Contact strain and folding instability of a multilayered body under compression

The contact strain which develops in a host rock during compression-folding of a more competent layer is treated mathematically and demonstrated by tests on composite models of rubber sheets and blocks with different rigidities.The contact strain is found to be negligible outside a zone about one initial wavelength wide on either side of the folded sheet. This theoretical conclusion based upon the contact deformation resulting from the initial small-amplitude buckles is also, according to the experimental tests, valid for rather strong buckling.Second-order folding of a thin competent layer laying within the contact zone of a thicker buckled competent layer is demonstrated by experimental tests.Considerations of the stresses connected with the contact strain and the stress distribution in the buckling competent layer itself give a simple expression for the initial stable wavelength which develops in response to compression parallel to the layering.The strain distribution in folded multilayers consisting of a set of thin competent sheets evenly spaced in an uniform less competent body is considered theoretically.In such multilayers the stable initial wavelength as developed during compression will, according to the theory, increase somewhat with decreasing spacing between the competent layers if all other conditions are equal. If the spacing is close enough (the limit depends upon the relative mechanical properties of the two substances) the multilayer will buckle as an unit in the sense that one half-wave covers the whole length of the body. This agrees with compression tests on multilayered rubber blocks.In the last two sections of the paper a theory of viscous buckling of thick layers is developed both for the case of a single layer enclosed in a large uniform body and for the case of a multilayer of alternating competent and incompetent layers. In this theory shear parallel to layering plays an important part. For a single embedded layer the thick-layer model gives a little smaller wavelength/thickness ratio than the simple but less realistic thin-layer model. For multilayers strain parallel to layering becomes very significant, particularly when the spacing between the competent layers is small, and the thick-layer model differs considerably from the simpler thin-layer model.A theory of buckling of a multilayer withn alternating competent-incompetent layers sandwiched between two very thick uniform bodies is also developed.