A general harmonic coordinate transformation to simulate the states of strain in inhomogeneously deformed rocks

Abstract

In order to investigate the possible states of strain that may exist in an inhomogeneously deformed body, a general deformation is proposed in the form of a harmonic coordinate transformation. This deformation differs from those previously considered by Jaeger, Ramsay & Graham and Hobbs in that it is capable of representing a wide variety of deformations; previous efforts had inbuilt assumptions regarding the mechanism of deformation. The transformation contains adjustable terms, all of which have distinct geometrical significance; some represent a homogeneous deformation, some represent inhomogeneous shortening, some represent inhomogeneous shear and others correspond to a ‘pinch and swell’ type of deformation. By combining these terms with different degrees of emphasis many kinds of deformation may be simulated. In this paper two constraints are developed in conjunction with the general harmonic transformation; these are the conditions for constant volume deformation (both locally and generally) and the condition for zero shear strain of lines initially normal to the distorted layer (again both locally and generally).