Design optimization of continuously and discretely graded foam materials for efficient energy absorption

• A semi-analytical approach is proposed to investigate the effect of gradation functions in graded foams.
• Discretely layered and continuously graded foams are considered in the analysis.
• For discretely layered foams, a convex gradient is shown to promote both energy consumption and strength.
• Depending on the application, both convex and concave continuous gradients can yield in optimal energy performance.

Design optimization is proposed for graded foams by investigating the effect of density gradation on the load bearing and energy absorption characteristics. Stress-strain curves obtained experimentally for polyurethane foams with five different nominal densities are first used to generate a data set containing the deformation response of foams over a wide range of densities. Using this data set as the input, an analytical approach is employed to study the local and global constitutive response and energy absorption of continuously graded and discretely layered foams. Results obtained for the discretely layered structures are experimentally verified by conducting uniaxial compression on layered foam structures fabricated in-house. Results indicate that for layered structures, the convex gradation functions yield in an improved energy absorption and load-bearing performance, as well as lower overall structural weight, compared with monolithic foams. The analysis has been extended to study continuously graded foams in order to determine the optimal gradation functions which promote improved strength as well as superior energy absorption, compared with the single phase foam of the same structural weight.

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