Shape transitions in soft spheres regulated by elasticity

TL;DR

This paper investigates how elastic properties and surface area changes induce shape transitions in soft spherical structures, revealing a critical point where buckling occurs and lower symmetry wrinkled states emerge.

Contribution

It introduces a theoretical framework for elasticity-driven shape transitions in core-shell spheres, linking surface area increase to buckling and wrinkling phenomena.

Findings

Identifies a critical excess surface area for buckling transition.

Describes the resulting lower symmetry wrinkled structures.

Relates theoretical results to experiments on gel-filled vesicles.

Abstract

We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.