Classifications

• • A—HUMAN NECESSITIES
  • A42—HEADWEAR
  • A42B—HATS; HEAD COVERINGS
  • A42B3/00—Helmets; Helmet covers ; Other protective head coverings
  • A42B3/04—Parts, details or accessories of helmets
  • A42B3/10—Linings
  • A42B3/12—Cushioning devices
  • A42B3/124—Cushioning devices with at least one corrugated or ribbed layer
• • A—HUMAN NECESSITIES
  • A42—HEADWEAR
  • A42B—HATS; HEAD COVERINGS
  • A42B3/00—Helmets; Helmet covers ; Other protective head coverings
  • A42B3/04—Parts, details or accessories of helmets
  • A42B3/10—Linings
  • A42B3/12—Cushioning devices
• • A—HUMAN NECESSITIES
  • A42—HEADWEAR
  • A42B—HATS; HEAD COVERINGS
  • A42B3/00—Helmets; Helmet covers ; Other protective head coverings
  • A42B3/04—Parts, details or accessories of helmets
  • A42B3/28—Ventilating arrangements
  • A42B3/281—Air ducting systems
  • A42B3/283—Air inlets or outlets, with or without closure shutters

Definitions

• the present invention relates to an impact absorbing structure. More particularly, the present invention relates to a hollow-cell impact absorbing structure. Even more particularly, the present invention relates to an impact absorbing structure formed as a stretch-dominated hollow-cell structure. The present invention also relates to impact absorbing structures where the impact surface is curved, such as a sports helmet or aerospace nose bumpers, at least part of the structure formed from a hollow-cell impact absorbing structure, and even more particularly a stretch-dominated hollow-cell impact absorbing structure
• TBI severe traumatic brain injury
• head injury is participation in sports. For example, a fall from a bicycle when riding may result in the head striking against a solid unyielding object or surface such as a road surface or similar.
• helmet usage is customary or mandatory in many sports such as bicycle, motorcycle and horse riding, rock climbing, American football and also winter or ice sports such as skating, ice hockey, and skiing.
• Another common cause of head injury is an impact caused by a falling object on a building or construction site.
• Sports helmets and safety helmets are individually designed so as to be particularly suited to their particular use.
• most or all of the helmets have common design elements such as a hard outer shell (formed from a stiff thermoplastic or composite) and a lining/liner, softer than the outer shell, but still stiff enough to retain it's shape when unsupported.
• the shell and liner act to absorb the force of an impact and to help prevent this force being transmitted to the head and brain.
• Virtually all helmets use expanded polystyrene as the energy absorbing liner.
• the expanded polystyrene is formed as a unitary structure (that is, without gaps) in the required shape.
• US3,447,163 describes and shows a safety or crash helmet intended for use by motorcyclists and/or racing motorists.
• the helmet has an outer shell formed as a double- skinned member, the two skins of the shell joined to one another around the periphery of the shell by a gently curved peripheral portion that has no sharp edges, and the space between the skins contains a layer of a honeycomb type of material, the cells of the honeycomb layer filled with an energy-absorbing foamed material.
• US7,089,602 describes and shows an impact absorbing, modular helmet having layers on the outer side of a hard casing that increase the time of impact with the intention of reducing the intensity of the impact forces.
• the layers are made up of a uniformly consistent impact absorbing polymer material, a polymer layer filled with air or a polymer structure. These impact-absorbing layers can also be made and used as an
• US6,247,186 describes and shows a helmet having a housing, an inner impact resistant layer shaped to the head of rider, a protective covering spaced above and formed integrally with the housing, and a chamber enclosed by the housing and protective covering that is open in the front for ventilation.
• the chamber has a net strap in the front side for preventing foreign objects from entering and one or more inner channels in communication with the inner space of helmet through a passageway. In use, fresh air flows through the passageway and into the impact resistant layer.
• Sports helmets and safety helmets often have to be worn for extended periods, and the weight of the helmet is an important design consideration.
• the overall weight (and shape and size) of the helmet and the impact-absorbing properties.
