Cutting and slicing weak solids

Abstract

Dicing soft solids with a sharp knife is quicker and smoother if the blade is sliding rapidly parallel to its edge in addition to the normal squeezing motion. We explain this common observation with a consistent theory suited for soft gels and departing from the standard theories of elastic fracture mechanics developed for a century. The gel is assumed to locally fail when submitted to stresses exceeding a threshold $\sigma_1$. The changes in its structure generate a liquid layer coating the blade and transmitting the stress through viscous forces. The driving parameters are the ratio $U/W$ of the normal to the tangential velocity of the blade, and the characteristic length $\eta W/\sigma_1$, with $\eta$ the viscosity of the liquid. The existence of a maximal value of $U/W$ for a steady regime explains the crucial role of the tangential velocity for slicing biological and other soft materials.