Dynamic Compressive Behavior of Graded Auxetic Lattice Metamaterials: A Combined Theoretical and Numerical Study

Auxetic metamaterials, characterized by negative Poisson’s ratio, have garnered significant interest due to their exceptional impact resistance. This study presents a type of auxetic metamaterial organized in re-entrant arrowhead lattices. The uniaxial impact behavior of a uniform auxetic lattice was first investigated through experiment and finite element simulation, which showed good agreement. Subsequently, two graded auxetic lattices with density-gradient profiles were proposed by varying the radius of the bars in the basic auxetic lattice. Numerical simulations demonstrate that, across various compression velocities, both graded architectures achieve higher plateau stresses and enhanced energy absorption compared to their uniform counterpart. Notably, the graded lattice with lower density at the impact end exhibited a reduced initial peak stress. An analytical framework was also established to characterize the compressive behavior of these auxetic lattices. Theoretical analyses elucidate the underlying mechanisms of impact energy dissipation and provide a solid basis for predicting dynamic compressive performance. Furthermore, a gradient-parametric study revealed that the stress–strain response is significantly influenced by both the density gradient and impact velocity, further demonstrating a high consistency between the theoretical predictions and the simulation results. This research is desirable to provide insights for designing graded auxetic metamaterials with tailored impact properties.