• Increasing the amount of impact-absorbing material will increase the overall weight of the helmet, and may also result in an increase in the external dimensions, which can in turn make wearing the helmet relatively more unwieldy and uncomfortable to wear, especially where aerodynamic considerations may also be important.
• impact protection can be compromised if the helmet has too little impact-absorbing material.
• Foams such as the foams used in helmets are typically excellent energy absorbers because they are characterised by a long plateau stress, and in most impacts the area is constant so the stress can be directly converted to force, providing a long plateau force. This means all the energy can be absorbed whilst maintaining a low peak force and acceleration, optimal in reducing brain damage. However, in an oval shape helmet, the area when crushing is not constant.
• other external documents, or other sources of information this is generally for the purpose of providing a context for discussing the features of the invention. Unless specifically stated otherwise, reference to such external documents is not to be construed as an admission that such documents, or such sources of information, in any jurisdiction, are prior art, or form part of the common general knowledge in the art.
• the present invention may broadly be said to consist in an impact absorbing structure, comprising a unitary material formed as a stretch-dominated hollow cell structure.
• substantially all the cells of the hollow cell structure are 2D hollow- cells.
• substantially all the cells are aligned substantially out of plane.
• the cells are formed as a micro-truss lattice.
• the cells are formed as a crystal lattice structure. In an embodiment, at least a plurality of the cells are configured to tessellate.
• At least a plurality of the cells are configured to tessellate with a cell axis normal to the surface or out-of-plane.
• At least a plurality of the cells are hexagonal.
• At least a plurality of the cells are triangular.
• At least a plurality of the cells are square.
• At least a plurality of the cells are a combination of octagons and squares co-located in a tessellating pattern.
• the unitary material is formed to have a relative density substantially between 0.05 and 0.15.
• the cell shape, size, cell wall thickness, cell width and cell length can be freely varied relative to one another.
• the ratio of cell wall thickness to cell length is significantly small.
• the wall has a maximum thickness of substantially 1 mm.
• the unitary material is a polymer material.
• the unitary material is an elastomer.
• the unitary material is elastic-plastic and elastic-brittle.
• the unitary material is Nylon 1 1.
• the unitary material is ST Elastomer.
• the hollow cell structure is manufactured by Laser Sintering.
• the present invention may broadly be said to consist in a helmet, comprising an inner impact resistant liner at least partly formed form an impact absorbing structure as claimed in any one of the preceding statements.
• the helmet further comprises an outer shell formed to substantially cover the inner impact resistant liner.
• the outer shell is at least partly formed from a composite material.
• the outer shell is at least partly formed from a thermoplastic material.
• At least one vent slot is formed in the outer shell.
• the invention may broadly be said to consist in a method of optimising an impact absorbing structure for improved impact absorption, comprising the steps of: (i) choosing a material;
• substantially all the cells of the hollow cell structure are formed as 2D hollow-cells.
• substantially all the cells are formed so as to be aligned substantially out of plane.
• the cells are formed as a micro-truss lattice.
• the cells are formed as a crystal lattice structure.
• At least a plurality of the cells are formed so as to tessellate.
• At least a plurality of the cells are formed so as to tessellate with a cell axis normal to the surface or out-of-plane.
• the hollow cells are formed to have a topology that propagates radially to a curved surface.
• At least a plurality of the cells are formed as hexagons.
• At least a plurality of the cells are formed as triangles.
• At least a plurality of the cells are formed as squares.
• At least a plurality of the cells are formed as a combination of octagons and squares co-located in a tessellating pattern.
• the material is formed in such a manner that the material has a relative density substantially between 0.05 and 0.15.
• the cells are formed so that the cell shape, size, cell wall thickness, cell width and cell length can be freely varied relative to one another.
• the cells are formed so that the ratio of cell wall thickness to cell length is significantly small.
• the cells are formed so that the wall has a maximum thickness of substantially 1 mm.
• the unitary material is a polymer material.
• the unitary material is an elastomer.
• the unitary material is elastic-plastic and elastic-brittle. In an embodiment of the method, the unitary material is Nylon 11 .
• the unitary material is ST Elastomer.
• the hollow cell structure is manufactured by Laser Sintering.
