Force decomposition and toughness estimation from puncture experiments in soft solids

Several medical applications, like drug delivery and biosensing, are critically preceded by the insertion of needles and microneedles into biological tissue. However, the mechanical process of needle insertions, especially at high velocities, is currently not fully understood. Here, we explore the insertion of hollow needles into transparent silicone samples with an insertion velocity v ranging from 0.1 mm s^-1 to 2.3 m s^-1 (with needle radius R = 101.5 μm, thus strain rates ∼v/R ranging from 1 s^-1 to 2.3 × 10⁴ s^-1). We use a double-insertion method, where the needle is inserted and re-inserted at the same location, to estimate the fracture properties of the material. The deflection of the specimen's free surface is found to be different between insertion and re-insertion experiments for identical needle positions, which is associated with different force magnitudes between insertion/reinsertion. This aspect was previously neglected in the original double-insertion method, thus here we develop a method based on imaging, image analyses and force measurements to decompose the measured force into individual force components, including deflection force F_d, frictional and spreading force F_f + F_s, and cutting force F_t. We estimate that the toughness Γ of our silicone samples, calculated using the cutting force F_t and the crack dimensions, increases with needle velocity, and ranges within observed values in previous literature for the same material and for some soft biological materials. In addition to toughness Γ, other parameters, such as critical force F_c and mechanical work W_c, also show strain-rate dependence, suggesting tissue stiffening, due to accumulated strain energy, at high speeds.