This study explores how geometry-driven design strategies can tailor the dynamic response of two dimensional (2D) elastic lattices under transient impact loading. The aim is to establish a unified, physics-based framework linking lattice geometry, irregularity, and mass grading to controllable stress-wave mitigation in 2D elastic metamaterials. A total of 108 lattices based on 18 distinct unit-cell geometries are analyzed under equal global mass and wall length. Three geometric factors are examined: unit-cell topology, controlled irregularity introduced as random perturbations at wall junctions, and spatial wall-thickness grading (mass shifting). Finite element (FE) simulations show that unit-cell geometry dictates stress wave propagation trajectories. Controlled irregularity can further adjust wave propagation by promoting a switch from stretching- to bending-dominated deformation. A central contribution is the analytical modeling of graded lattices as a one-dimensional lumped mass–spring system employing the Gibson–Ashby model. A closed-form solution for a two-degree-of-freedom case provides physical insight into the effect of mass shifting. Results reveal that shifting mass towards the impact point reduces input acceleration and transmitted force, improving wave mitigation. The proposed model, while simple, captures these effects accurately and aligns well with FE results, offering a fast and reliable tool for designing mechanical metamaterials for stress wave attenuation. These results provide practical guidelines for designing 2D lattice metamaterials with tailored transient wave mitigation for vibration-sensitive applications.
