Hierarchical buckling of elastic fiber under transverse confinement

Hierarchical buckling is a novel phenomenon observed in elastic fibers subjected to transverse confinement; however, the deformation mechanisms and modal transitions of this unique phenomenon remain to be elucidated. This paper investigates the hierarchical buckling of elastic fibers with elliptical (circular) cross-sections under transverse confinement through analytical derivations and numerical simulations. Various magnitudes of hierarchical buckling of fibers are observed with the variation of the controlled elastic matrix stiffness. An analytical solution is first derived for the fiber’s buckling phenomenon, and the hierarchical buckling is accomplished through the superposition of buckling at various modes. The theoretical results are validated against the finite element simulations with good agreement. It is demonstrated from the parametric results that the hierarchical buckling phenomenon is primarily influenced by the stiffness of the external transverse confinement (matrix), which is defined as a dimensionless parameter. It is thus illustrated from the computational results that the buckling of elastic fibers within a solid or fluid matrix can be controlled and customized. The present work provides theoretical guidance for the application of elastic fibers in stretchable conductor fibers and flexible electronic devices.