Recent progress in experimental biomechanics has provided reliable hyperelastic constitutive parameters for a variety of soft biological tissues like brain, kidney and liver. These laboratory verified strain energy functions enable accurate analytical and numerical evaluation of complicated mechanical response of soft bio tissues, at large strains. Advances in diagnosis, numerical simulation and design of medical procedures have followed accordingly. In particular, research of soft tissues ballistic impact phenomena (perforation and penetration) is now within the framework of nonlinear continuum mechanics. This development stands in marked contrast to earlier studies, performed over decades, where substitute materials like ballistic soap or ballistic gelatin were used to assess the resistance of bio tissues to ballistic impact.
The present work aims at deriving a basic theory of the mechanics of deep penetration of rigid projectiles into soft tissues. The study centers on the cavitation model which has been successfully employed in solid targets penetration analysis. The underlying assumptions are rigid point headed projectiles, normal impact at small firearms velocity range and straight penetration path. Material behaviour is hyperelastic, isotropic and incompressible, with simple failure criteria. Inertia effects are accounted for and both spherical and cylindrical patterns are considered.
We start with a brief historical review of soft tissues penetration mechanics (hyperelastic material behavior and cavity expansion method), discussing several open questions which have motivated the present work. New elegant solutions for steady state cavitation fields will be presented next, including derivation of several formulae for the cavitation pressure.
We shall examine sensitivities of the cavitation pressure to material parameters (type of tissue), failure criteria and presence of material inertia. Also discussed is the difference between spherical and cylindrical cavitation patterns. Finally, assuming that tissue resisting force applied on the projectile is given essentially by the cavitation pressure, we shall estimate the penetration depth and compare with available experimental data.
As not much work of similar nature has been done, possible limitations of the present results will be discussed along with suggestions for future research.
