$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

Viscous fluid materials provide a constitutive relation for the dependence of the viscous stress $\boldsymbol{\tau}$ on the rate of deformation tensor $\mathbf{D}^{f}$ of a fluid.