  Accurate prediction of the force required to puncture a soft material is
critical in many fields like medical technology, food processing, and
manufacturing. However, such a prediction strongly depends on our understanding
of the complex nonlinear behavior of the material subject to deep indentation
and complex failure mechanisms. Only recently we developed theories capable of
correlating puncture force with material properties and needle geometry.
However, such models are based on simplifications that seldom limit their
applicability to real cases. One common assumption is the incompressibility of
the cut material, albeit no material is truly incompressible. In this paper we
propose a simple model that accounts for linearly elastic compressibility, and
its interplay with toughness, stiffness, and elastic strain-stiffening.
Confirming previous theories and experiments, materials having high-toughness
and low-modulus exhibit the highest puncture resistance at a given needle
radius. Surprisingly, in these conditions, we observe that incompressible
materials exhibit the lowest puncture resistance, where volumetric
compressibility can create an additional (strain) energy barrier to puncture.
Our model provides a valuable tool to assess the puncture resistance of soft
compressible materials and suggests new design strategies for sharp needles and
puncture-resistant materials.
