🤖 AI Summary
This study addresses the challenges of quantifying experimental data informativeness and achieving high data–parameter alignment in constitutive model calibration under complex multiaxial loading. We propose a novel mechanics-informatics paradigm featuring: (i) a first-principles “stress-state entropy” framework to quantify the information content of mechanical experiments; (ii) entropy-guided, high-information-efficiency constitutive learning and specimen design—e.g., high-entropy cruciform and low-entropy Pierrce pure-shear specimens; and (iii) a hybrid Bayesian optimization–transfer learning strategy to mitigate modeling uncertainty. The methodology integrates information theory, anisotropic inelastic constitutive modeling, and experimental mechanics. Experimental validation demonstrates substantial improvements in parameter identification accuracy and robustness; entropy-optimized specimens maximize information yield per test; and transfer learning enables accurate calibration without costly physical experiments, preserving fidelity.
📝 Abstract
Efficient and accurate learning of constitutive laws is crucial for accurately predicting the mechanical behavior of materials under complex loading conditions. Accurate model calibration hinges on a delicate interplay between the information embedded in experimental data and the parameters that define our constitutive models. The information encoded in the parameters of the constitutive model must be complemented by the information in the data used for calibration. This interplay raises fundamental questions: How can we quantify the information content of test data? How much information does a single test convey? Also, how much information is required to accurately learn a constitutive model? To address these questions, we introduce mechanics informatics, a paradigm for efficient and accurate constitutive model learning. At its core is the stress state entropy, a metric quantifying the information content of experimental data. Using this framework, we analyzed specimen geometries with varying information content for learning an anisotropic inelastic law. Specimens with limited information enabled accurate identification of a few parameters sensitive to the information in the data. Furthermore, we optimized specimen design by incorporating stress state entropy into a Bayesian optimization scheme. This led to the design of cruciform specimens with maximized entropy for accurate parameter identification. Conversely, minimizing entropy in Peirs shear specimens yielded a uniform pure shear stress state, showcasing the framework's flexibility in tailoring designs for specific experimental goals. Finally, we addressed experimental uncertainties and demonstrated the potential of transfer learning for replacing challenging testing protocols with simpler alternatives, while preserving calibration accuracy.