Bumper design regulations for low-speed vehicular impacts (Part 581, Bumper Standard, formerly FMVSS 215) and high-speed pedestrian impacts (ECE 127/GTR 9) possess a contradictory set of requirements. Essentially, an ideal bumper structure should be stiff under low-velocity vehicular impacts while exhibiting a softer response when impacting pedestrians at elevated velocities to satisfy both regulations. A series of energy absorbing structures capable of passively adapting their mechanical responses based on the loading conditions were investigated using finite element modelling tools which were validated to a series of experimental testing observations. The preferred structure consisted of a rectangular array of trapezoidal cells which buckle under single-cell impacts while resisting lateral deformation and artificially increasing the overall stiffness under large area impacts. A geometric study of this dissipater demonstrated the potential to increase total energy absorption by 37.3% by adding thin-walled crossbars at the bases of adjacent cells. Additionally, a parametric study identified a combination between upper cell angle and the ratio between the wall thicknesses as the most critical parameter to consider when tailoring the overall mechanical response.