• This invention may also be said broadly to consist in the parts, elements and features referred to or indicated in the specification of the application, individually or collectively, and any or all combinations of any two or more said parts, elements or features, and where specific integers are mentioned herein which have known equivalents in the art to which this invention relates, such known equivalents are deemed to be incorporated herein as if individually set forth.
• Figures 1a - c show schematic views of single cells that form part of a cellular solid, showing the joints j and struts s which the cell shares with adjoining cells, the struts s forming surrounding faces that enclose the cells, figure 1 a showing a bending-dominated structure where the joints are locked and the frame bends as the structure is loaded, stretch-dominated structures shown in figures 1b and 1c where the members carry tension or compression when loaded, giving higher modulus and strength.
• Figures 2a and 2b show plots summarising the difference between stretch and bending-dominated structures in terms of relative modulus E/E s and relative strength ⁇ / ⁇ 3 against relative density p/p s .
• Figure 3 shows a perspective view from above, looking downwards and sideways, of a honeycomb hollow cell structure according to an embodiment of the present invention.
• Figure 4 shows a top view from directly above of the hollow cell structure of figure 3.
• Figure 5 shows a section of a periodic lattice of hexagonal cells, showing the positions of the joints /and struts sfor this stretch dominated structure
• Figure 6 shows a perspective view from one side of an inner impact resistant liner of a cycle helmet, the inner impact resistant liner formed from a hollow cell structure similar to that shown in figures 3, 4, and 5, the liner shaped to follow and substantially conform to the top portion of a user's head.
• Figure 7 shows a perspective view directly from the rear of the inner impact resistant liner of figure 3, with an outer shell covering the inner impact resistant liner, vent slots formed in the outer shell to allow air to circulate within the inner impact resistant liner.
• Figure 8 shows a perspective schematic view from the front and to one side of a test rig used to test samples of a hollow cell structure.
• Figure 9 is a graph showing the Head Injury Criterion (HIC) and peak acceleration for a range of test samples.
• HIC Head Injury Criterion
• Figures 10 to 12 show test samples of honeycomb hollow cell structure according to embodiments of the present invention post-testing, each sample having a different relative density, figure 10 showing brittle failure at a relative density of 0.111 , figure 11 showing plastic work at a relative density of 0.143, and figure 12 showing linear elastic deformation at a relative density of 0.25.
• Figure 13 shows a graphical plot of energy per volume vs peak acceleration for a range of test materials and conditions.
• Figure 14 shows graphical plots of acceleration vs time and force vs displacement for test pieces formed from Nylon 11 , Elasto and EPS
• the liner foam is entirely responsible for dissipating the impact energy.
• the reaction force is determined by the compressive strength of the foam.
• a foam lattice is assumed to have a flat plateau compressive strength over its densification strain.
• the foam only provides an ideal force- displacement curve if the compressed region is uniform in area.
• the impact area or crush area is not constant, or planar: the contact area increases with displacement. This causes the reaction force to also increase.
• the force-displacement gradient will be further reduced.
• a foam liner needs to be thicker in order to provide adequate energy absorption by maintaining the peak acceleration below the safety legislation.
• the consistent plateau stress of foam limits it's effectiveness as an energy absorbing structure when used as a curved structure (such as for example in a helmet) due to the inherent curved contact surface.
• the other assumption is that the liner is formed as a unitary structure (that is, without gaps).
• a structure that has a stiffness and strength higher than would otherwise be the case if creating the structure as a unitary structure formed from e.g. foam, for a given relative density p/p s (where p is the density of the foam and p s that of the bulk material), and this allows more energy to be dissipated per volume. It is also possible to create a structure that provides an initially high strength when the contact area is very low and which has a gradual post-yield softening proportional to the increase in contact area.
• the impact-absorbing structure is formed as a hollow-cell structure which is stretch-dominated, such as for example a micro-truss lattice or out-of-plane honeycomb.
• ⁇ d densification strain
• the post-yield softening counteracts the area increase of a oval shaped helmet dissipating energy at a more uniform plateau force.
