Harnessing Functional Gradients for Enhanced Shock Absorption in Foam Materials

Abstract

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, simultaneous optimization of energy absorption and transmitted
stress attenuation can be achieved, facilitating designs for application-specific shock-mitigation.