On the response of re-entrant auxetic structures under dynamic crushing: analytical approach and finite element simulations

The present work focuses on the dynamic compressive response of dynamically crushed auxetic structures. The aim is to propose a simplified methodology to assess the influence of geometrical/topological and material parameters on the impact response of these structures. The response also depends on the impact velocity. Based on an analogy with the propagation of shock waves in a rigid, perfectly plastic, locking (RPPL) material model, two approaches are developed to study the collapse of the structure crushed by a rigid impactor: (i) an analytical development and (ii) an iterative procedure, are proposed to evaluate the energy transfer and the impactor deceleration, thus allowing the physical quantities of interest to be deduced: dynamic stress, crushed length and strain, time for densification, stop time for the impactor. The methodology is presented and illustrated with the conventional 2D re-entrant auxetic, of which every range of geometrical data can be taken into account in the proposed formulas. Finite Element explicit simulations were carried out to confirm the analytical prediction. Results show good agreement between analytical and Finite Element results.