Ice rheology (under construction)

• explain viscous deformation with contrast to elastic deformation

• introduce the power law

• introduce Glen’s flow law

• plot of stress vs strain for different values of \(n\)

Glen’s flow law

Glen’s flow law is the most common flow law used to describe the viscous flow of ice in glaciology. So far we have written is as \(\dot{\epsilon} = A\tau^n\), without specifying which stress \(\tau\) and strain rate \(\dot{\epsilon}\) are involved. A more complete formulation is:

\[ \dot{\epsilon_{ij}} = A\tau_E^{n-1}\tau_{ij} \]

where \(\tau_{ij}\) are the elements of the deviatoric stress tensor \(\underline{\underline{\tau}}\) and \(\tau_E\) is the so-called effective stress, defined as the second invariant of the deviatoric stress tensor as:

\[ \tau_E^2 = \frac{1}{2}(\tau_{xx}^2+\tau_{yy}^2+\tau_{zz}^2)+\tau_{xz}^2+\tau_{xy}^2+\tau_{yz}^2 \]