Induced stresses in quasi-spherical elastic vesicles: local and global Laplace-Young law

TL;DR

This paper develops a theoretical framework to analyze how geometric perturbations induce stresses in elastic vesicles, leading to a modified Laplace-Young law during budding transitions.

Contribution

It introduces a novel approach to quantify stress distributions in perturbed elastic vesicles and derives a modified Laplace-Young law considering these effects.

Findings

Stress distribution varies with membrane perturbations

Modified Young-Laplace law accounts for induced stresses

Analysis of stress during budding transition

Abstract

On elastic spherical membranes, there is no stress induced by the bending energy and the corresponding Laplace-Young law does not involve the elastic bending stiffness. However, when considering an axially symmetrical perturbation that pinches the sphere, it induces nontrivial stresses on the entire membrane. In this paper we introduce a theoretical framework to examine the stress induced by perturbations of geometry around the sphere. We find the local balance force equations along the normal direction to the vesicle, and along the unit binormal, tangent to the membrane; likewise, the global balance force equation on closed loops is also examined. We analyze the distribution of stresses on the membrane as the budding transition occurs. For closed membranes we obtain the modified Young-Laplace law that appears as a consequence of this perturbation.