• the relative density of a stretch-dominated structure can be much lower providing a greater densification strain and therefore increasing the potential energy dissipated over the same displacement.
• stretch-dominated structure is a cellular solid.
• a cellular solid is one made up of an interconnected network of solid struts or plates that form the edges and faces of cells.
• the mechanical behaviour of cellular solids can be distinguished by bending-(foam) and stretch-(lattice) dominated mechanisms.
• the Maxwell stability criterion is used to distinguish between bending- and stretch -dominated structures.
• Cellular solids can be thought of as joints /, joined by struts s, which surround faces that enclose cells, as shown in figure 1.
• stretch-dominated structures as impact absorbing structures are as follows: firstly, the post-yield softening counteracts the area increase of a oval shaped helmet dissipating energy at a more uniform plateau force, and;
• the impact absorbing structure is formed as a lattice - i.e. from interconnected hollow cells.
• a periodic lattice i.e. the cells are regularly shaped and sized. Hexagonal cells were used as this shape has the largest number of side and which will still regularly tessellate - i.e. without requiring a second shape to fill gaps (for example, if a regular octagon lattice was chosen, a regular square shape would be inherent). Hexagonal honeycomb cells have the highest number of cell walls for each cell, and therefore the lowest connectivity, which has been shown to be effective in high specific strength.
• lattice structure described above can be generally described as 2D hollow cell structures. Where these are referred to in this specification, this indicates a three- dimensional structure, with the cells of the structure formed in such a way as to have depth, but so that when viewed at a certain angle the cells will have a uniform or identical cross-section at any position perpendicular to the view angle. That is, a cross section taken at any position would be identical to one taken at any other position.
• a honeycomb cell structure viewed in plan or from directly above will provide a uniform cross-section at any depth through the cells. This can be translated to curved shapes such as the ovoid shape necessary to form a helmet, for example. When viewed at any particular point looking inwards towards the centre of the interior, the cells will appear identical to those viewed from another point also looking inwards towards the centre of the interior.
• stretch dominated structures will also provide the same advantages.
• 3-D stretch-dominated structures such as a truss structure or a structure similar to a crystal lattice structure can also be formed, which will provide the same impact absorption benefits.
• the hollow cell stretch dominated structure 1 used in a first embodiment of the present invention is a unitary material formed into a honeycomb structure. It is preferred that the cells are hexagonal, as hexagonal cells 2 such as those used in the hollow cell structure 1 tessellate and so form a structure where each cell wall is common with an adjacent cell.
• a grid formed from hexagonal cells also provides a balance between overall grid density (the total amount of material), and the
• Hexagonal honeycomb can be thought of as a stretch dominated structure by applying the Maxwell criterion:
• Figure 4 shows a section of a periodic lattice of hexagonal cells, showing the positions of the joints / and struts s for this stretch-dominated structure.
• the honeycomb structure In practical use, and when experiencing an impact, the honeycomb structure will experience both in-plane and out-of-plane loading.
• Stretch-dominated structures such as the hexagonal hollow cell structure 1 are generally used in a planar or sheet form, either flat or curved, and the impacts received by the hollow cell structure have a primary force component directed into the plane perpendicular to the point of impact. That is, in the opposite direction to out-of-plane arrow 3 in figure 1.
• the forces received by the hollow cell structure have a primary force component directed into the plane perpendicular to the point of impact. That is, in the opposite direction to out-of-plane arrow 3 in figure 1.
• the theory behind this is discussed in detail in Appendix C.
• the impact absorption properties of a stretch-dominated structure such as the hollow cell structure 1 are determined by the material used to form the structure, and the specific geometry of the structure: i.e. cell size, cell wall thickness, cell width and cell length as shown in figure 4.
• the lattice is designed so that the axial part of the cell is always perpendicular to the surface of the head. This is important as the crush strength of honeycomb significantly diminishes as the impact angle increases away from perpendicular to the axial part of the cell.
• h is assigned a value of 1
• ⁇ has a value of 30 (degrees)
• the ratio of cell wall thickness (f) to cell length (/) is significantly small.
