9 - Stress and deformation

Summary

At any point in a glacier, there are three normal and six shear stresses.Coordinate axes can be chosen so that the shear stresses vanish. The remaining normal stresses are known as the principal stresses. Certain combinations of the stresses do not vary with the orientation of the coordinate axes. These are known as invariants of the stress tensor. The second invariant is one half the sum of squares of all nine stresses in the tensor. This stress is used in the common flow law for ice, so the deformation rate depends on all the stresses acting, not just on those acting in the direction of the deformation.Balancing forces on an element of ice at a point leads to an equation for the conservation of linear momentum. The strain along a line is defined as the change in length per unit length. There are also three normal and six shear strain rates. Again, axes can be chosen so that the shear strain rates disappear.The remaining normal strain rates are called the principal strain rates.In an isotropic material the principal axes of stress and strain rate coincide. Ice is commonly assumed to be isotropic for purposes of theoretical calculations, although this is clearly not true.