GB2455167A - Bimetallic or bimaterial members and systems which exhibit negative Poisson's ratio - Google Patents

Bimetallic or bimaterial members and systems which exhibit negative Poisson's ratio Download PDF

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Publication number
GB2455167A
GB2455167A GB0816016A GB0816016A GB2455167A GB 2455167 A GB2455167 A GB 2455167A GB 0816016 A GB0816016 A GB 0816016A GB 0816016 A GB0816016 A GB 0816016A GB 2455167 A GB2455167 A GB 2455167A
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systems
different
pressure
compressibility
material
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GB0816016D0 (en
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Joseph Noel Grima
Ruben Gatt
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University of Malta
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University of Malta
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L7/00Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements
    • G01L7/02Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements in the form of elastically-deformable gauges
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L7/00Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements
    • G01L7/02Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements in the form of elastically-deformable gauges
    • G01L7/022Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements in the form of elastically-deformable gauges constructional details, e.g. mounting of elastically-deformable gauges
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L7/00Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements
    • G01L7/02Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements in the form of elastically-deformable gauges
    • G01L7/08Measuring the steady or quasi-steady pressure of a fluid or a fluent solid material by mechanical or fluid pressure-sensitive elements in the form of elastically-deformable gauges of the flexible-diaphragm type

Abstract

Systems with negative Poisson's ratios (auxetic) exhibit the unusual property of expanding when stretched and getting thinner when compressed whilst systems with negative compressibility exhibit the unusual property that they get smaller (at least in one dimension) when subjected to a decrease in external pressure (partial vacuum) and vice-versa, they get larger when subjected to an increase in external pressure. Materials with negative thermal expansion undergo a reduction in their dimensions as a result of heating. Here, we describe systems and mechanisms with these unusual properties which may also be controlled/adjusted as well as rods/ligaments made from two materials which bend when subjected to a change in pressure. The drawing shows a triangular system comprising two different materials A and B which are interconnected by pin joints C. Materials A and B may be plastics or metals and have different Young's moduli and/or different Poisson's ratios. The construction is such that a reduction in the external pressure results in component B increasing in length with a rate of increase which is larger than that for A which causes the triangle structure to becoming shorter. Other structures having similar properties are discussed and shown in other drawings.

Description

Details of Invention:

Short Background theory on Bi-Material rods

Bi-material strips are usually used to translate a change in temperature to a displacement i.e. the bi-material strip will bend. This bending is caused by the different strains each material would experience in the free (unbound) state. This mismatch in strains would result in internal stresses which in turn bend the bi-material strip.

Short Background theory on NPRs

Systems with a negative Poisson's ratio (NPR) undergo a lateral expansion when stretched in a particular direction, as opposed to conventional positive Poisson ratio materials. Materials with a Poisson's ratio of approximately zero also may exist, and these materials undergo no lateral expansion or contraction when loaded in a particular direction. Systems with NPRs exist as natural materials (for example the minerals: low-cristobalite and natrolite) and also as synthetic structures (rotating squares) and materials (auxetic foams).

Short Background Theory on NTE

Many materials which we encounter in everyday life expand upon heating, albeit at different rates. This is the basis of the bimetallic strip where two metals joined together expand at different rates and curve as a result. The coefficient of thermal expansion is not constant but varies with temperature itselL There are cases where a material or a structure may possess the property of negative thermal expansion (NTE) where heating the system results in the system becoming smaller (or cooling the system results in expansion of the same system). Heating ice to the transition to the liquid state is a well-known example of the phenomenon.

Short Background theory on NC

Another property of materials which measures deformations is the compressibility' (linear, area or volume) which defines how a material deforms when subjected to a hydrostatic pressure. Most materials contract in all directions under a hydrostatic pressure so that the linear argument is usually positive. Unless the material is isotropic (i.e. its properties are independent of direction), linear deformations along each of the orthogonal axis occur to a different extent. It is interesting to note that the relative magnitudes of the Poisson's ratios of a material can give insight into the way that it deforms when subjected to a hydrostatic pressure. Examples of materials with a negative compressibility are selenium and tellurium.