• the material used to create the hollow cell structure 1 in this embodiment is Nylon 11 and ST
• Elastomer This is a readily available material, which is lightweight, easily formed and malleable, and is therefore suitable or at least analogous to the type of material that would be used for mass-manufactured helmets.
• the hollow cell structure 1 was manufactured by additive manufacturing. The process is briefly described in Appendix B. Tests were carried out as detailed in Appendix A, and Appendix D, with the objective of determining how varying the relative density of the honeycomb hollow cell structure 1 (this type of structure also known as 'out-of-plane honeycomb') would affect the hollow cell structure 1 when subjected to impact testing. As shown in Appendix A, the relative density was varied between 0.1 and 0.33 by changing the cell size (s) from between a minimum of 6mm and a maximum of 20mm, with the wall thickness maintained at a constant 1 mm.
• results indicate that an acceptable range of optimum relative densities lies between 0.125 and 0.175 for this material and for the particular cell/lattice size and shape used during testing, for the reasons outlined in the 'Results from Impact Testing' section of Appendix A, and Appendix D.
• the results indicate that the cell size, cell wall thickness, cell width and cell length can be freely varied relative to one another, and as long as the relative density lies between 0.03 and 0.17, then the structure will provide optimised impact absorption properties.
• helmet design is generally a trade-off between the overall weight of a helmet, and the impact-absorbing properties.
• a helmet such as helmet 5 shown in figures 3 and 4, constructed using a structure the same as or similar to the inner impact resistant liner 7 (formed as a hexagonal hollow-cell stretch-dominated structure) covered by an outer shell 6, formed from nylon 12 or a similar material, will provide a lightweight structure capable of meeting and exceeding the relevant standards for impact absorption, in particular BS EN 1078.
• the test results indicate the elastic- plastic honeycomb has a 3x greater EPV than a typical expanded polystyrene helmet. This is clearly shown by the plots of the experimental results shown in figures 13 and 14. The reasons can be summarised as follows:
• Stretch dominated structures have higher specific strength for the same relative density, so it is possible to increase the densification strain, as the relative density is lower in a stretch dominated structure.
• an impact-absorbing structure can be formed from any appropriate material and at any shape and size (e.g. all honeycomb topology and materials), and will still provide the advantages as outlined above.
• 2D hollow cells are referred to in this specification, this indicates a three-dimensional structure, with the cells of the structure formed in such a way as to have depth, but so that when viewed at a certain angle the cells will have a uniform or identical cross-section at any position perpendicular to the view angle. That is, a cross section taken at any position would be identical to one taken at any other position.
• a honeycomb cell structure viewed in plan or from directly above will provide a uniform cross-section at any depth through the cells.
• a range of hollow cell structures were manufactured from nylon 12 by Selective Laser Sintering. Each sample had a cross-sectional area of 100cm 2 , and a depth of 10cm.
• a single axis accelerometer was placed in the head form, at the Centre of Mass.
• the sampling rate was set to 1000Hz in LabView.
• HIC Head Injury Criterion
• a kerbstone shape was used as the impacting projectile in a drop weight system.
• the geometric parameters of the honeycomb was varied in each impact: cell width, cell wall thickness, cell height and cell liner.
• Each honeycomb sample had a constant cross sectional area of 100 mmx100 mm, and was placed so the cell walls were always axial to the z direction shown in the test rig schematic.
• Polycarbonate sheets of 0.375 mm, 0.5 mm, 1 mm and 2 mm thickness were laid on top of the sample to represent the shell.
• a helmet was sectioned into nine parts, each having a surface area approximately the same as the honeycomb structures. As the EPS sections were not flat, a hard Polyfiller was moulded to provide a curved support.
• the impact speed for the kerbstone anvil is 4.57 ⁇ 0.1 ms- 1 with a mass of 5 kg.
• a drop tower was used to replicate the 1078 standard shock absorption test.
• High speed photography at 2000 frames per second was used to trace the impact of the anvil and film the response of the honeycomb structure.
• the high speed camera was triggered using a light gauge 15 mm before impact.
• the impactor anvil was connected to a rod that is suspended in a rigid cage, ensuring that it can only travel in the z axis. When the anvil and rod impact, the rigid cage continues to move freely until contact is made with dampers.
