Inhomogeneous deformation: The theory and geological application of finite strain compatibility

A geologically useful form of the finite strain compatibility equations is developed. The coordinate grid compatibility equations are derived, and the relationship between coordinate transformations and material deformations is discussed. The grid compatibility equations are then used to derive several forms of the finite strain compatibility equations. While these equations are not easily solved for general strain fields, it is shown that many common geologic strain patterns have simple geometries for which the compatibility equations can be interpreted directly. For deformations having constant strain in one direction, compatibility provides an iterative method for determining the strain throughout a deformed region if the strain is intially known at one point. Two applications of this technique are demonstrated. Simple and often useful interpretations of the equations are also found for inhomogeneous pure shear, parallel and similar folding, deformations with large axial ratios, and deformations of no shape change.