Professor Norman A. Fleck
Cambridge University Engineering Department
Trumpington Street, Cambridge CB2 1PZ, U.K.
The injection of skin by hypodermic needles and more recently by liquid jets is reviewed, with a comparison
of their relative performance outlined. The underlying mechanisms by which skin and other soft solids are
penetrated are described.
A mechanical description of skin is given based on the notion of nodal connectivity. The difference in
modulus of the dermis and of collagen fibres (factor of 1000) is traced to the fact that the collagen
network deforms by local bending until it locks up at large elongations. The model predicts that the stress
versus strain curve for skin scales with the Young's modulus of the collagen. To explore the assumptions of
the model, experimental data are reported for the effect of strain rate upon skin response, using a split
Kolsky bar. It is found that the shape of the stress versus strain curve is unchanged but the level of
stress increases by an order of magnitude as the strain rate is increased from 0.001/s to 3000/s. This is
consistent with the change in measured modulus of the skin.
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, hyper-elastic, 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. 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).
The talk concludes with a comparison of the sharp-tipped injection model with the performance of a number of
commercial liquid jet injectors. The model provides a useful prediction of the efficacy of each device.
Reference
Mechanisms of deep penetration of soft solids, O A Shergold and N A Fleck, Submitted to Proc. Roy. Soc.
Lond. A.
