Dynamic crushing of honeycombs and features of shock fronts

The in-plane dynamic crushing of 2D hexagonal-cell honeycombs has been simulated using finite elements to explore the dynamic response of cellular materials and to investigate the features of the crushing front and to examine the assumptions employed in a one-dimensional shock theory [Reid SR, Peng C. Dynamic uniaxial crushing of wood. Int J Impact Eng 1997;19:531-70; Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S. Dynamic compressive strength properties of aluminium foams. Part II - shock theory and comparison with experimental data and numerical models. J Mech Phys Solids 2005;53:2206-30]. It has been demonstrated that progressive cell crushing is observed to propagate through the material in a 'shock' like manner when the crushing velocity exceeds a critical value. The simulations show that there exists a zone at the shock front across which there are essentially discontinuities in the material 'particle velocity', 'stress' and 'strain' as defined herein. At supercritical crushing velocities the thickness of this zone remains about one cell size, which varies little with the crushing velocity and the relative density. Densification strain increases as crushing velocity increases and asymptotes to a limit once a shock front forms. It has also been shown that the one-dimensional shock theory [Reid SR, Peng C. Dynamic uniaxial crushing of wood. Int J Impact Eng 1997;19:531-70; Tan PJ, Reid SR, Harrigan JJ, Zou Z, Li S. Dynamic compressive strength properties of aluminium foams. Part II - shock theory and comparison with experimental data and numerical models. J Mech Phys Solids 2005;53:2206-30], which was based on an equivalent rigid-perfectly plastic-locking stress-strain curve, tends to overestimate slightly the crushing stress and energy absorbed.