Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin

Abstract

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 treated as an incompressible, hyperelastic, isotropic solid described by a one-term Ogden strain energy function. Penetration of the soft solid by a flat-bottomed punch is by the formation of a mode-II ring crack that propagates ahead of the penetrator tip. The sharp-tipped punch penetrates by the formation of a planar mode-I crack at the punch tip, followed by wedging open of the crack by the advancing punch.For both modes of punch advance the steady-state penetration load is calculated 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 a wedge using a finite-element approach. Analytical methods suffice for the flat-bottomed punch. In both models the crack dimensions are such that the load on the punch is minimized.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.

Deep penetration and liquid injection into adipose tissue

“…The characteristics of the puncture force response, shown in Figure 1, are consistent with force response observed in [Shergold et al 2006] for punches that Application of the Shergold-Fleck ring-cracking model. Shergold and Fleck [2004] observed that a flatbottomed punch generated a mode II ring crack below the punch. Their model is sketched in Figure 5b.…”

“…The function f (b/R) does not exist in closed form but is defined in Equation (3.17) of [Shergold and Fleck 2004]; the details are omitted here. The pressure given by (3) attains a minimum for a particular value of b/R and, following that paper, we take the minimum value to be the penetration pressure for ring cracking.…”

“…Penetration pressure is a useful quantity for comparison with the penetration models of [Shergold and Fleck 2004] defined by…”

“…This compares to 30 MPa needed to penetrate adipose with a 0.4 mm diameter flat-tipped punch. Shergold and Fleck [2004] have developed two models for the deep penetration of a soft solids (see Section 1). In order to select the appropriate Shergold-Fleck penetration model for comparison with the measured penetration pressures it is necessary to determine the mode of hole formation, during penetration.…”

“…Shergold and Fleck [2004] have recently developed two penetration models for soft solids; a model based on the formation of a planar crack and a model based on the formation of a ring-crack. They demonstrated that the force to penetrate dermis with a sharp metal punch depends upon the Young's modulus and toughness of the tissue, and upon the diameter and tip geometry of the punch.…”