Uncertainty quantification of rheological properties of soft materials under shear

Rheologically complex soft solids such as thermal greases consist of filler particles within a polymer matrix. These materials find applications in improving the conformity of solid-solid contacts and enhancing heat transfer. Complex soft solids exhibit a transient non-Newtonian rheological response, including thixotropy and viscoelasticity. From a microscopic point of view, these rheological behaviors arise from the particles' inhomogeneous mixing or separation/settling over time. Previous literature has used deterministic approaches to extract values of the rheological parameters of such complex soft solids, assuming a particular model for stress evolution. Specifically, stress relaxation and buildup in sheared commercial thermal greases were successfully captured using a thixotropic-elasto-visco-plastic (TEVP) and a nonlinear elasto-visco-plastic (NEVP) model, respectively. However, the previous model calibration methods ignored parameter and model uncertainty arising from epistemic and aleatoric sources. Therefore, in this study, we use statistical methods, specifically a state-of-the-art hierarchical Bayesian inference methodology, to obtain distributions of the parameters in the rheological models. We further propagate these uncertainties through the rheological models to obtain uncertainties within the transient shear stress distributions at different imposed shear rates. Our approach provides a systematic way to understand model identifiability and, therefore, provides a more robust way of empirical model selection for thixotropic soft solids of unknown microstructure.