DO PRINCIPAL SURFACES OF STRESS AND STRAIN ALWAYS EXIST

Variations of stress and strain are commonly expressed by patterns of stress or strain trajectories: three mutually orthogonal families of c ontinuous lines, parallel to maximum, intermediate and minimum stress or strain axes. It might be assumed that there are equivalent continuo us principal surfaces of stress or strain, for any state of continuous ly varying stress or strain. We demonstrate that this will nor general ly be the case for three-dimensionally varying states of stress or str ain. Whether or not principal surfaces of stress or strain exist is go verned by the abnormality of the vector field of principal trajectorie s. We consider the Z vector fields for examples of many types of three -dimensional heterogeneous deformation, and show that most of these do not lead to definable principal XY strain surfaces. An alternative ge ometric test is presented, termed the continuity loop, for simply demo nstrating the existence (or not) of principal surfaces, using geometri cal and orientational information. It is important to the understandin g of geological structures to know which kinds of heterogeneous deform ation give rise to principal surfaces of stress or strain. We conclude with examples of structures which might be indicative of the absence of continuous principal surfaces of stress (segmented faults, echelon veins and dykes), a discussion of the implication for strain fabrics a nd foliations, and a warning that foliation trace trajectories on maps or sections may not necessarily indicate the existence of real foliat ion surfaces in three dimensions. (C) 1997 Elsevier Science Ltd.