A theory of concentric, kink, and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: I. Introduction

Most folds in stratified rock are similar in form to ideal kink, concentric or chevron folds, in which there are discontinuities in slope or curvature of bedding planes. In this respect most folds appear to be closely related to faults, traces of which can be considered to be lines across which there are discontinuities of displacement of layers. Further, the close association of reverse faults and folds or monoclinal flexures seems to indicate that theories of faulting and folding should be closely related.The theory of characteristics is a mathematical tool with which we can obtain insights into processes involving discontinuities. Theoretical characteristic lines are directions across which certain variables might be discontinuous and they are directions along which discontinuities propagate. The theory has been widely applied in plasticity theory and in fluid mechanics and theoretical studies of faulting have suggested that faults are analogous to the lines of discontinuity predicted by plasticity theory. Elasticity and viscosity theories, on which theories of folding have been founded, exclude the existence of characteristic lines in the materials unless the equilibrium equations, rheological properties or strains are nonlinear. However, all folding theories are nonlinear to some extent and the theories can be modified so that they predict lines of discontinuity for some conditions of loading and deformation.Theories of folding will be developed in subsequent papers of this series in order to predict conditions under which characteristic lines can exist in multilayered materials and in order to determine the conditions that must be satisfied across and along the characteristic lines. The theory should help us to recognize lines of apparent discontinuity in natural and experimental folds and study of these lines should provide further understanding of mechanisms of folding.Experimental studies of folding of a wide variety of materials, including alternating layers of rubber and gelatin, modeling clay and grease or graphite, and potter's clay and rubber or cardboard, suggest that the patterns of folding in these materials begin with sinusoidal forms, transform into concentric or kink forms and then into chevron forms as the multilayers are shortened axially. A suitable theory of folding of multilayers should account for these observations.