Abstract:

The integration of gradient design into foam materials offers a promising approach to regulating their mechanical properties and improving energy absorption. In this study， foam materials with both layered and continuous gradient structures are designed and fabricated using Voronoi diagrams and 3D printing technology. A finite element model， which considers the strain rate of the matrix material， is developed and validated through quasi-static compression tests. The dynamic mechanical properties and deformation behaviors of the gradient foam materials are subsequently investigated. The results reveal that for foams with a positive gradient， under varying loading velocities， the lower-density end （i.e.， the loading end） deforms first and the deformation propagates toward the support end， forming a distinct plastic shock wave， referred to as the forward single-wave mode. In contrast， for foams with a negative gradient， as the loading velocity increases， they sequentially exhibit reverse single-wave mode， double-wave mode， and forward single-wave mode. The deformation modes of layered gradient and continuous gradient foams are similar， with the difference diminishing as the number of layers increases. The theoretical models for single-wave and double-wave behaviors of gradient foams， based on stress wave theory， accurately predict the stresses at both the impact and support ends under different impact velocities. Furthermore， the analysis of the critical velocity for negative gradient foams indicates that when the gradient rate is small， the support end， with its larger cells， is more likely to deform， thus reducing the inertial effect associated with increased loading velocities. This leads to an increase in the second critical velocity range for the double-wave mode， that is， the second critical velocity increases， while the first critical velocity exhibits lower sensitivity to the gradient rate. With the rise in impact velocity， the energy absorption performance of negative gradient foams is significantly enhanced.

Key words: gradient foam, 3D printing, dynamic response, dual-wave model, critical velocity