• head injury criterion is a measurement of magnitude and duration of deceleration, above 750 - 1000 s-g 25 represents a 16% risk of severe injury.
• the table below represents the 'best' structures s found by testing different material samples.
• the table above lists the HIC values for EPS foam, Elastomer honeycomb and elastic- plastic (PA1 1 ) honeycomb for 2, 5 and 10 ms. The three variations showed an unusually low HIC value with PA1 1 delivering the lowest HIC value at 44. A higher HIC value is predicted when the helmet is conditioned to +50 °C and -20 °C given in the safety legislation. The relationship between magnitude of acceleration and duration has been shown to be significant in causing brain damage.
• WSTC Tolerance curve
• the Energy absorbed Per Volume is the amount of kinetic energy lost from the projectile across the maximum displaced volume of the structure, this was measured using digital image correlation. At a higher EPV, the structure dissipates or stores more kinetic energy over the same volume. This is also equivalent to the integral of the stress-strain curve used by Gibson and Ashby to create a continuous energy absorption diagram.
• the optimal peak acceleration is more than 60% lower, highlighting the suitability of this type of structure and material for a helmet, ft is clear that above 0.15 relative density the elastic-plastic (Nylon 11 ) honeycomb structure was too stiff and responded with extremely high peak accelerations, for example at 0.33 density, a peak acceleration of 650 g was obtained. However, at around 0.1 density (in blue) the peak acceleration was similar to EPS but with a three times greater EPV. The response of Nylon 11 honeycomb was both plastic buckling and fracturing of the cell walls.
• Laser sintered PA 12 showed both strain rate and temperature dependence, confirming that the polymer was amorphous. Above energy density 0.37 J/mm2 the mechanical properties worsened at low, medium and high strain rate. /3 transition could be found at approximately 1000 s- 1 and -50° C, between the T g and /3 there is a natural temperature dependence.
• Elastomer and elastic-plastic material was produced as a honeycomb through Additive Manufacturing as outlined in Appendix B.
• the structure was impacted in the out-of-plane under safety legislation impact conditions and compared with sections of expanded polystyrene cut from a bicycle helmet.
• the elastomer honeycomb showed elastic buckling deformation, whilst the elastic-plastic honeycomb saw plastic buckling through localised plastic hinges and fracture of the cell wall.
• the elastomer honeycomb and EPS foam showed very similar force-displacement curves, where force is proportional to displacement.
• the elastic-plastic honeycomb attained a higher initial force that was maintained across the sample, which meant that the impact energy was dissipated at a lower peak load over a shorter duration.
• Additive Manufacturing provides a fast process for creating complex geometries that would be impossible or highly expensive compared to conventional subtractive/formative methods.
• Additive Manufacturing works by directly building computer aided designs by depositing material in a layer by layer process.
• Laser Sintering is a form of Additive Manufacturing whereby a thin layer of powder is deposited onto a preheated build area, a CO2 laser is then used to selectively consolidate the powder.
• Laser Sintering was chosen as the process to manufacture the hexagon structures because of the comparatively higher mechanical properties.
• Laser Sintering is still a relatively young manufacturing technique and requires a specific thermal window to consolidate, so only a selection of materials were available.
• the microstructure can be varied by using a range of different processing conditions.
• the mechanical properties of Laser Sintering can in part be attributed to the degree of particle melt (DPM), which defines the quantity variations in the consolidation of sintering.
• DPM degree of particle melt
• the cell walls In compression the cell walls initially compress axially, so that the Young's modulus varies linearly with the relative density and the Poisson's ratio is that of the solid. In elastomeric material the cell walls will buckle, once the elastomer is unloaded the honeycomb recover the buckling (typically there is a hysteresis effect as energy is loss through heat).
• Ductile materials have a yield point, after which permanent deformation occurs through localised plastic hinges (buckling of cell wall). Ceramic material typically fail through fracture of cell walls.
• honeycomb material used to gather the test results was a laser sintered viscoelastic polyamide and elastomer.
