A study of mechanical and capillary bifurcation phenomena in soft elastic materials

Emery, Dominic Robert

Abstract

Stress-induced pattern formations in soft elastic materials are bifurcation phenomena which can be localized or periodic. Certain localized pattern formations such as necking or bulging are associated with zero wavenumber, whereas periodic pattern formations such as wrinkling or buckling are associated with a strictly positive wavenumber. Whilst the near-critical behaviour of the periodic case is well understood, studies of the localized case have only recently gathered momentum, and are conceptually more challenging to undertake. Despite this, a remarkable amount of analytical progress can be made. We will highlight this generally underappreciated fact by studying theoretically the complete bifurcation behaviour of localized patterns, as well as the competition from periodic patterns, in elastic materials under various effects.
Firstly, the bifurcation behaviour of soft incompressible hollow tubes under elasto-capillary effects is studied. Analytical bifurcation conditions for localized pattern formation are initially derived using established results from a prototypical problem. A linear bifurcation analysis then shows that an axi-symmetric zero wavenumber bifurcation mode is favoured over periodic modes for a range of boundary conditions and loading scenarios. A weakly non-linear analysis provides an explicit connection between this zero wavenumber mode and localized necking or bulging, and a phase-separation-like evolution of these localized patterns into a final Maxwell state is described analytically. The effect of material compressibility on localized pattern formation in soft cylinders is also studied analytically, and comparisons with recently published numerical simulation results are made.
We then consider the formation of a self-contacting crease on the free surface of a compressed elastic half-space. This is a highly unique localized pattern since its inception is an inherently non-linear bifurcation phenomenon. Therefore, unlike localized bulging or necking, it is undetectable through a linear analysis. We derive a new analytical bifurcation condition for creasing by reformulating the analysis of a recent ground-breaking study.

Citation

Emery, D. R. A study of mechanical and capillary bifurcation phenomena in soft elastic materials. (Thesis). Keele University. https://keele-repository.worktribe.com/output/515651

• Thesis Type: Thesis
• Deposit Date: Jul 11, 2023
• Publicly Available Date: Jul 11, 2023
• Public URL: https://keele-repository.worktribe.com/output/515651
• Award Date: 2023-06