On the conical indentation response of elastic auxetic materials: Effects of Poisson's ratio, contact friction and cone angle

Abstract

The linear elastic analytical solution of an axisymmetric probe indenting a semi-infinite half-space forms the backbone of most indentation data analysis protocols. It has been noted in the literature that the theoretical solution relies on a boundary condition that is ill-posed which leads to discrepancies from the actual response that depends, among other parameters, on the Poisson's ratio of the indented material. While correction factors have been proposed, prior studies have concentrated on the positive Poisson's ratio regime and have neglected an exciting and developing class of materials: the auxetic systems. The finite element method is used to simulate the conical indentation response of elastic materials with Poisson's ratios covering the whole thermodynamically possible range, − 1 ≤ ν ≤ 0.5 . Consistent with theoretical predictions, the indentation resistance and hardness of auxetic materials is enhanced compared to their non-auxetic counterparts. The stress profiles and contact details are systematically analyzed and the increase in resistance is traced to the shear stiffening and the reduction of contact area compared to conventional materials. Furthermore, it is shown that the analytical linear elastic solution falls short in accurately describing the indentation response, especially for negative Poisson's ratio materials. In contrast to the theoretical prediction, the contact area reduces as the Poisson's ratio increases resulting in increased required force to penetrate the material and an enhanced pressure distribution beneath the indenter. The analytical solution is corrected for the whole ν range and best fit polynomials are proposed for ease-of-use. The effects of contact-friction and indenter cone-angle are also studied and quantified.