High Intensity Impulsive Loading

Impulses in Water

Explosions under water create high intensity shock fronts which propagate through the fluid and interact with the surface of a structure to cause dynamic deformation and (sometimes) fracture. The pressure created within the shock front in water can be very large. Figure 1 shows a computed pressure-time waveform for a water shock front resulting from a small (10’s of gm) explosion in water. In such test, the impulse in the water causes the pressure to rise to a peak, p0, almost instantaneously. The pressure subsequently decreases at a nearly exponential rate, with a time constant θ of order milliseconds such that p = p0exp(-t/θ), where t is measured from the instant of impulse arrival. Damped oscillations of the gas bubble containing the explosive products leads to secondary impulses, but these generate smaller pressures, and are much less damaging.

G.I. Taylor (in the UK) and R.H. Cole (in the US) found that the reflection of a water borne shock front by a rigid body doubled the incident impulse transferred into the structure. They noted that beneficial fluid structure interactions can occur in water when the shock impacted structure is able to move away from the shock front. This can occur with sandwich panels that have light (thin) faces and cores whose compressive strength is less than the shock over-pressure. To investigate fundamental aspects of both the fluid structure interaction and cellular materials concepts for under water shock mitigation, we have set up controlled explosive experiments with collaborators in the US Navy. Figure 1 shows a schematic illustration of their dynocrusher apparatus used for this purpose.

Figure 1: A DYSMAS prediction of the free field pressure p versus time t history generated by the denotation of the explosive sheet. The prediction is shown for a point located at a stand-off of H = 0.1m from the explosive sheet and t = 0 is defined as the time at which the pressure pulse reaches the measurement location. For comparison, the exponential pressure pulse given by analytical expressions (Eq. (1)) with the choices p0 = 260 MPa and θ = 0.023 is also included.


Figure 2 shows a detailed view of the specimen and four strain gauged columns used to measure the blast loads transmitted through by the sandwich panel. A quasi-planar shock fronted impacts the face sheet of a test structure at zero obliquity. The strain gauged columns enable the forces transmitted by the test structure to be measured. Their integrated value (over time) gives the impulse transmitted by the structure/explosion combination.

Figure 2: Sketch of the dyno-crusher apparatus with key dimensions marked.


To investigate the effects of core strength, a variety of cellular structures (see Figures 3-6) have been fabricated and tested in the Dynocrusher. Figure 7 shows the compressive stress-stain relations. Figure 8 shows the pressure transmitted by a rigid incompressible (solid) block of aluminum as well as its impulse. Figure 9 shows the change in transmitted pressure when the various core topologies are used to mitigate the same shock wave form. Figure 10 shows the impulse reductions for each topology.

Figure 3: Sketches of the (a) square-honeycomb and (b) triangular honeycomb sandwich


Figure 4: Sketch illustrating the manufacturing route of the triangular honeycomb. (a) The 2 shapes of slotted sheets employed, (b) the slotting together of the constituent elements and (c) the assembled triangular honeycomb core.


Figure 5: Sketch of the multi-layer pyramidal truss sandwich core. The unit cell of the core with all relevant core dimensions mared in mm is also included.


Figure 6: Sketches of the (a) triangular corrugation and (b) diamond corrugation sandwich cores. The unit cells of the core with all relevant core dimensions marked in mm are also included.


Figure 7: Measured quasi-static compressive normal stress versus nominal strain responses of the (a) square and triangular honeycomb cores and (b) the prismatic corrugation and pyramidal truss cores.


Figure 8: The measured temporal variations of the transmitted (a) pressure σ and (b) impulse I for blast loading of a reference solid A1 cylinder. Time t = 0 is defined as the time when the blast wave impinges on the wet face of the cylinder.


Figure 9: The measured temporal variations of the transmitted pressure pt for the five sandwich cores investigated here. (a) square-honeycomb, (b) triangular honeycomb, (c) multi-layer pyramidal truss (d) triangular corrugation and (e) diamond corrugation. Time t = 0 is defined as the time when the blast wave impinges on the wet face of the sandwich panels.


Figure 10: The measured temporal variations of the transmitted impulse I for the five sanwich cores investigated here. (a) square-honeycomb, (b) triangular honeycomb, (c) multi-layer pyramidal truss, (d) triangular corrugation and (e) diamond corrugation. Time t = 0 is defined as the time when the blast wave impinges on the wet face of the sandwich panels.


These experiments as well as others conducted in water shock tubes with collaborators at Cambridge University (UK) and Northwestern University and related simulations have shown that sandwich structures with compressible cellular cores can reduce the reflected shock amplitude, decreasing the impulse transmitted by the structure. They also reveal significant opportunities to reduce the accelerations of substructures protected by these panels. Our group has extended these concepts to edge clamped plates that are centrally (locally) loaded by water propagated shocks and continues to be interested in this and related concepts for impulsive mitigation in water.

