Although a substantial body of work has been dedicated to deriving viscoelastic constitutive equations for particular classes of materials directly from physical considerations, these models often cannot sufficiently describe the diverse response space of viscoelastic materials in common experimentally and industrially relevant conditions. Recently, the advent of widely available machine learning (ML) tools has given rise to a new approach: learning constitutive models directly from data. While current ML approaches have shown some success in very particular circumstances, they are not easily portable to different flow conditions, tend to accommodate training data taken only by specific experimental protocols, and do not enforce key physical constraints such as invariance to rotating frames of reference. Here, we present a framework for learning physically-informed differential viscoelastic constitutive equations that combines the salient features of ML and physically-informed approaches. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. These models respect physical constraints such as frame invariance and tensor symmetry by construction. They may be trained using data characterizing any observable related to the stress or strain in an arbitrary flow protocol, and subsequently applied in simulations of different flow kinematics, including as part of a multidimensional computational fluid dynamics simulation. With the increased availability of a wide breadth of experimental data for viscoelastic materials, this robust machine learning framework will open new avenues for efficient and accurate data-driven rheological modeling.
Authors: Kyle R. Lennon1, Gareth H. McKinley2, James W. Swan1
1Department of Chemical Engineering, Massachusetts Institute of Technology, USA
2 Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
