Mechanics of poking a cyst
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.03716
- arXiv:
- arXiv:2408.03716
- Bibcode:
- 2024arXiv240803716Z
- Keywords:
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- Condensed Matter - Soft Condensed Matter;
- Physics - Biological Physics;
- Quantitative Biology - Tissues and Organs
- E-Print:
- 6 pages, 4 figures