Scientific machine learning for modeling complex fluids with thixotropy and plasticity

Abstract Complex fluids that exhibit thixotropy and plasticity play a pivotal role in a range of industries including fast moving consumer goods, additive manufacturing as well as in the energy, resource extraction and automotive sectors. The soft matter material systems used in such applications are often collectively labeled thixo-elasto-visco-plastic (TEVP) fluids and the complexity of their rheological response requires new constitutive theories for accurately capturing their stress-strain-deformation rate behaviors. Existing constitutive models have struggled to accurately capture the intricate coupling between viscoelastic responses at small strains and the progressive transition to irreversible plastic deformation and time-dependent thixotropic flow at large strains and long times. A key limitation is the reliance on human-biased model construction and simple analytic constitutive formulations, which fail to capture the complexities of empirical rheological data. To overcome such restrictions, we leverage scientific machine learning techniques constrained by fundamental physical principles to formulate a universal fractional differential equation framework for these materials. Informed by established physics, and augmented with a neural network, this framework learns targeted data-driven corrections to the empirically uncertain terms within an established fractional constitutive model directly from experimental data, rather than replacing the physics with a stand-alone black box. The improvements reported here arise from combining this constrained physics with a neural network, and not from the network alone. The resulting digital fluid twin provides accurate predictions of material responses over a wide range of nonlinear deformation processes. Moreover, this framework enables the time- and deformation-dependent evolution of internal variables which parameterize the material microstructure to be inferred from available training data.By enabling physics-informed discovery of these internal processes and learning accurate constitutive relations for these complex fluids, the framework described significantly advances the modeling capabilities of rheological universal differential equations (RUDES).