The design strain and dead mass of energy absorbing materials and structures: mathematical principles and experimental determination

The most important design parameters of energy absorbers are a) the maximal ratio of energy density W to stress σ, i.e. (W/σ)max, misnamed ‘efficiency’, and b) the maximal admissible strain ɛmax at this ratio. This paper models standard energy absorbing elements and determines the theoretical (W/σ)max and ɛmax. The theoretical data are then compared to experimental ones, obtained from compression experiments. A method for correcting (W/σ)max of materials with pronounced negative modulus (over a defined strain window) is introduced. The maximal gradient, of logW versus logσ, i.e. at the optimum point, is unity. (W/σ)max ranges from 0.2 to 0.55, and ɛmax from 0.48 to 0.81. Materials with negative modulus have higher (W/σ)max and ɛmax values. Better shock absorbers, with larger (W/σ)max, have less ‘dead mass’.