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Mechanisms of deep penetration of soft solids

Micromechanical models are developed for the deep penetration of a soft solid by a flat-bottomed and by a sharp-tipped cylindrical punch. The soft solid is taken to represent mammalian skin and silicone rubbers, and is represented by an incompressible, hyper-elastic, isotropic solid described by a one term Ogden strain energy function. The flat-bottomed punch penetration model assumes that penetration is by the formation of a mode II ring crack that propagates ahead of the penetrator tip. The sharp-tipped punch penetration model assumes that penetration is by the formation of a planar mode I crack which is wedged open by the advancing punch. In both models the steady-state penetration load is obtained by equating the work done in advancing the punch to the sum of the fracture work and the strain energy stored in the solid. For the case of a sharp penetrator, this calculation is performed by considering the opening of a plane strain crack by wedge loading, using a finite element approach. Analytical methods suffice for the flat-bottomed punch. In both models, the crack dimensions are determined by minimising the load on the punch with respect to crack geometry. For both geometries of punch tip, the predicted penetration pressure increases with diminishing punch radius, and with increasing toughness and strain hardening capacity of solid. The penetration pressure for a flat-bottomed punch is two to three times greater than that for a sharp-tipped punch (assuming that the mode I and mode II toughnesses are equal), in agreement with experimental observations reported in a companion paper (Experimental Investigation Into the Penetration of Soft Solids, by O A Shergold and N A Fleck, submitted to the Journal of Biomechanics).