  Thermal greases, often used as thermal interface materials, are complex
paste-like mixtures composed of a base polymer in which dense metallic (or
ceramic) filler particles are dispersed to improve the heat transfer properties
of the material. They have complex rheological properties that impact the
performance of the thermal interface material over its lifetime. We perform
rheological experiments on thermal greases and observe both stress relaxation
and stress buildup regimes. This time-dependent rheological behavior of such
complex fluid-like materials is not captured by steady shear-thinning models
often used to describe these materials. We find that thixo-elasto-visco-plastic
(TEVP) and nonlinear-elasto-visco-plastic (NEVP) constitutive models
characterize the observed stress relaxation and buildup regimes respectively.
Specifically, we use the models within a data-driven approach based on
physics-informed neural networks (PINNs). PINNs are used to solve the inverse
problem of determining the rheological model parameters from the dynamic
response in experiments. This training data is generated by startup flow
experiments at different (constant) shear rates using a shear rheometer. We
validate the ``learned'' models by comparing their predicted shear stress
evolution to experiments under shear rates not used in the training datasets.
We further validate the learned TEVP model by solving a forward problem
numerically to determine the shear stress evolution for an input step-strain
profile. Meanwhile, the NEVP model is further validated by comparison to a
steady Herschel--Bulkley fit of the material's flow curve.
