What it could feel like to press on an auxetic: effect of Poisson’s ratio on the indenter

Abstract The behaviour of an indenter having a hard inner core and a softer outer shell, meant to emulate a human finger, pressing upon a sample covered with an isotropic negative/zero/positive Poisson’s top protective layer was investigated through static finite-element simulations. It was shown that if the material being indented had a comparable Young’s modulus to the outer shell of the indenter, a very negative Poisson’s ratio (NPR) results in more pronounced deformations and stresses within the indenter due to the auxetic material offering a higher resistance to indentation. Pressing of an auxetic material with Poisson’s ratio of −0.90 having the same Young’s modulus as that of the softer outer core of the indenter (1 MPa), was found to result in stresses in the indenter which were approximately double to those measured when pressing a conventional material with same Young’s modulus having Poisson’s ratio +0.45. This indicates that auxetics with a very high NPR may feel more uncomfortable when pressed with a finger compared to materials of the same Young’s modulus having a conventional positive Poisson’s ratio (PPR). However, it was also shown that in such scenarios, the auxetic protective layer being indented could be made much thinner whilst still retaining the same functionality. In fact, the simulations suggest that a conventional material with Poisson’s ratio +0.45 indents more than five times as much as an auxetic material with Poisson’s ratio of −0.90 having the same Young’s modulus of 1 MPa. It was also shown that in situations where the material being indented had a much higher Young’s modulus to that of the indenter, the deformations and stresses within the indenter are practically identical irrespective of the Poisson’s ratio, i.e. a human finger is unlikely to be able to perceive the difference between an auxetic and a conventional PPR material.