On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint

Implications of the negative Poisson ratio with regard to the quasi-static and dynamic indentation compliances for isotropic homogeneous materials are considered. It has been shown that analogously to some solutions for three-dimensional stress or displacement fields concentrations, the indentation, vibrational, and impact compliances are significantly affected when Poisson’s ratio of the material assumes negative values. It was observed that the friction at the contact interface between the indenter and the surface of an elastic medium strengthens the negative Poisson ratio effect. In the Hertzian contact problem, it was found out that the location of the maximum shear stress approaches the contact interface as Poisson’s ratio is made sufficiently negative. In view of this fact, the local indentation of a coated elastic half-space, which is reinforced with an elastic plate, has been considered. It was shown that the reinforcement preserves the negative Poisson ratio effect, and the perfect bonding of the plate to the surface of an auxetic half-space significantly strengthens it. This theoretical work be considered as a first step towards an indentation and impact analysis of real auxetic materials.