Related Publications

Fabrication and Structural Performance of Periodic Cellular Metal Sandwich Structures, H.N.G. Wadley, N.A. Fleck, and A.G. Evans, Composite Science and Technology Special Issue, Composites Science and Technology, 63, p. 2331-2343, 2003.

Multifunctional Periodic Cellular Metals, H.N.G. Wadley, Proc Roy. Soc. A, 364, p.31-68, 2006.

Analysis and Interpretation of a Test for Characterizing the Response of Sandwich Panels to Water Blast, Z. Wei, A.G. Evans, K.P. Dharmasena and H.N.G. Wadley, International Journal of Impact Engineering, 34, p.1602-1618, 2007.

Deformation and Fracture Modes of Sandwich Structures Subjected to Underwater Impulsive Loads, L. F. Mori, S. Lee, Z. Y. Xue, A. Vaziri, D. T. Queheillalt, K. P. Dharmasena, H. N. G. Wadley, J. W. Hutchinson, H. D. Espinosa1, Journal of Mechanics of Materials and Structures, 2 (10), p. 1981-2005, 2007.

The Resistance of Metallic Plates to Localized Impulse, Z. Wei, V.S. Deshpande, A.G. Evans, K.P. Dharmasena, D.T. Queheillalt, H.N.G. Wadley, Y. Murty, R.K. Elzey, P. Dudt, Y. Chen, D. Knight, and K. Kiddy, Journal of Mechanics & Physics in Solids, 56, p. 2074-2091, 2008.

Dynamic Rupture of Polymer-Metal Bilayer Plates, G.J. McShane, C. Stewart, M.T. Aronson, H.N.G. Wadley, N.A. Fleck and V.S. Deshpande, International Journal of Solids and Structures, 45, p. 4407-4426, 2008.

Mechanical Response of Metallic Honeycomb Sandwich Panel Structures to High Intensity Dynamic Loading, K.P. Dharmasena, H.N.G. Wadley, Z. Xue, and J.W. Hutchinson, International Journal of Impact Engineering, 35, p. 1063-1074, 2008.

Compressive Response of Multilayered Pyramidal Lattices During Underwater Shock Loading, H.N.G. Wadley, K. Dharmasena, Yungchia Chen, Philip Dudt, David Knight, Robert Charette, and Kenneth Kiddy, International Journal of Impact Engineering, 35, p. 1102-1114, 2008.

Deformation and Failure Modes of I-Core Sandwich Structures Subjected to Underwater Impulsive Loads, L.F. Mori, D.T. Queheillalt, H.N.G. Wadley, and H.D. Espinosa, Experimental Mechanics, 49(2) Special Issue, p. 257-275, 2009.

Dynamic Response of a Multilayer Prismatic Structure to Impulsive Loads Incident from Water, K.P. Dharmasena, D.T. Queheillalt, H.N.G. Wadley, Y.Chen, P.Dudt, D.Knight, Z. Wei and A.G Evans, Int. J. Impact Engineering, 36, p. 632-643, 2009.

Dynamic Compression of Metallic Sandwich Structures During Planar Impulsive Loading in Water, K.P. Dharmasena, D.T. Queheillalt, H.N.G. Wadley, P. Dudt, Y. Chen, D. Knight, A.G. Evans, V.S. Deshpande, European Journal of Mechanics-A/Solids, 29, p. 56-67, 2010.


Air Shock Loading

Explosions in air create shock fronts that propagate at or above the speed of sound. A schematic shock waveform is show in Figure 1(a). When such a shock impinges upon a rigid structure, it is reflected and exerts a pressure that increases with the incident peak shock pressure. The impulse, I transmitted into the face sheet of a sandwich panel with a weak core, such as the one shown in Figure 1(a), is sensitive to the incident peak pressure (Po) and the mass per unit area of the impacted face sheet (the product of the face sheet density and thickness). Figure 2 from the work of J.H. Hutchinson (Harvard) and R. Radovitzky (MIT) shows that substantial reductions in impulse transfer (relative to a thick rigid structure) are possible for high shock pressures and light (thin) face sheets.

Figure 1. Air shock mitigation by a (compressible)cellular core sandwich panel. (a) Shows the air shock waveform and structure. (b) shows the compressive stress strain response at low and high straining rates. (c) shows that the transmitted force is controlled by the crush strength of the cellular material which can be much less than the incident peak shock pressure.


Figure 2. Hutchinson’s comparison of the reduction in impulse, I transferred to a thin face sheet (normalized by the impulse transferred into a rigid i.e. thick plate) as a function of the fluid structure interaction parameter for air shocks. This parameter depends inversely upon the mass per unit area of the face plate (i.e. the density thickness product of the plate).

