Compressive Stress-Strain Relations and Shock Hugoniot Curves of Flexible Foams

Based on the general shape of the curves describing experimental compressive stress-strain relations of flexible porous materials (e.g., flexible foams) which are known to depend on their relative density, a general mathematical functional dependence of the stress on the strain is proposed. The general function includes two constants. Using experimental and empirical information the values of these constants are determined, so that a final compressive stress-strain relation, in which the relative density is a parameter, is obtained. Good agreement is found when the presently developed empirical stress-strain relations are compared to experimental ones for a wide range of relative densities. The proposed compressive stress-strain relations are then used to derive shock Hugoniot relations for flexible porous materials. With the aid of these relations one can investigate the dynamic behavior of foams struck head-on by shock waves. The finally obtained empirical shock Hugoniot relations are found to be similar to experimental relations which are proposed in the literature. In addition, a mathematical investigation of the asymptotic behavior of the shock Hugoniot relations is conducted. The results of this investigation are found to agree excellently with actual experimental data.