Geometry underlies the mechanical stiffening and softening of an indented floating film

TL;DR

This paper investigates how geometric effects cause nonlinear stiffening and softening in a floating polymer film under indentation, supported by experiments, simulations, and theoretical analysis.

Contribution

It demonstrates that geometric nonlinearities lead to both stiffening and softening in floating films, extending previous predictions with comprehensive experiments and theory.

Findings

Support for predicted stiffening response

Observation of softening at large slopes

Identification of geometric features driving nonlinear behavior

Abstract

A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [Vella & Davidovitch, Phys. Rev. E 98, 013003 (2018)], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.