Soft coring: How to get a clarinet out of a flute?
Résumé
Cutting mozzarella with a dull blade results in poorly shaped slices: the process occurs in a configuration so deformed as to yield unexpectedly curved surfaces. We study the morphogenetics arising from such process through the example of coring: when a thin cylindrical hollow punch is pushed into a soft elastomer, the large transverse expansion occurring during the cutting is responsible for the ''clarinet-shape'' of the extracted core, which reaches diameters far smaller than those of the tool. With contributions from fracture mechanics and large strain theory, we build a simple yet quantitative understanding of the observed discrepancy, which is shown to occur when the size of the punch is smaller than a characteristic, tomo-elastic length scale. Moreover, material nonlinearity and friction appear to play a crucial role in this phenomenon.
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