Optimization for Improved Energy Absorption and the Effect of Density Gradation in Cellular Materials

Cellular foam materials are used increasingly in a wide range of applications involving energy absorption and impact protection as they are capable of absorbing a large amount of energy without a significant increase in load. In this study, the optimum relative density of cellular material that maximizes the energy absorption performance is investigated for low impact velocity applications. Idealized material models are employed to represent the material behavior at low impact velocities. Quasi-static compression experiments covering a wide range of densities are performed to extract material model parameters for rigid polyurethane foam. Using the material models with experimentally determined parameters, the optimal density is identified and the relative increase in energy absorption of the functionally graded material over a uniform density material is determined. It is shown that the uniform density configuration has a superior energy performance. It is also shown that density gradation is advantageous up to a certain value of average relative density, designated as the critical average relative density. This critical average relative density is shown to be 0.2 for rigid polyurethane foam.