Inverse Design and Boundary Effects in Impact Waveform Control of Graded Foam Metals

To achieve the precise generation of high-amplitude impact waveforms required for aviation safety testing and related fields, this study investigates the impact waveform regulation mechanisms of graded cellular metals under different boundary conditions. Based on the conservation laws of mass and momentum, theoretical models for impact waveform generation using graded cellular metals are established for both free and elastic boundary conditions. Furthermore, an inverse design method for density gradient is proposed, which incorporates an average relative density constraint combined with Gauss-Newton iteration, enabling the reverse solution from a prescribed acceleration waveform to the material density gradient distribution. Finite element results demonstrate that the proposed method can effectively generate required waveforms—such as triangular and half-sine waves—under both boundary conditions. The study also reveals that: free boundaries are more suitable for generating high amplitude and long duration waveforms, whereas elastic boundaries can improve the realizability of low-amplitude waveforms through stiffness regulation; boundary conditions do not alter the impact duration but exert a significant influence on waveform shape; and excessive impedance mismatch between adjacent layers will intensify waveform oscillations, thereby compromising the waveform generation accuracy. The proposed inverse design strategy for density gradients exhibits favorable versatility and provides both theoretical support and a practical design tool for the development of high-amplitude impact testing technologies.