Discovery of Constitutive Behaviour with Tomography based Full Field Measurements

The discovery of constitutive models using full-field measurements has been a long-standing challenge, primarily due to the reliance on surface measurements using state-of-the-art DIC methods. However, recent advances in tomography-based techniques such as DVC have enabled the acquisition of high-resolution volumetric full-field measurements in nominally homogeneous solids, without the addition of artificial speckle. In this study, we collect full-field displacement data and global force-displacement data on a range of engineering polymeric solids and perform constitutive model parameterizations. Our approach involves using displacement data and a selection of canonical hyperelastic materials models suitable for different material classes, such as Neo-Hookean, Arruda-Boyce and other exemplars for general hyperelastic behavior. The <i>a priori</i> assumed constitutive models are then calibrated using numerous forward Finite Element simulations (FEMU) to yield a best match to experimentally observed volumetric displacement and force data. Additionally, we explore the performance of stress-unsupervised machine-learning frameworks in discovering the materials’ constitutive model, in comparison to the FEMU approach. To the best of our knowledge, this presents the first attempt in utilizing real three-dimensional full-field displacement and (total) strain measurements in data-driven constitutive modelling of homogeneous materials. Notably, if used in conjunction with x-ray diffraction elastic strain measurements, the technique used in this study opens avenues to accessing 3-D plastic strain data in metals.