A theory of concentric, kink, and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: II. Initial stress and nonlinear equations of equilibrium

Abstract

Part of the necessary background for our theory of folding of multilayered elastic materials is a nonlinear theory of equilibrium. The nonlinear theory presented here is for plane-strain conditions and it is a special case of a three-dimensional theory developed by V.V. Novozhilov. The nonlinear theory accounts for finite deformations as well as for finite distortions of bounding surfaces of bodies or elements of bodies. The theory is linearized so that it can be used to describe the initiation of folds but the linearized theory is quite different from the classical linear theory of elasticity. For example, the linearized theory indicates that an elastic material subjected to high uniaxial compression is more easily deformed by simple shear along planes normal than along planes parallel to the direction of compression. Thus, the material behaves as though it were anisotropic with respect to shear, or as though it were a deck of slippery cards layered normal to the direction of axial compression. Further, the compression can become so large that the material has no resistance to shear stress along those planes; the material then behaves much as a plastic except that strains are completely recoverable if the stresses are relaxed. The theory suggests that the problem of estimating rheological properties of rocks at times of folding is even more complicated than we have believed heretofore.