Background: 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, analysis of soft tissues ballistic impact phenomena can now be performed within the framework of nonlinear continuum mechanics. This development stands in marked contrast with available studies, performed over decades, where substitute materials like ballistic soap or ballistic gelatin have been used to assess the resistance of bio tissues to ballistic impact.
Methods: The present work aims at establishing a simple theory of the mechanics of deep penetration of rigid projectiles into soft tissues. The study employs the cavitation model which has been successfully used in solid targets penetration analysis. Material behaviour is modelled as hyperelastic, isotropic and incompressible, with simple failure criteria.
Results: Integral type dynamic cavitation solutions for incompressible SEF are derived, with two alternative damage criteria. Comparison of our theoretical predictions with experimental data for penetration depth reveals good agreement in the range of low impact velocities (20-300 m/s).
Conclusion: To the best of our knowledge, this is apparently the first study attempting at analytical solutions for dynamic cavitation in context of penetration analysis for biological tissues. Several open questions emerging from this work, suggesting future directions, will be briefly discussed.