Modeling the mechanical response of auxetic metamaterials to dynamic effects

The paper investigates the mechanical response of a 3D auxetic structure created on the basis of a unit cell with pre-buckled structural elements to dynamic loading. The aim of the work is to study deformations of the auxetic structure made of an alpha titanium alloy during uniaxial compression at 100 m/s, to evaluate dissipative properties of the structure during high-speed deformation, and to estimate the characteristic time of the metamaterial’s compaction with a relative density of 0.0115. The numerical simulation of the metamaterial at effective strain rate of 2000 1/s has been performed using LS DYNA solver. To describe the mechanical behavior of the titanium alloy in frame elements, we use a model of an elastic-plastic damaged medium, which takes into account the strain rate sensitivity of the plastic flow, temperature changes due to dissipative effects, and the effect of the stress state triaxiality parameter on nucleation and growth of structural damages. The numerical studies have shown that the auxetic effect in the studied metamaterial is retained under high-rate elastoplastic deformation. At a speed of the uniaxial compression of 100 m/s, deformation in the volume of the metamaterial proceeds nonuniformly. Under dynamic loading of the considered auxetic metamaterial, the deformation and fracture modes depend not only on the parameters of the cell geometry, but also on the mechanical behavior of the framework material, as well as on the relative density. This makes it possible to control the deformations of the cells under mechanical stress. Layers of compacted cells are formed near the dynamic loading surface. The instability of the cells of the auxetic metamaterials increases the absorbed energy. The calculated value of the specific absorbed energy under dynamic uniaxial compression reaches 3.4 kJ/kg, and is comparable with the values for frame structures made of Ti-6Al-4V with an equivalent specific mass density. The results indicate the possibility of creating protective structures using auxetic cellular structures on the base of the pre-buckled elements of the rolled metal.