If fluids have zero shear modulus, how do I make sense of graphs like strain rate vs shear stress (to classify fluids as Newtonian or non-Newtonian)?

Question

Following the definition on the wiki: Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it.

If fluids have zero shear modulus, shouldn't the shear stress be zero regardless of the strain rate?

Thanks

score 8 · Accepted Answer · answered Feb 12 '18 at 01:01

Solids have a shear modulus that relates the shear stress to the shear strain. Liquids have a viscosity that relates the shear stress to the shear strain rate. Apply a shear stress to a solid and it deforms a bit, reaching a new equilibrium shape that remains motionless until the stress is removed. Apply a shear stress to a liquid and it continues to deform at a constant rate until the stress is removed. No matter how small the stress, the strain will become arbitrarily large given enough time: shear modulus of liquids is zero.

If fluids have zero shear modulus, how do I make sense of graphs like strain rate vs shear stress (to classify fluids as Newtonian or non-Newtonian)?

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