An impact-absorbing structure that includes a plurality of interconnected cells forming a sheet, each cell having a sidewall and a longitudinal axis. Each cell may be configured to absorb energy through plastic deformation in response to an applied load, and a sidewall of at least one cell may include a geometric perturbation that is oriented in a direction that is not parallel to the longitudinal axis of the cell. The geometric perturbation may reduce the load required to cause plastic deformation of the cell.