Propagation Of Compaction Waves Research Articles

Dynamic characteristics of density-graded cellular materials for impact mitigation

Due to their exceptional impact resistance capabilities, density-graded cellular materials have immense potential in applications where crashworthiness requirements are of prime importance. Under impact loading, the deformation in these materials is characterized by compaction front propagation. Previous studies have utilized numerical techniques to solve the equations governing compaction shock propagation for cellular materials with density gradation. In this study, analytical solutions are formulated using compaction front position as the independent variable. The expressions for the velocity of the impinging rigid mass, energy absorption, incident stress, and transmitted stress are determined. The analytical solutions are shown to be in excellent agreement with the cell-based finite element solutions. The effect of density gradient on energy absorption and stresses is studied. The impact resistance factor is employed to assess different density-graded cellular materials for their effectiveness in impact mitigation. This study demonstrates that density-graded cellular materials can offer superior impact protection to objects at both the incident and transmitted ends. Lower density toward the incident end enhances impact resistance to objects located there, and likewise, lower density at the transmitted end offers more impact resistance to objects at that end.

Multi-objective optimization of additive manufactured functionally graded lattice structures under impact

A multi-objective optimization procedure to effectively design gradient lattice structures under dynamic loading is presented. It aims both at maximized energy absorption characteristics and a lightweight design. The reduction of the peak crushing force and a maximized specific energy absorption are simultaneously optimized. Design variables like the relative density and density gradient of the lattice structure are investigated, considering different topologies of the lattice unit cells. To model and simulate the lattice structures efficiently, a simplified beam-based simulation finite element model is introduced and validated against experimental tests. They cover the range from dynamic equilibrium up to compaction wave propagation as impact deformation phenomena. Based on large numbers of simulations, an artificial neural network is used to predict the energy absorbing characteristics for the given design parameters and to find the optimal configuration of the lattice structures. The neural network is trained using a multi response adaptive sampling algorithm allowing parallel simulation with automatically generated finite element models during each iteration step. Subsequently, a multi-objective genetic algorithm is used to find optimal combinations of the design parameters of lattice structures under different impact velocities and cell topologies.

Compaction Wave Propagation in Layered Cellular Materials Under Air-Blast

The propagation of compaction waves in layered cellular material subjected to air-blast is analyzed to examine the mechanism of compaction wave and reveal the phenomena that develop at the interface between the cellular layers. Similar to the previous studies of cellular materials under dynamic loading, the topology of cellular materials is neglected and homogeneous properties are assumed. The rigid-perfectly plastic-locking (R-PP-L) material idealization and the simple shock theory are employed to analyze the compaction situations. Analytical solutions for compaction wave propagation of double-layer cellular materials with two gradient-arrangements under air-blast loading have been worked out. The densification wave occurs at the blast end and then gradually propagates to the distal end for layers’ densities increase in the propagation direction (positive gradient). While compaction waves simultaneously form in both layers and propagate to the distal end in the same direction for the negative gradient. The finite element (FE) models using the Voronoi technique are carried out with practical aluminum foam to verify the predictions of the theoretical analysis. The potential of layered cellular materials to design efficient structural components under air-blast load is discussed, which would outperform their corresponding single counterpart with equal mass.

Experimental characterization of compaction wave propagation in cellular polymers

A great-deal of literature is available in the study of compaction wave propagation in cellular materials. However, experimental investigations concerning the spatial variation of the deformation features of compaction waves are limited. In this study, the formation and propagation of compaction wave in a low density polymeric foam under intermediate velocity projectile impact loading is investigated experimentally. The results are discussed in terms of the compaction wave characteristic parameters such as compaction wave velocity, axial strain, particle velocity, etc. In addition, spatial distribution of inertia stress during compaction wave propagation, and the critical velocity required to form shock are estimated. The stress jump across the compaction wave is also calculated using an inertia stress analysis and compared with the shock theory. It was observed that an elastic precursor propagates, at a velocity of 740 m/s, along the material upon impact, and it decays as it propagates along the specimen. Whereas, the compaction wave formed following the elastic precursor was propagated at a constant velocity much slower than the elastic precursor. Inertia stress calculations shows that the fast moving elastic precursor is reflected from the distal end and reduces the inertia component of the total stress. On the other hand, the compaction thickness is seen to be approximately constant during the entire duration of the compaction wave propagation after the achievement of the quasi-steady condition.

Stress Distribution in Graded Cellular Materials Under Dynamic Compression

Dynamic compression behaviors of density-homogeneous and density-graded irregular honeycombs are investigated using cell-based finite element models under a constant-velocity impact scenario. A method based on the cross-sectional engineering stress is developed to obtain the one-dimensional stress distribution along the loading direction in a cellular specimen. The cross-sectional engineering stress is contributed by two parts: the node-transitive stress and the contact-induced stress, which are caused by the nodal force and the contact of cell walls, respectively. It is found that the contact-induced stress is dominant for the significantly enhanced stress behind the shock front. The stress enhancement and the compaction wave propagation can be observed through the stress distributions in honeycombs under high-velocity compression. The single and double compaction wave modes are observed directly from the stress distributions. Theoretical analysis of the compaction wave propagation in the density-graded honeycombs based on the R-PH (rigid-plastic hardening) idealization is carried out and verified by the numerical simulations. It is found that stress distribution in cellular materials and the compaction wave propagation characteristics under dynamic compression can be approximately predicted by the R-PH shock model.

