International Journal of Non-Linear Mechanics paper: Axisymmetric indentation of curved elastic membranes by a convex rigid indenter

This paper looks at how an elastic membrane deforms when a rigid indenter is pushed into it. The membrane is allowed to have an arbitrary shape and elastic properties, while the indenter may also take any convex shape.

- International Journal of Non-Linear Mechanics, doi:10.1016/j.ijnonlinmec.2011.04.030

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.

Highlights ► Axisymmetric indentation of elastic membranes. ► General axisymmetric indenter profiles considered. ► Initially curved elastic membranes, not just flat membranes. ► Strain-energy function important for large deformations.