Seeking the most informative design of test specimens for learning constitutive models

Accurate calibration of constitutive models is vital for predicting the mechanical behavior of engineering materials under various loading conditions. Traditionally, the calibration process involves a series of experiments on specimens with simple geometries to capture the complexities in the constitutive models. Each single test conveys a small amount of information that a well-trained human brain can handle, resulting in a large number of experiments needed for a complete calibration. Therefore, traditional calibration approaches are usually costly and time-consuming. With recent advancements in computational techniques, there is an emerging opportunity to leverage geometrically complex specimens in experiments to obtain a larger amount of information for computers to learn and calibrate the model. Despite some initial success, the most important question remains unsettled: How much information does a mechanical test convey? In this work, we answer this question by incorporating information entropy as a quantitative measure in the design of mechanical test specimens. We demonstrate the viability of the proposed approach by comparing the performance of selected test specimens for learning the plasticity model of sheet metal, e.g., the Hill48 anisotropic elastic-plastic model in this case. An optimal entropy criterion is proposed for selecting the appropriate heterogeneous test specimen for inverse calibration, depending on the cardinality of the stress state space considered in the model. Finally, Bayesian optimization is applied to uniaxial and biaxial tension specimens, using the stress state entropy as an objective function, to investigate the general principles of designing specimens with maximum information for learning constitutive models.