Patent Publication Number: US-2018027914-A1

Title: An impact absorbing structure and a helmet comprising such a structure

Description:
FIELD 
     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. 
     BACKGROUND 
     Injury to a person or damage to an object can occur when the person or object is subjected to an impact of sufficient force. Considerable developmental effort has been expended in order to produce materials and structures that provide protection from potentially damaging or injurious impacts. 
     Impact protection is particularly important for preventing head injury. A blow to the head can result in severe traumatic brain injury (TBI). It is common for brain trauma to occur as a consequence of either a focal impact upon the head, or by a sudden acceleration/deceleration within the cranium, or from a combination of both impact and movement. Traumatic brain injury can cause long-term issues, and there are limited treatment options. 
     One of the most common causes of 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. In order to help prevent injury, 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. However, 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&#39;s shape when unsupported. In combination, 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. 
     U.S. Pat. No. 3,447,163 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. 
     U.S. Pat. No. 7,089,602 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 independent, detachable, external protective cover that can be attached over a hard casing helmet. 
     U.S. Pat. No. 6,247,186 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. When designing a helmet, there will generally be a trade-off between 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. Conversely, 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. 
     In this specification where reference has been made to patent specifications, 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. 
     SUMMARY 
     It is an object of the present invention to provide a range of optimised impact absorbing structures for improved impact absorption, or which at least provide the public or industry with a useful choice. It is a further object of the invention to provide a range of optimised impact absorbing structures that can be used to reduce traumatic brain injury by reducing peak acceleration and force to the brain and directing energy away from vulnerable areas of the brain, or which at least provide the public or industry with a useful choice. It is a yet still further object of the invention to provide a helmet at least partly formed from an optimised impact absorbing structure that assists with reducing traumatic brain injury by reducing peak acceleration and force to the brain and directing energy away from vulnerable areas of the brain, or which at least provides the public or industry with a useful choice. It is a yet still further object of the present invention to provide a method of optimising an impact absorbing structure for improved impact absorption. 
     The term “comprising” as used in this specification and indicative independent claims means “consisting at least in part of”, and is intended as an inclusive rather than exclusive term. When interpreting each statement in this specification and indicative independent claims that includes the term “comprising”, features other than that or those prefaced by the term may also be present. Related terms such as “comprise” and “comprises” are to be interpreted in the same manner. 
     As used herein the term “and/or” means “and” or “or”, or both. 
     As used herein “(s)” following a noun means the plural and/or singular forms of the noun. 
     Accordingly, in a first aspect 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. 
     In an embodiment, substantially all the cells of the hollow cell structure are 2D hollow-cells. 
     In an embodiment, substantially all the cells are aligned substantially out of plane. 
     In an embodiment, the cells are formed as a micro-truss lattice. 
     In an embodiment, the cells are formed as a crystal lattice structure. 
     In an embodiment, at least a plurality of the cells are configured to tessellate. 
     In an embodiment, at least a plurality of the cells are configured to tessellate with a cell axis normal to the surface or out-of-plane. 
     In an embodiment, at least a plurality of the cells are hexagonal. 
     In an embodiment, at least a plurality of the cells are triangular. 
     In an embodiment, at least a plurality of the cells are square. 
     In an embodiment, at least a plurality of the cells are a combination of octagons and squares co-located in a tessellating pattern. 
     In an embodiment, the unitary material is formed to have a relative density substantially between 0.05 and 0.15. 
     In an embodiment, the cell shape, size, cell wall thickness, cell width and cell length can be freely varied relative to one another. 
     In an embodiment, the ratio of cell wall thickness to cell length is significantly small. 
     In an embodiment, the wall has a maximum thickness of substantially 1 mm. 
     In an embodiment, the unitary material is a polymer material. 
     In an embodiment, the unitary material is an elastomer. 
     In an embodiment, the unitary material is elastic-plastic and elastic-brittle. 
     In an embodiment, the unitary material is Nylon 11. 
     In an embodiment, the unitary material is ST Elastomer. 
     In an embodiment, the hollow cell structure is manufactured by Laser Sintering. 
     In a second aspect, 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. 
     In an embodiment, the helmet further comprises an outer shell formed to substantially cover the inner impact resistant liner. 
     In an embodiment, the outer shell is at least partly formed from a composite material. 
     In an embodiment, the outer shell is at least partly formed from a thermoplastic material. 
     In an embodiment, at least one vent slot is formed in the outer shell. 
     In a third aspect, 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;   (ii) forming the material into a stretch-dominated hollow cell structure.       

