How friction and adhesion affect the mechanics of deep penetration in soft solids

The mechanics of puncture and soft solid penetration is commonly explored with the assumption of frictionless contact between the needle (penetrator) and the specimen. This leads to the hypothesis of a constant penetration force. Experimental observations, however, report a linear increment of penetration force with needle tip depth. This force increment is due to friction and adhesion, and this paper provides its correlation with the properties of the cut material. Specifically, the force-depth slope depends on the rigidity and toughness of the soft material, the radius of the penetrator and the interfacial properties (friction and adhesion) between the two. We observe that adhesion prevails at relatively low toughness, while friction is dominant at high toughness. Finally, we compare our results with experiments and observe good agreement. Our model provides a valuable tool to predict the evolution of penetration force with depth and to measure the friction and adhesion characteristics at the needle-specimen interface from puncture experiments.