The compatibility equations and the pole to the Mohr circle

Abstract

We derive a new form of the compatibility equations for large deformations. These equations show that in a continuous inhomogeneous deformation, the strain gradients are related to the curvatures of the principal strain trajectories. In the case of uniform area strain, the equations express a direct relationship between the shape of the strain ellipse at a point and the curvatures of the principal trajectories. These relationships become particularly useful if the fabric in a deformed rock is taken as parallel to the principal strain trajectories.