     In an embodiment of the method, substantially all the cells of the hollow cell structure are formed as 2D hollow-cells. 
     In an embodiment of the method, substantially all the cells are formed so as to be aligned substantially out of plane. 
     In an embodiment of the method, the cells are formed as a micro-truss lattice. 
     In an embodiment of the method, the cells are formed as a crystal lattice structure. 
     In an embodiment of the method, at least a plurality of the cells are formed so as to tessellate. 
     In an embodiment of the method, 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. 
     In an embodiment of the method, the hollow cells are formed to have a topology that propagates radially to a curved surface. 
     In an embodiment of the method, at least a plurality of the cells are formed as hexagons. 
     In an embodiment of the method, at least a plurality of the cells are formed as triangles. 
     In an embodiment of the method, at least a plurality of the cells are formed as squares. 
     In an embodiment of the method, at least a plurality of the cells are formed as a combination of octagons and squares co-located in a tessellating pattern. 
     In an embodiment of the method, the material is formed in such a manner that the material has a relative density substantially between 0.05 and 0.15. 
     In an embodiment of the method, 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. 
     In an embodiment of the method, the cells are formed so that the ratio of cell wall thickness to cell length is significantly small. 
     In an embodiment of the method, the cells are formed so that the wall has a maximum thickness of substantially 1 mm. 
     In an embodiment of the method, the unitary material is a polymer material. 
     In an embodiment of the method, the unitary material is an elastomer. 
     In an embodiment of the method, the unitary material is elastic-plastic and elastic-brittle. 
     In an embodiment of the method, the unitary material is Nylon 11. 
     In an embodiment of the method, the unitary material is ST Elastomer. 
     In an embodiment of the method, the hollow cell structure is manufactured by Laser Sintering. 
     With respect to the above description then, it is to be realised that the optimum dimensional relationships for the parts of the invention, to include variations in size, materials, shape, form, function and manner of operation, assembly and use, are deemed readily apparent and obvious to one skilled in the art, and all equivalent relationships to those illustrated in the drawings and described in the specification are intended to be encompassed by the present invention. 
     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. 
     Therefore, the foregoing is considered as illustrative only of the principles of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Further aspects of the invention will become apparent from the following description which is given by way of example only and with reference to the accompanying drawings which show an embodiment of the device by way of example, and in which: 
         FIGS. 1 a - 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,  FIG. 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  FIGS. 1 b  and 1 c    where the members carry tension or compression when loaded, giving higher modulus and strength. 
         FIGS. 2 a  and 2 b    show plots summarising the difference between stretch and bending-dominated structures in terms of relative modulus E/E s  and relative strength σ/σ s  against relative density p/p s . 
         FIG. 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. 
         FIG. 4  shows a top view from directly above of the hollow cell structure of  FIG. 3 . 
         FIG. 5  shows a section of a periodic lattice of hexagonal cells, showing the positions of the joints j and struts s for this stretch dominated structure. 
         FIG. 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  FIGS. 3, 4, and 5 , the liner shaped to follow and substantially conform to the top portion of a user&#39;s head. 
         FIG. 7  shows a perspective view directly from the rear of the inner impact resistant liner of  FIG. 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. 
         FIG. 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. 
         FIG. 9  is a graph showing the Head Injury Criterion (HIC) and peak acceleration for a range of test samples. 
         FIGS. 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,  FIG. 10  showing brittle failure at a relative density of 0.111,  FIG. 11  showing plastic work at a relative density of 0.143, and  FIG. 12  showing linear elastic deformation at a relative density of 0.25. 
         FIG. 13  shows a graphical plot of energy per volume vs peak acceleration for a range of test materials and conditions. 
         FIG. 14  shows graphical plots of acceleration vs time and force vs displacement for test pieces formed from Nylon 11, Elasto and EPS. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present invention will now be described with reference to the figures. As outlined above in the background section certain structures are known to be suited for impact absorption. However, it has not been fully understood how these could be structured in order to optimise the impact absorption properties. Outlined below are examples of optimised structures for improved impact absorption. These can be used to form items intended to reduce traumatic brain injury such as bicycle helmets. A method of optimising the structure for improved impact absorption is also described. 
     Previously, it has been assumed when assessing energy dissipation in helmets or similar impact absorbing structures that 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. However, the foam only provides an ideal force-displacement curve if the compressed region is uniform in area. In a curved structure such as a helmet with a substantially ovoid shape, 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. Furthermore, if the curved helmet surface impacts another curved surface, the force-displacement gradient will be further reduced. The consequence of this is that 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&#39;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). 
     As outlined below, it is possible to create 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. 
     This is achieved by forming the impact-absorbing structure as a hollow-cell structure which is stretch-dominated, such as for example a micro-truss lattice or out-of-plane honeycomb. 
     In this type of structure, the mechanism of deformation involves ‘hard’ modes such as compression and tension rather than bending. For the same relative density as foam, stretch dominated structures have a comparatively higher modulus and yield stress. This is discussed below. 
     In stretch-dominated hollow-cell structures, 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 (ε d ), which can be calculated from 
     
