Mixed-mode crack propagation during needle penetration for surgical interventions

An accurate description of the penetration mechanics of flexible needles into target soft tissues is a complex task, including friction at the needle-tissue interface, large strains, non-predetermined penetration trajectories, fracture under mixed-mode loading and so on. In the present work, a finite element algorithm is employed to simulate the two-dimensional deep penetration of a flexible needle in a soft elastic material. The fracture process of the target material during penetration is described by means of a cohesive zone model, with a suitable mixed-mode criterion for determining the propagation direction of the crack. To illustrate the potential of the numerical algorithm, we have performed some simulations of the insertion of a flexible needle with an asymmetric tip, and the results are presented in terms of force-penetration curves as well as of the obtained penetration paths in the target tissue.