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The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material. 

Precise and reliable prediction of soft and structured materials’ behavior under flowing conditions is of great interest to academics and industrial researchers alike. The classical route to achieving this goal is to construct constitutive relations that, through simplifying assumptions, approximate the time- and rate-dependent stress response of a complex fluid to an imposed deformation. The parameters of these simplified models are then identified by suitable rheological testing. The accuracy of each model is limited by the assumptions made in its construction, and, to a lesser extent, the ability to determine numerical values of parameters from the experimental data. In this work, we leverage advances in machine learning methodologies to construct rheology-informed graph neural networks (RhiGNets) that are capable of learning the hidden rheology of a complex fluid through a limited number of experiments. A multifidelity approach is then taken to combine limited additional experimental data with the RhiGNet predictions to develop “digital rheometers” that can be used in place of a physical instrument.