Primary and Reflected Compaction Waves in a Foam Rod Due to an Axial Impact by a Small Mass

Abstract

The propagation of compaction waves in a stationary foam block subjected to an impact by a small mass is studied in order to examine the mechanism of compaction within the primary and reflected stress waves. The analysis is focused on aluminium strain rate insensitive foam that exhibits strain hardening under quasistatic compression. A theoretical approach is applied using a uniaxial model of compaction in which the compacted strains, being functions of the velocity variation, are not predefined but are obtained as a part of the solution. The present approach allows one to obtain the strain histories and strain distributions within the primary compaction wave as well as within the reflected wave, which propagates in a media with non-uniform density increasing monotonically in the direction of loading. FE simulations considering aluminium based foam Cymat with density 411.5 kg/m3 are carried out in order to verify the proposed theoretical model. A comparison between the impact velocity attenuation predicted by the present model and classical Rigid Perfectly-Plastic Locking material model for cellular materials is discussed. The light weight and enhanced energy absorption capacity of cellular materials with different topologies under dynamic loading make these materials attractive for various applications. Therefore efforts are made to develop models of the dynamic compaction when introducing various simplifications. Despite the similar common characteristic of an extended strain region with slowly varying stresses, different mechanisms of compaction develop depending on the material topology. A distinction can be made between cellular materials which exhibit local softening during the response, as honeycombs under out-of-plane impact, and open and closed cellular materials, which exhibit mainly hardening during the quasi-static compression. While the first class of materials is characterized by inertia sensitivity and stress increase proportional to the impact velocity, the latter class of materials is characterized by a dynamic stress enhancement proportional to the velocity squared. Therefore the majority of the theoretical efforts to characterize the cellular materials are focused on the second class. KeywordsA shock wave propagation model in cellular materials was proposed by Reid and Peng (1997) to explain the crush enhancement of wood specimens assuming a rigid perfectly-plastic locking (RPPL) mechanism. A thermo-mechanical approach was used in the formulation of the dynamic compaction process to provide a first-order understanding of two impact scenarios (Tan et al., 2005a) supported by the experimental observation of compaction of low density open cell material (Tan et al., 2005b). Retaining the basic characteristics of the one dimensional shock wave models, more detailed material models were used to account for the elastic material properties. An elastic-plastic model with hardening was proposed by Harrigan et al. (2005) while an elastic perfectly-plastic-with rigid locking model was applied by L...

Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling

“…Refs. [147][148][149] ( ) P t In the theoretical framework of continuum mechanics, unified 1D shock models have been developed by Karagiozova et al [172,255,[260][261][262] and Zheng et al [106,169] mainly for the first two loading scenarios shown in Table 3 Examples of typical plasticity models for cellular materials are listed in Many studies have shown that the yield surfaces described by the plasticity models summarised in Table 5 are in reasonably good agreement with experimental results for multiaxial loading [14,60,62,272,274,275] (e.g. Fig.…”

Propagation of compaction waves in cellular materials with continuously varying density

“…A new compaction resulting from the wave reflected from the stationary boundary can arise at t ¼ t 1 if the initial impact energy is not entirely absorbed within the primary wave (Karagiozova and Alves, 2015). At t ¼ t 1 , the compacted cellular block has thickness L 1 ¼ hðt 1 Þ, which depends on the initial impact velocity and striking mass.…”

“…The equations of motion for t > t 1 with respect to the new compacted zone with thickness h 2 and additional displacement u 2 are (Karagiozova and Alves, 2015) dV…”

The equivalent method of double V-wing honeycombs on the in-plane dynamic impact

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