Harnessing functional gradients for enhanced shock absorption in foam materials

Shock generating high-velocity impacts produce intense stress waves and rapid accelerations — unlike low-velocity impacts that deform materials under dynamic equilibrium — posing severe risks to human organs, structures, and sensitive equipment. Functionally graded protective foams are promising candidates for shock mitigation due to their spatially tunable density and constitutive profile. However, limited mechanistic understanding of energy absorption and stress attenuation during compaction shock formation in graded foams may hinder their application-specific design. Here, in an integrated experimental and theoretical study, we investigate the compaction shock characteristics of graded foams using intrinsically graded vertically aligned carbon nanotube (VACNT) foams as a model system. Our analysis shows that while energy absorption is governed by compaction shock evolution from impact to the protected boundary, transmitted dynamic stress is primarily dictated by local material impedance. Using our generalizable shock modeling framework applicable to diverse functionally graded foam types, we demonstrate how density and density-dependent constitutive gradation dictate compaction shock characteristics. By selecting appropriate foam types and tailoring functional gradients, we provide design insights to enhance energy absorption while reducing transmitted stress simultaneously, facilitating designs for application-specific shock-mitigation.