The impingement of shock fronts transmitted through air upon sandwich structures with thin faces has been investigated by our group to see if the beneficial FSI can be realized in practice. Figure 3 shows an experimental test arrangement where an explosive cylinder or sphere is detonated in front of a test panel like that shown in Figure 4 with a soft pyramidal lattice core. The response of a stainless steel sandwich panel with thin faces (0.76mm thick) and a soft pyramidal lattice is shown in Figure 5. The low mass of the face sheet combined with inertial stabilization of the pyramidal trusses results in the shock impacted face sheet moving much faster than the rate of core crushing. This leads to local deformation gradients in the face sheet, and for strong shocks, causes the front face to rupture around each core face sheet node on the impacted face. The back face remains intact, but suffers a significant bending (stretching) deformation. The extent of the deflection depends upon the stand-off distance between the charge and test structure, but it is difficult to realize a beneficial FSI effect.

Figure 3. An experimental test set up to create intense air shock loadings of sandwich panel structures).

Figure 4. A typical stainless steel sandwich panel with a pyramidal lattice core and thin faces.

Figure 5. Response of a sandwich panel with 0.76mm thick face sheets.


Figure 6 shows a typical result of the stand-off effect (only a quarter of the panel is shown for a thicker face sheet sandwich panel). The deflections of the back face of the sandwich are about the same as that of a solid plate of the same mass/unit area. Using decoupled finite element simulations, our collaborators at Harvard have quite successfully modeled the deformation of the airshock loaded sandwich structures. A typical result is shown in Figure 7.

Figure 6. Effect of decreasing the standoff distance for sanwich panels with a face sheet thickness of 1.52 mm)


Figure 7. FEM simulations showing the effect of changing the standoff distance (constant face sheet thickness = 1.52 mm)


The relative performance of the sandwich panels compared to equal mass per unit area solid plates has been found to depend upon the panel geometry. For example, Figure 8 shows how an increase of the panel mass per unit area (by increasing face sheet thickness) results in a smaller sandwich panel back face deflection than an equivalent solid plate. The design of a much more massive stainless steel honeycomb core panel is shown in Figure 9. It has much thicker (5mm) faces, and this core is much stronger than the pyramidal lattice. Figure 10 shows what happens when several kg of TNT are detonated a few inches from the panel. Remarkably, the back face is deflected only as half a much as an equal mass solid plate.

Figure 8. A comparison of the deflection at the center of sandwich panels and equal mass per unit solid plates (normalized by the half-span of the plates) verses the mass per unit area of the panels after the same air shock loading. The back face deflection of the sandwich becomes less than that of the solid plate as the faces of the sandwich increase and the panels bending stiffness becomes (much) greater than the solid plate.

Figure 9. A stainless steel honeycomb core sandwich panel. This design has a very strong core and much thicker faces (around 5 mm thick). It therefore has a very high through thickness compression and bending resistance.

Figure 10. Center deflection comparison of square honeycomb panel with equivalent 24” x 24” x 0.5” solid plate. The calculated peak shock pressure and impulse were 365.8 Pa, and 21.5 kPa.s


The results of these experiments can be extrapolated to other testing scenarios using Hopkinson scaling as shown in Figure 11.

Figure 11. Peak pressure and impulse as a function of distance R from an explosion of a mass M of TNT.

Related Publications

Metal Foams: A Design Guide, Authors: Michael F. Ashby, Anthony Evans, Norman A. Fleck, Lorna J. Gibson, John W. Hutchinson, Haydn N.G. Wadley, Butterworth Heinemann, 2000.

Multifunctional Periodic Cellular Materials, H.N.G. Wadley, Proc Roy. Soc. A, 364, p.31-68, 2006.

Inertial Stabilization of Buckling at High Rates of Loading and Low Test Temperatures: Implications for Dynamic Crush Resistance of Aluminum-Alloy-Based Sandwich Plates with Lattice Core, Xin Tang, Vikas Prakash, John J. Lewandowski, Gregory W. Kooistra, Haydn N.G. Wadley, Acta Materialia, 55, p. 2829-2840, 2007.

Mechanical Response of Metallic Honeycomb Sandwich Panel Structures to High Intensity Dynamic Loading, K.P. Dharmasena, H.N.G. Wadley, Z. Xue, and J.W. Hutchinson, International Journal of Impact Engineering, 35, p. 1063-1074, 2008.

An Active Concept for Limiting Injuries Caused by Air Blast, H. N. G. Wadley, K.P. Dharmasena, M. Y. He, R. M. McMeeking, A. G. Evans, T. Bui-Tanh and R. Radovitzky, International Journal of Impact Engineering, 37, p. 317-323, 2010.

