Mechanics of poking a cyst

TL;DR

This paper investigates the complex mechanical behavior of biological cysts under indentation, revealing new scaling laws through theoretical and simulation approaches, which help understand their material properties.

Contribution

It introduces a nonlinear elastic shell model and derives new scaling exponents for force-displacement relations in cysts, supported by finite-element simulations and experiments.

Findings

New scaling exponents for force-displacement in cysts

Robustness of exponents in thick shells and under pressure

Experimental validation of theoretical predictions

Abstract

Indentation tests are classical tools to determine material properties. For biological samples such as cysts of cells, however, the observed force-displacement relation cannot be expected to follow predictions for simple materials. Here, by solving the Pogorelov problem of a point force indenting an elastic shell for a purely nonlinear material, we discover that complex material behaviour can even give rise to new scaling exponents in this force-displacement relation. In finite-element simulations, we show that these exponents are surprisingly robust, persisting even for thick shells indented with a sphere. By scaling arguments, we generalise our results to pressurised and pre-stressed shells, uncovering additional new scaling exponents. We find these predicted scaling exponents in the force-displacement relation observed in cyst indentation experiments. Our results thus form the basis for inferring the mechanisms that set the mechanical properties of these biological materials.