Axisymmetric Indentation of Curved Elastic Membranes by a Convex Rigid Indenter

TL;DR

This paper models the axisymmetric indentation of curved elastic membranes by rigid indenters, analyzing load-indentation behavior, wrinkling phenomena, and applications to seed germination mechanics.

Contribution

It introduces a comprehensive model for curved elastic membranes under indentation, including wrinkling effects and various indenter shapes, extending previous flat membrane analyses.

Findings

Load-indentation curves for spheroidal tips are derived.

Wrinkling occurs in initially curved membranes under certain conditions.

The model aids in measuring seed endosperm mechanical properties.

Abstract

Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load-indentation curves that result for a range of spheroidal tips are obtained for both flat and curved membranes. Wrinkling may occur when the membrane is initially curved, and a relaxed strain-energy function is used to calculate the deformed profile in this case. Applications to experiments designed to measure the mechanical properties of seed endosperms are discussed.