An elastically stabilized spherical invagination

TL;DR

This paper investigates elastically stabilized spherical invaginations in elastic membranes, combining experiments and mathematical modeling to understand stability mechanisms involving friction and force balance.

Contribution

It introduces a novel scheme to find stable solutions for elastic membrane invaginations, highlighting the role of friction and force inequalities in stabilization.

Findings

Friction is crucial for stabilization of invaginations.

Stable solutions align well with experimental observations.

Force balance is governed by an inequality, not an equality.

Abstract

Invaginations are partial enclosures formed by surfaces. Typically formed by biological membranes; they abound in nature. In this paper, we consider fundamentally different structures: elastically stabilized invaginations. Focusing on spherical invaginations formed by elastic membranes, we carried out experiments and mathematical modeling to understand the stress and strain fields underlying stable structures. Friction plays a key role in stabilization, and consequently the required force balance is an inequality. Using a novel scheme, we were able to find stable solutions of the balance equations for different models of elasticity, with reasonable agreement with experiments.