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general stress-strain relation for fluid

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Is it possible to define a general stress-strain relation for non-Newtonian laminar flow? Laminar flow seems to require you to define a dynamic viscosity. However I am trying to implement a flow law with a complicated stress-strain relation that does not yield a simple analytical equation for viscosity (see attached). Is it possible to define fluid properties more generally (other than externally solving for viscosity as a function of strain rate and then inputting an interpolation function for the viscosity)?


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