Buckling folds of a single layer embedded in matrix – Theoretical solutions and characteristics

In addition to the conventionally known buckling fold, which has a basic fold-form comprising of single frequency and non-decaying amplitudes, folds with other fold-forms having dual frequencies or decaying amplitudes also exist in nature. This research explores whether these three types of buckling folds, which have been found in elastic material, still exist for visco-elastic or pure viscous materials. Analytical solutions of the fold-forms for visco-elastic and pure viscous materials are accordingly proposed. The theoretical solutions were then examined by conditions including extremely fast or slow strain rates. The results reveal the following physical characteristics of buckling fold. (1) For the studied materials, all three types of fold-forms are possible; (2) although pure viscous material itself is strain rate dependent, a strain rate does not influence the fold-form for a viscous layer embedded in viscous matrix; (3) given the same competence contrast, both the elastic and the viscous materials have the same wavelength versus the lateral shortening relationship, and (4) two measures (IVIV and IEIE) representing the effect of strain rate on folding, characterized with a range from 0 to 1, are proposed for strain rate dependent cases.