Instationary compaction wave propagation in highly porous cohesive granular media

We study the collision of a highly porous granular aggregate of adhesive $$\upmu $$ m-sized silica grains with a hard wall using a granular discrete element method. A compaction wave runs through the granular sample building up an inhomogeneous density profile. The compaction is independent of the length of the aggregate, within the regime of lengths studied here. Also short pulses, as they might be exerted by a piston pushing the granular material, excite a compaction wave that runs through the entire material. The speed of the compaction wave is larger than the impact velocity but considerably smaller than the sound speed. The wave speed is related to the compaction rate at the colliding surface and the average slope of the linear density profile.

Propagation of compaction waves in cellular materials with continuously varying density

Theoretical analysis of the propagation of stress waves in cellular solids with non-uniform density, and consequently strength, is carried out to deepen the understanding of their dynamic compaction due to impact loading. Materials with continuously varying density in the direction of loading are considered when analysing the response to two types of loading conditions: an impact of a stationary cellular block by a rigid mass and an impact of a cellular block on a rigid wall. It is assumed that the local stress–strain characteristics of the graded materials exhibit strain hardening. The plastic strain field in the deformed graded cellular solid is sought here as a function of the impact velocity and material properties when using the Hugoniot material representation. It is shown that the initial density variation with respect to the boundaries of a finite thickness block has a significant effect on the history of the stresses and strains during the compaction process.FE models using ABAQUS are constructed and numerical simulations are carried out to verify the predictions of the theoretical analysis. Attention is paid to the energy absorption capacity of the materials depending on their initial density distribution when comparing their dynamic responses with the response of equivalent mass cellular block with uniform density. Significant advantages in using density graded cellular solids in finite thickness layers are not identified for the analysed loading rate.

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

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.

Compaction of a double-layered metal foam block impacting a rigid wall

The propagation of compaction waves in layered metal foam materials subjected to impact loading is analysed in order to examine the mechanism of compaction and reveal the phenomena that develop at the interface between the foam layers. The analysis is focused on double-layered configurations in which the individual materials exhibit strain hardening in the quasi-static regime of loading.Complex patterns of compaction due to impact are revealed depending on the foam quasi-static stress–strain characteristics, sequence of layers and impact velocity. The compaction of the individual foam layers under an increasing and decreasing velocity is distinguished. It is established that either a strong discontinuity wave or a simple compression wave can start propagating from the layers interface inside the distal layer depending on the material properties. It is shown that a secondary compaction of the proximal foam layer is possible to occur due to the propagation of the reflected wave from the layers interface when a particular layer sequence is arranged. This can lead to a significant stress increase at the interface.The present analysis is based on uniaxial models of compaction in which the compacted strains are not predefined but are obtained as a part of the solution being functions of the velocity variation. The proposed analytical models are verified by numerical simulations considering aluminium based foam Cymat with densities 253 and 570kg/m3 and Alporas with density 245kg/m3. The influence of the elastic material properties is briefly discussed.

Propagation of Compaction Waves in a Double-Layer Metal Foam Block Subjected to Impact

Propagation of Compaction Waves in a Double-Layer Metal Foam Block Subjected to Impact

Propagation of compaction waves in metal foams exhibiting strain hardening

One-dimensional models for compaction of cellular materials exhibiting strain hardening are proposed for two different impact scenarios. The models reveal the characteristic features of deformation under the condition of decreasing velocity during the impact event. It was established that an unloading plastic wave of strong discontinuity propagates in the foam and it has a significant dynamic effect on the foam compaction and energy absorption. The proposed models are based on the actual experimentally derived stress strain curves. The compaction mechanism in three aluminium based foam materials, two of them with relatively low density – Alporas and Cymat with 9% and 9.3% relative density, respectively and a higher density Cymat foam with 21% relative density, is analysed. Numerical simulations were carried out to verify the proposed models.The predictions of the proposed models are compared with published analytical models of compaction of cellular materials which assume a predefined densification strain. It is shown that the approximation of a cellular material with significant strain hardening by the Rigid Perfectly-Plastic-Locking (RPPL) model can lead to an overestimation of the energy absorption capacity for the observed stroke due to the non-uniform strains along the compacted zone of the actual material in contrast to the predefined constant densification strain in the RPPL model. The assumption of a constant densification strain leads also to an overestimation of the maximum stress, which occurs under impact.

Dynamic and Quasi-Static Propagation of Compaction Waves in a Low-Density Epoxy Foam

We conducted dynamic and quasi-static compression experiments with low-density (ρ = 120 kg/m3) epoxy foam specimens. The specimens had a 10.0-mm-square cross-section and a length of 19.3 mm. Dynamic experiments were conducted with a modified split Hopkinson pressure bar (SHPB), and the quasi-static experiments were conducted with a hydraulic load frame device (MTS-810). In both cases, the specimens were loaded from one end at a constant velocity. Equally spaced grid lines were marked on the specimens to monitor the deformation history. Digital images taken at equally spaced time intervals gave the positions of each grid line. These images showed that a constant end-face velocity V produced a compaction wave front that traveled at a constant velocity C in both dynamic and quasi-static experiments. We described these results with a shockwave analysis that used a locking solid material model.

Derivation of Forchheimer terms and their verification by application to waves propagation in porous media

Forchheimer terms are developed for the macroscopic momentum and energy balance equations considering saturated thermoelastic porous media, and for the macroscopic momentum balance equations in the case of multiphase porous media. It is shown that these terms represent the exchange between the interacting phases at their common interface. Using these Forchheimer terms, a very good agreement was evident when the 1-D numerical simulation of the propagation of compaction waves in a saturated thermoelastic porous medium was compared with shock tube experiments.