Theoretical Puncture Mechanics of Soft Compressible Solids

Abstract

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 article, 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 dimensionless 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.