       
         
           
             
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     where p is the density of the structure and p s  that of the bulk material, and where p crit /p s  is the relative density (or volume fraction solid) at which the structure locks up. 
     Apart from light weight and ventilation, there are potentially two key benefits of using hollow-cell stretch-dominated structures as an impact absorbing structure. Firstly, the post-yield softening counteracts the area increase of a oval shaped helmet dissipating energy at a more uniform plateau force. Secondly, for a given yield stress, 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. 
     One particular form of 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. Typically 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 j, joined by struts s, which surround faces that enclose cells, as shown in  FIG. 1 . 
     The effect of material in the faces stiffens the structure by a constant. In  FIG. 1   a,  when the frame is compressed it has no stiffness or strength in the loading direction. If the joints are frozen (locked) the frame in  FIG. 1 a    will bend as the structure is loaded and can be called a bending-dominated structure. In the stretch-dominated structures in  FIG. 1 b    and  1   c,  the members carry tension or compression when loaded, giving higher modulus and strength. This is shown in  FIGS. 2 a  and 2 b   , which summarise the difference between stretch and bending-dominated structures in terms of relative modulus E/E s  and relative strength σ/σ s  against relative density p/p s . In the structures in  FIGS. 1 a    and  1   b,  the structure carries self-stress, which means the struts carry stress even though the structure carries no external load (this is prevalent in  FIG. 1 c   ). For example if the vertical strut is shortened, it pulls the other struts into compression. 
     The two key benefits of using 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; secondly, for a given yield stress, 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. This is discussed in detail in Appendix E. 
     In the embodiments described below, the impact absorbing structure is formed as a lattice—i.e. from interconnected hollow cells. Also, in order to simplify manufacture, a periodic lattice is described (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. 
     Other shapes (e.g. triangles and squares) will also tessellate, but have fewer sides. However, the number of sides has been shown to correlate positively with the dissipated energy per unit mass of the structure (SAE). 
     The types of 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. For example, 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. 
     It should be noted that other types of structure, formed as stretch dominated structures, will also provide the same advantages. For example, 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. 
     As shown in  FIGS. 3 and 4  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 layout/location of the cell wall material and the empty space which the cell walls encompass. That is, tessellation is achieved with the cell walls distributed over a given planar or curved surface as evenly as possible, with no overloaded focal areas, or over-large uncovered areas. 
     Hexagonal honeycomb can be thought of as a stretch dominated structure by applying the Maxwell criterion: 
         M   honeycomb =30−3×12+6=0
 
       FIG. 4  shows a section of a periodic lattice of hexagonal cells, showing the positions of the joints j and struts s for this stretch-dominated 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  FIG. 1 . However, as noted there will frequently be a force component at an angle to this, and 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  FIG. 4 . 
     If used in an impact-absorbing structure such as a helmet, 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. 
     If the cell dimensions are known, a value of hollow cell relative density (or volume fraction solid) can be calculated using the equation shown below: 
     
       
         
           
             
               
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     For the particular embodiments of the honeycomb structure  1  of the invention described, h is assigned a value of 1, θ has a value of 30 (degrees), and the ratio of cell wall thickness (t) to cell length (l) is significantly small. 
     A proposed use for the hollow cell structure  1  would be in bicycle helmets. 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 6 mm and a maximum of 20 mm, with the wall thickness maintained at a constant 1 mm. 
     The 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. 
     As outlined in the ‘background’ section, helmet design is generally a trade-off between the overall weight of a helmet, and the impact-absorbing properties. Based on the results of the tests detailed in Appendix A and Appendix D, a helmet such as helmet  5  shown in  FIGS. 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 3× greater EPV than a typical expanded polystyrene helmet. This is clearly shown by the plots of the experimental results shown in  FIGS. 13 and 14 . 
     The reasons can be summarised as follows:
         Stretch dominated structures rely on ‘hard’ modes of deformation through compression and tension. A long plateau force is achieved, as the stress response softens as the area increases.   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.   All stretch dominated structures have similar mechanical responses. Therefore, 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.       

     As briefly noted above, where 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. For example, a honeycomb cell structure viewed in plan or from directly above will provide a uniform cross-section at any depth through the cells. It should also be noted that when a structure is referred to as ‘stretch-dominated’, this is according to the Maxwell criterion as outlined herein. It should further be noted that the phrases ‘relative density’ and ‘volume fraction solid’ essentially have the same meaning and are used interchangeably within this specification.