Impact response of a viscoelastic plate made of a material with negative Poisson's ratio1

In this article, the problem on impact response of a viscoelastic plate, made of viscoelastic auxetic with fractional viscosity, has been formulated for the case, when the shear operator is governed by the fractional derivative model, resulting in auxetic's Poisson's ratio as a time-dependent operator changing its values from negative to positive magnitudes with time. The proposed mathematical model and numerical calculations based on the obtained asymptotic solutions of the stated problem have verified existing experimental results, which demonstrate enhancing indentation and impact resistance in auxetic materials.