Simple Fluids and Fading Memory
Incompressible simple fluids are fluids which depend only on the history of the first spatial gradient of the deformation, on ∇χt(x,τ)=F t(τ) Nearly all of the constitutive equations used for amorphous liquids are of this type. On the face of it, this is a very restrictive assumption. Certainly, we would not want to restrict attention to fluids whose histories are represented only by first derivatives with respect to time. Fluids whose constitutive equation depends on second or higher gradients, or the objects to which series of such higher gradients might approximate, are not described as simple fluids, but they could be important.
KeywordsConstitutive Equation Rate Equation Undeformed State Extra Stress Fourth Order Tensor
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