Response of Metallic Pyramidal Lattice Core Sandwich Panels to High Intensity Impulsive Loading in Air, K.P Dharmasena, H.N.G. Wadley, K. Williams, Z. Xue, J.W. Hutchinson, International Journal of Impact Engineering, 38, p. 275-289, 2011.


Soil Impact

If an explosion occurs under soil, the conversion of solid explosive to reactant gases causes a rapid build-up of pressure which can then accelerate the surrounding soil. To scientifically study this phenomenon we have used small spherical explosive charges surrounded by annular shells of synthetic sand (200 m diameter silica spheres). A video of one of these events can be viewed at Sand Video. A sequence of images showing the radial motion of the sand is given in Figure 1.

Figure 1: High speed video image sequence of the detonation of a spherical high explosive charge inside an annular shell of water saturated sand.

The sand acquires a significant radial velocity that depends upon the sand shell thickness, the level of water saturation in the sand and the mass of the explosive. Figure 2 shows the radial position of the sand front verses time for dry and water saturated sand. The momentum of a small area element of the sand can be calculated from its mass velocity product integrated through the sand shell thickness. We have used an emerging particle based simulation technique (AFEA Impetus) to numerically analyze experiments of this type. The predicted radial locations of the sand fronts are shown in Figure 2. The slope of these lines is the sand velocity. It is well above the speed of sound in air – its hypersonic sand.

Figure 2: The radial position of a sand front verses time for dry and water saturated sand accelerated by the same charge.

The momentum carried by the sand and the hydrodynamic pressure applied by it can cause significant damage to a structure. A simulated time resolved event is shown in Figure 3 where the target is a stainless steel plate. Severe events can fracture the plate by petalling or by shear-off at the clamps.

Figure 3: Simulations of the interaction of high radial velocity sand with an edge clamped steel plate.

It is interesting to compare the severity of deformation of a plate when loaded by just the bare explosive (an air blast), and by the same charge encased in wet and dry sand. The deformation increases with reduction in distance between the charge and the plate (the stand-off), Figure 4. However, encasing with sand, and especially wet sand can cause much larger deformations, Figure 4. Our group collaborates with colleagues at the University of Cambridge, Harvard University and the Norwegian University of Science and Technology to explore the origins of these effects.

Figure 4: A comparison of the maximum plate deflection for the bare explosive charge and ones encased in dry and water saturated sand.

We have found that sandwich panels with cellular cores usually suffer smaller back side deflections than solid plates of the same mass per unit area. Our colleagues at Cambridge (Fleck/Deshpande) have developed a particle-based model of the soli loading and interfaced it with a finite element code to simulate the deformations of various structures. The calculations agree well with the experiments and reveal that the benefits of sandwich structures come from their higher bending resistance – not a fluid structure interaction (FSI) effect.

FSI effects can be important during sand loading and it is an area of continuing interest to our group. Experiments with aluminum sandwich structures and detailed simulations show that sand particles can be strongly reflected at the gripping locations during a test. Even local dents on a surface increase the local reflection coefficient elevating the locally applied momentum and perpetuating a damage cascade, Figure 6. The angle that the sand impacts the structure has a big effect as well (oblique impacts transfer less momentum).

Figure 5: Comparison between the measurements and predictions of the deflected profiles of the (a) monolithic and (b) sandwich panels subjected to wet and explosions at a stand-off of 20 cm.  These photographs show the mid-span section of the plates.

Related Publications

Dynamic Compression of Foam Supported Plates Impacted by High Velocity Soil, T. Liu, H.N.G. Wadley, V.S. Deshpande, International Journal of Impact Engineering, 63, p. 88-105, 2014.

Constitutive Model for Predicting Dynamic Interactions Between Soil Ejecta and Structural Panels, V.S. Deshpande, R.M. McMeeking, H.N.G. Wadley and A.G. Evans, Journal of Mechanics and Physics of Solids , 57, p. 1139-1164, 2009.

A Discrete Particle Approach to Simulate the Combined Effect of Blast and Sand Impact Loading of Steel Plates, T. Borvik, L. Olovsson, A.G. Hanssen, K.P. Dharmasena, H. Hannson, H.N.G. Wadley, Journal of the Mechanics and Physics of Solids, 59, 940-958, 2011.

Wet-sand Impulse Loading of Metallic Plates and Corrugated Core Sandwich Panels, J.J. Rimoli, B. Talamini, J.J. Wetzel, K.P. Dharmasena, R. Radovitzky, H.N.G. Wadley, International Journal of Impact Engineering, 38, p. 837-848, 2011.

Discrete Element Calculations of the Impact of a Sand Column Against Rigid Structures, S.M. Pingle, N.A. Fleck, H.N.G. Wadley, V.S. Desphande, International Journal of Impact Engineering, 45, p. 74-89, 2011.