Propagation of compaction waves in cellular materials with continuously varying density

Theoretical analysis of the propagation of stress waves in cellular solids with non-uniform density, and consequently strength, is carried out to deepen the understanding of their dynamic compaction due to impact loading. Materials with continuously varying density in the direction of loading are considered when analysing the response to two types of loading conditions: an impact of a stationary cellular block by a rigid mass and an impact of a cellular block on a rigid wall. It is assumed that the local stress–strain characteristics of the graded materials exhibit strain hardening. The plastic strain field in the deformed graded cellular solid is sought here as a function of the impact velocity and material properties when using the Hugoniot material representation. It is shown that the initial density variation with respect to the boundaries of a finite thickness block has a significant effect on the history of the stresses and strains during the compaction process.FE models using ABAQUS are constructed and numerical simulations are carried out to verify the predictions of the theoretical analysis. Attention is paid to the energy absorption capacity of the materials depending on their initial density distribution when comparing their dynamic responses with the response of equivalent mass cellular block with uniform density. Significant advantages in using density graded cellular solids in finite thickness layers are not identified for the analysed loading rate.