Second-Order Fluids in Simple Shearing Flow

3 SECOND-ORDER FLUIDS IN SIMPLE SHEARING FLOW 

Let us take the configuration at time / as the configuration of reference. If the coordinates of the point at time t are Xi, X2, and X3, the coordinates at time 0 will be 

The components of the relative deformation gradient Fy and the symmetrical tensor Jy can be calculated, respectively, from Eqs. (13.7) and (13.8), giving 

The constitutive equation of second-order fluids indicates that the stress tensor is determined by — u), and consequently Gy t) is independent of t and depends only on and Af Thus the function dy reduces to a function y, and the constitutive equation for second-order fluids [Eq. (13.9)] can be expressed as 

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Second-Order Fluids in Simple Shearing Flow 515... 

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