Journal Club Theme of December 2009: Impact Behaviour of Materials with Cellular Structures
Welcome to the forum! Discussion topics were suggested initially as follow:
Metal foams, cell deformation (bending, buckling, plasticity and fracture), constitutive stress-strain behaviour of cellular materials, energy absorption, hypervelocity impact, shock wave behaviour, 1D shock modelling, shock attenuation, shock enhancement, Material Point Method (MPM) simulation and microscopic tomography experimental observation;
and later were extended to many related:
Natural cellular materials, sunflower stem, negative Poisson’s ratio, nanoscale deformation in nacre, mesh-free methods, eXtended Element Free Method (XEFG), eXtended Finite Element Method (XFEM), simulating discontinuities, hyperelastic model, poroelasticity, loading rate effect, fluid-structure interaction, structural optimization, iMorph software, foam geometry, pattern formation, Kelvin problem, quasicrystal, trabecular bone, gyroid, bulk metallic glass foam, peridynamics.
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1. Cellular materials, such as metal foams, are used as impact energy absorbers in crash and blast protection due to their unique constitutive behaviour. Three stages can be identified for the stress-strain curves of the uniaxial compression of metal foams: Stage I: The deformation is, in general, reversible. For closed-cell metal foam this is in the form of bending of the cell walls and edges. At the end of this stage some cells suffer collapse. This may be due to elastic buckling, plastic deformation or fracture. Stage II: The almost constant compressive stress, plateau stress, appears in a wide range of strain. Buckling and plastic collapse occur successively until all cells are collapsed. The deformation in this stage is unrecoverable. Stage III: Cell walls and edges contact each other and are crushed; giving rise to a steeply rising stress.
2. Energy absorbers for crush and blast protection are chosen so that the plateau stress is just below the stress that will cause damage to the packaged object; the best choice is then the one which has the longest plateau, and therefore absorbs the most energy.
3. Impact velocities can vary from a few meters per second to some tens of kilometers per second (hypervelocity). Hypervelocity is relevant to the field of space exploration such as the impact by space debris. Using of metal foams in this field is still under investigation.
4. Analytical solutions of shock waves in cellular materials. For 1D analysis, Reid and Peng (1997) firstly treated cellular materials subject to uniaxial compression using a simplified rigid, perfectly-plastic, locking (RPPL) model. In the RPPL model, the constitutive behaviour in stage-I is simplified as rigid; stage-II is treated as perfect plastic at the yielding plateau stress, and the second stage ends at the locking (densification) strain; stage-III is again idealized as rigid. Radford et al. (2005) used RPPL model to study the shock behaviour in a metal foam projectiles. Harrigan et al. (2009) compared RPPL with other analytical approaches on modelling shock behaviours.
5. Shock waves propagating in cellular materials will, in general, be attenuated by cell collapse at low impact speed. However, shock enhancement will occur during high speed impact; this will affect the structure design. The group led by Professor Han Zhao at the Universit´e Paris VI investigated the shock enhancement both numerically and experimentally.
6. Simulating impact behaviour of cellular materials using the Material Point Method (MPM). MPM was adopted by the U.S. Department of Energy’s ASCI (Accelerated Strategic Computing Initiative) Center for the Simulation of Accidental Fires and Explosions in simulating high speed impact on plastic bonded explosives. The group led by Prof. Hongbing Lu at the Oklahoma State University worked on MPM for many years; his group recently studied the cell-wall buckling, shear-band formation and collapse-wave propagation using MPM simulations (Daphalapurkar et al., 2008). The microstructure of the foam was determined using μ-CT and was converted to material points. The properties of the cell-walls were determined from nanoindentation on the wall of the foam. Features of the microstructures from simulations were compared qualitatively with the in-situ observations of the foam under compression using μ-CT.
Daphalapurkar, N.P., Hanan, J.C., Phelps, N.B., Bale, H., Lu, H., 2008. Tomography and simulation of microstructure evolution of a closed-cell polymer foam in compression. Mech. Adv. Mater. Struct. 15, 594-611.
Harrigan, J.J., Reid, S.R., Yaghoubi, A.S., in press. The correct analysis of shocks in a cellular material. Int. J. Impact Eng..
Pattofatto, S., Elnasri, I., Zhao, H., Tsitsiris, H., Hild, F., Girard, Y., 2007. Shock enhancement of cellular structures under impact loading: Part II analysis . J. Mech. Phys. Solids 55, 2672–2686.
Radford, D.D., Deshpande, V.S., Fleck, N.A., 2005. The use of metal foam projectiles to simulate shock loading . Int. J. Impact Eng. 31, 1152–1171.
Reid, S.R., Peng, C., 1997. Dynamic uniaxial crushing of wood. Int. J. Impact Eng. 19, 531-570.