Dynamic in-plane compression of Miura-ori patterned metamaterials

摘要

The responses of Miura-ori patterned metamaterials to in-plane dynamic compression are studied for several scenarios, namely: compression of uniform density metamaterials at a constant velocity and impulsive loading modelled as an impact with initial velocity, and a mass impact of a metamaterial with graded density. Analytical models of the dynamic strength enhancement, impact velocity attenuation and energy absorption are proposed for materials with uniform initial density and materials with positive density gradient. Attention is paid to the influence of the material topology governed by the initial dihedral angle gamma(0) on the dynamic response of origami based stationary blocks with equal densities. The propagation of disturbances-velocity and nominal strains-along the samples is analysed and it is shown that the localisation is more pronounced for small values of gamma(0). Different from other open cell materials (e.g. foam and honeycomb), the propagation speed of the yield stress, which corresponds to the quasi-static strength, is not related to the elastic properties of the metamaterial in the form of precursor elastic wave as it is governed by the inertial properties of the cells due to the local structural softening. Therefore, the in-plane dynamic compression of Miura-ori patterned metamaterials cannot be directly interpreted by means of the shock wave theory commonly used for cellular materials with different topologies. Nonetheless it is shown that, similarly to other cellular materials, the Miura-ori patterned metamaterials exhibit increased energy absorption capacity when increasing the loading rate. However, the dynamic energy absorption capacity of the analysed metamaterials in not uniquely defined by their relative density and is strongly dependent on their topology. The analytical models are verified by numerical simulations.