Effects of geometry and boundary constraint on the stiffness and negative Poisson's ratio behaviour of auxetic metamaterials under quasi-static and impact loading

Auxetic metamaterials exhibit a negative Poisson's ratio and superior energy dissipation characteristics under dynamic (impact) loading. This makes them attractive candidates for components that provide crash or impact protection (such as crumple zones) in automotive and aerospace applications. However, little prior work on the effect of boundary constraint on the behaviour of these structures exists. Therefore, the primary goal of this investigation is to assess the effect of boundary constraint on the energy-absorbing properties of auxetic metamaterials. Specifically, auxetic metamaterials (lattice structures) were fabricated from stainless steel powders via 3-D laser printing (selective laser melting). Additional structures were printed with constraining walls attached in order to evaluate the effects of boundary constraint on the auxetic behaviour. A comprehensive investigation of the mechanical performance of the structures was then carried out under both quasi-static and dynamic (impact) loading conditions. Poisson's ratio and elastic modulus values were determined from the experimental results and compared with theoretical calculations. Dissipation of vertical forces into the lateral boundaries was confirmed by about 20% less negative Poisson's ratios, for otherwise identical auxetic structures. In addition, dynamic loading simulations have shown that with optimized geometric parameters, auxetic metamaterials are capable absorbing over 90% of the energy of an impact. However, critical overestimation of the energy absorbing abilities of auxetic crash protectors could occur if the effects of lateral constraint are not carefully considered.