Energy-absorbing structures operate under impact and dissipate kinetic energy through material failure and structural collapse. One inherent challenge for the topology design of such structures is to solve impact problems and derive sensitivity, which are often associated with a formidable nonlinearity. To remedy this problem, this article views the problem as finding a material configuration that maximizes the specific energy absorption while satisfying both force and deformation constraints, and proposes a decoupling strategy that solves the optimization problem in a nested loop, where the outer loop performs dynamic analysis to evaluate structural performance and ensure the feasibility of the solution, while the inner loop solves the topology optimization problem with the stiffness as the design objective. After the validity of the method had been confirmed by a standard two-dimensional example, it was extended by considering the constant cross-section manufacturing constraints and plastic hinge effects pertaining to thin-walled structures.