Embracing Nonlinearity and Geometry: A dimensional analysis guided design of shock absorbing materials

Abstract: Protective applications require energy-absorbing materials that are soft and compressible enough to absorb kinetic energy from impacts, yet stiff enough to bear crushing loads. Achieving this balance requires careful consideration of both mechanical properties of the material and geometry of the shock-absorbing pads. Conventional shock-absorbing pads are typically made from very thick foams that exhibit a plateau of constant stress in their stress-strain response, while foams with a non-linearly stiffening stress-strain response are often considered ineffective. Contrary to this belief, we demonstrate that foams with a nonlinear stress-strain response can be effective for achieving protective pads that are both thin and lightweight, particularly for pad geometries requiring a large cross-sectional area. We introduce a new framework for the thickness or volume-constrained design of compact and lightweight protective foams while ensuring the desired structural integrity and mechanical performance. Our streamlined dimensional analysis provides geometric constraints on the dimensionless thickness and cross-sectional area of a protective foam with a given stress-strain response to limit the acceleration and compressive strain within desired critical limits. We also identify optimal mechanical properties that will result in the most compact and lightest protective foam pad for absorbing the given kinetic energy of impact. Guided by this design framework, we achieve optimal protective properties in hierarchically architected vertically aligned carbon nanotube (VACNT) foams, enabling next generation protective applications in extreme environments.