Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operators

Machine learning (ML) is emerging as a transformative tool for the design of architected materials, offering properties that far surpass those achievable through lab-based trial-and-error methods. However, a major challenge in current inverse design strategies is their reliance on extensive computational and/or experimental datasets, which becomes particularly problematic for designing micro-scale stochastic architected materials that exhibit nonlinear mechanical behaviors. Here, we introduce a new end-to-end scientific ML framework, leveraging deep neural operators (DeepONet), to directly learn the relationship between the complete microstructure and mechanical response of architected metamaterials from sparse but high-quality in situ experimental data. The approach facilitates the inverse design of structures tailored to specific nonlinear mechanical behaviors. Results obtained from spinodal microstructures, printed using two-photon lithography, reveal that the prediction error for mechanical responses is within a range of 5 - 10%. Our work underscores that by employing neural operators with advanced micro-mechanics experimental techniques, the design of complex micro-architected materials with desired properties becomes feasible, even in scenarios constrained by data scarcity. Our work marks a significant advancement in the field of materials-by-design, potentially heralding a new era in the discovery and development of next-generation metamaterials with unparalleled mechanical characteristics derived directly from experimental insights.

Identifying Constitutive Parameters for Complex Hyperelastic Solids using Physics-Informed Neural Networks

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of Physics-Informed Neural Networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a new PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal time-dependent experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even amidst noisy data. Our results reveal that our framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework sets the stage for a transformative approach in modulus identification for complex solids, especially for those with geometrical and constitutive intricate.

Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review

For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is exploding, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano- and micro-mechanics, architected materials, and 2D material. Finally, we highlight some current challenges of applying ML to multi-modality and multi-fidelity experimental datasets and propose several future research directions. This review aims to provide valuable insights into the use of ML methods as well as a variety of examples for researchers in solid mechanics to integrate into their experiments.

Dynamic fracture of a bicontinuously nanostructured copolymer: A deep learning analysis of big-data-generating experiment

Here, we report the dynamic fracture toughness as well as the cohesive parameters of a bicontinuously nanostructured copolymer, polyurea, under an extremely high crack-tip loading rate, from a deep-learning analysis of a dynamic big-data-generating experiment. We first invented a novel Dynamic Line-Image Shearing Interferometer (DL-ISI), which can generate the displacement-gradient - time profiles along a line on a sample's back surface projectively covering the crack initiation and growth process in a single plate impact experiment. Then, we proposed a convolutional neural network (CNN) based deep-learning framework that can inversely determine the accurate cohesive parameters from DL-ISI fringe images. Plate-impact experiments on a polyurea sample with a mid-plane crack have been performed, and the generated DL-ISI fringe image has been inpainted by a Conditional Generative Adversarial Networks (cGAN). For the first time, the dynamic cohesive parameters of polyurea have been successfully obtained by the pre-trained CNN architecture with the computational dataset, which is consistent with the correlation method and the linear fracture mechanics estimation. Apparent dynamic toughening is found in polyurea, where the cohesive strength is found to be nearly three times higher than the spall strength under the symmetric impact with the same impact speed. These experimental results fill the gap in the current understanding of copolymer's cooperative-failure strength under extreme local loading conditions near the crack tip. This experiment also demonstrates the advantages of big-data-generating experiments, which combine innovative high-throughput experimental techniques with state-of-the-art machine learning algorithms.