The role of stress in ductile deformation

The concept of progressive ductile deformation has previously been discussed mainly in kinematic terms. Little attention has been paid to the principal stresses that control the formation of ductile deformation patterns. Many deformation patterns of rocks may have been created in a stress field of stable orientation. An equation derived here directly links the orientation of the major axis of deviatoric stress to the stretch and rotation components of plane isochoric deformation in isotropic rocks. Estimations of rotation and stretch of finite strain ellipsoids may therefore aid the recovery of palaeostress axes using a nomogram introduced here. The inclination of the major principal deviatoric stress axis with respect to a reference plane controls both the particle movement paths and mode of progressive deformation. The deformation tensor, obtained by integrating the rate-of-displacement or velocity gradient equations, is first expressed in time-dependent terms comprising only the normal and shear components of the strain rate tensor. Mohr's equations of stress can then be used to link strain rates to the major principal stress responsible for them. The rate of progressive deformation is determined by the rheology of the deforming rocks and the magnitude of the deviatoric stress. This derivation yields a time-dependent deformation tensor which is expressed in terms of the dynamic viscosity and the magnitude and orientation of the major deviatoric stress with respect to a reference plane. The significance of this deformation tensor is illustrated by forward modelling using computer-graphics. These allow the progressive deformation of a unit volume of rock in response to deviatoric stresses of various stable orientations to be visualized.