

Proposed method

• The framework uses a small experimental dataset of 107 microscale spinodal metamaterials tested via in situ and ex situ nanomechanical uniaxial compression to 40% strain.
• A physics-enhanced machine learning model is constructed using multiple partial input convex neural networks (PICNNs) to form a nonconvex potential, capturing complex nonlinear stress-strain behavior under large deformations.
• The forward model surrogate learns structure-to-property mappings from experimental data, incorporating physical constraints such as nonconvexity to improve generalization with limited data.
• An inverse optimization scheme employs gradient-based multi-initialization to identify spinodal morphologies that match a target finite-strain stress-strain response.
• The method is grounded in phase transformation theory, modeling instability-induced pattern formation through nonconvex energetic potentials derived from spinodal decomposition physics.
• The framework is validated using a high-throughput experimental campaign of 321 compressive tests, with consistent IP-Dip photoresist properties (E = 3.2 ± 0.3 GPa, σ_y = 77 ± 7 MPa) across batches.

Experimental results

Research questions

• RQ1 Can a physics-enhanced machine learning framework accurately predict finite-strain mechanical responses of spinodal metamaterials using only sparse experimental data?
• RQ2 How can nonconvex energetic potentials be modeled in machine learning to capture complex nonlinear behaviors such as buckling and large deformations in spinodal architectures?
• RQ3 To what extent can physics-based inductive biases reduce the need for large-scale computational simulations in inverse design of architected materials?
• RQ4 Can the framework identify spinodal morphologies that achieve a target stress-strain response even when that response lies outside the training data domain?
• RQ5 How does the integration of in situ and ex situ experimental data improve the physical interpretability and reliability of the ML model for complex metamaterials?

Key findings

• The framework successfully predicts finite-strain stress-strain responses, including energy absorption up to 40% strain, for various spinodal morphologies using only 107 experimental data points.
• The PICNN-based model accurately captures complex nonlinear behaviors such as geometric and material nonlinearities, buckling, and self-contact without relying on high-fidelity simulations.
• The method enables inverse design of spinodal structures that match target stress-strain curves, even when those targets lie outside the range of the training data.
• The experimental validation confirms consistent material properties across print batches, with Young’s modulus of 3.2 ± 0.3 GPa and yield strength of 77 ± 7 MPa for IP-Dip photoresist.
• The integration of in situ and ex situ testing revealed localized deformation mechanisms in thick-shelled spinodal morphologies, informing the physical interpretation of the ML model’s predictions.
• The framework demonstrates a 10× increase in data throughput compared to classical experimental approaches, enabling ML applicability in high-density architected materials.