On Mode i crack mechanism in the puncturing of soft tissues

In the present paper, the mechanics of puncturing is studied with refer to a foreign tool penetrating a soft (nearly incompressible) target solid. The penetrating tool is here described by a sharp tipped rigid needle with a circular cross section. Puncturing can be characterised as a Mode I fracture process, which is here analytically described by a two-dimensional model related to the plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that is, the strain energy stored in the target solid and the energy consumed in Mode I crack propagation. Such a penetration force is analytically demonstrated to be dependent on the fracture toughness of the material, its elastic modulus, and the sharpness of the penetrating tool.