• the plasticity and fracture of polymers is dependent on temperature and strain rate. At lower temperatures polymers are linear-elastic to
• the elastic buckling load is determined from Euler's buckling of columns formula
• K is an end constraint factor, typically equal to 4. If the cell height is large compared with I (> 31), then K is independent of the cell height. Walls with single thickness t will maintain the same load after they reach their initial collapse load P C rit,the total collapse load is 6P C nt divided by the load bearing cross sectional area: where ⁇ e ⁇ is the elastic buckling stress, 5.2 is the value found from the cell geometry of regular honeycomb where v 5 is assumed to be 0.3.
• Wierzbicki found that in compression the lowest plastic collapse strength (and so most likely to occur) is due to plastic buckling. Plastic buckling dissipates energy by a permanent rotation of the cell wall. Wierzbicki derived an approximation based on an isolated cell wall. The plastic collapse stress for regular hexagons with uniform wall thickness t is where o> s is the yield stress.
• the failure mechanism is elastic buckling and so most of the energy is stored elastically.
• the energy is stored elastically up to the yield point, after which energy is then dissipated through plastic bending or fracture of cell walls.
• W dissipated or stored
• the amount of energy absorbed W increases with little change in peak stress ⁇ ⁇ .
• the peak stress rises drastically with little change in W.
• Optimal use of the foam's energy absorbing capabilities is achieved by exploiting the shoulder of this curve, i.e: absorb as much energy as possible for a given peak stress.
• the envelope of shoulders for different foam densities is plotted in graph (b). The envelope describes a relationship between W and ⁇ ⁇ to pick the optimum relative density, at a particular strain rate and temperature.
• Modelling of the energy-absorbing diagrams can be applied for both elastomer and elastic- plastic materials where the linear elastic region is very small.
• the modelling process is identical between elastomer and elastic-plastic material, the final equation is in the form
• oD is the densification stress, which for a bending-dominated structure is assumed to be at the same level as the plateau stress.
• tV/naxis the maximum energy that can be absorbed. The equation developed above show that depends only on and , that is the diagram describes all elastomeric foams of all densities and material
• honeycomb material The response of a honeycomb material is critical if used for energy absorbing
• SHPB Hopkinson Pressure Bar
• the input and output bars were made of silver steel.
• the input bar is 1 m long, and gauged halfway along its length; the output bar was 500 mm long and gauged 50 mm from the bar-specimen interface. Reflected and transmitted gauge signals were used to derive the stress-strain relationship using the standard analysis. Petroleum jelly was used as the lubricant.
• nitrogen gas and heated filaments were used to obtain the necessary chamber temperature. Each sample was pre heated/cooled for between 5-10 minutes at the testing temperature to ensure thermal equilibrium.
• the high energy density samples were found to have a coarse surface area, showing large surface porosity. This porosity is likely to weaken the material since there is a lower volume fraction of solid.
• a stretch-dominated structure is a micro-truss lattice or out-of-plane honeycomb, where the mechanism of deformation involves 'hard' modes such as compression and tension rather than bending .
• the graph below shows a stress-strain curve of a stretch dominated structure with an elastic-plastic material. Yield stress occurs due to localised plastic buckling and brittle collapse of the struts. This is also known as the bifurcation point because the structure becomes unstable and a post yield softening regime ensues.
• the stress rises steeply at the densification strain which can be calculated from the following equation.
• the post-yield softening counteracts the area increase of the oval shaped helmet dissipating energy at a more uniform plateau force.
• line x in the graph below is the post yield softening seen in the experimental results, whereas line y shows the area increase of a particular head shape.
• the relative density of a stretch-dominated structure can be much lower. According to the equation below, the densification strain is inversely proportional relative density
• p is the density of the structure and p s that of the bulk material, and where is the relative density (or volume fraction solid) at which the structure locks up,
• stretch dominated structures require a lower relative density, and according to the equation above attain a greater densification strain. Because the amount of energy absorbed is the product of stress and strain, increasing strain would mean increasing the amount of energy absorbed (essentially stretch dominated structures require less material and so have longer displacement before the cell walls densify increasing potential energy absorbed.)

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