First Embodiment The system referred to in Claim 1, illustrated in Fig. 1, consists of a structure made up from two distinct materials, which may be metals (for example, but not limited to iron and copper), plastics or other naturally occurring / synthetic materials which are fused, glued or riveted together. Material [a] and material [b] have significantly different compressibility, which means that they have significantly different mechanical properties. When a change in pressure is applied, such system will bend since the strains each material would experience in the free (unbound) state would be different. To illustrate this, let us consider a cuboidal strip of dimensions xvz made from an isotropic material having compressibility /3, Young's modulus E and Poisson's ratio v. When this strip is subjected to a change dP in the external pressure, the strip will experience strains along each of the three dimensions of magnitude: =_!pdP= l_2Vdp 3 E Thus, when two isotropic materials [a] and [b] having different Young's moduli and / or Poisson's ratios are subjected to the same change in external pressure, they will experience different strains where the difference in strains, de, is given by: de=e2-e1 =_(fl2_fi)dP= E2v2 l_2vIJdP This difference in strain will result in a curvature of a bi-material strip made from components [a] and [b] when this is subjected to a change in the externally applied pressure, where, the extent of curvature will be affected by the difference in the Young's moduli and Poisson's ratio of the two components of the strip and their thickness. In this respect if material [b] has a lower Young's modulus than material [a], then the difference in the strains (which effects the magnitude of the curvature) will be enhanced if material [b] will have a negative Poisson's ratio whilst material [a] will have a positive Poisson's ratio. For example, if we let E2 = E1 = E, then the difference in strain (and hence the curvature) will be 14 times more pronounced when v1 -l and v1 = +0.3 when compared to a system with v2 = v1 = +0.3.

This system may also be made up of two sheets or grids or structures of different materials as in Claim 2, illustrated in Figs. 2 & 3: Material [a] and material [b] are materials with different properties (compressibility, Poisson's ratios and/or Young's moduli) which may be metals (for example, but not limited to iron and copper), plastics or other naturally occurring / synthetic materials which are fused, glued or riveted together. Since the material properties of the two sheets (sheet [a] and sheet [b]) are different, their volume changes in a different way when a change in pressure is applied.

The system will form a dome shape since the strains that each material would experience in the free (unbound) state would be different.

Second Embodiment The system referred to in Claim 3, illustrated in Figure 4, is a finite system coniposed of three parts [a], [bJ and [ci where component [a] is rod-shaped made from a different material than component [b] which is also rod-shaped. Parts [a] and [hi may be made from metals (for example, but not limited to iron and copper), plastics or other naturally occurring / synthetic materials provided that component [a] and component [b] have different Young's moduli and / or different Poisson's ratios. Component [ci is ideally a pin-joint which may connect components [a] and [b] but may also be another type of connector. Component [a] and component [b] may have identical linear and radial dimensions. The construction must be such that a reduction in the external pressure results in component [b] increasing in length with a rate of increase which is larger than that for components [a] and this results in the triangle structure ( = Structure in Figure 4) becoming shorter in the direction orthogonal to the side comprised by component [b].

The principle of different Young's moduli and / or different Poisson's ratios for component [a] and component [hi, specifically [a] and [b] must have either different Young's moduli or different Poisson's ratios or both and [b] must have the lower Young's modulus, the lower Poisson's ratios (which may even be negative) or both, allows for the possibility of component [b] extending more than component [a]. Note that it is also possible to make the three sides of the triangles from three different materials and there is no constraint on the lengths of the rods provided that the combinations of materials and lengths used permit triangle formations and permit the thangle to become shorter when subjected to a reduction in external pressure.

The piston-containing system in Claim 4 may be constructed as described in Figure 5-1 which shows a construct composed of three parts [a], [b] and [c]. Component [a] is a joint such as a pin-joint which connects components [b] and [ci. Component [b] is a rod-shaped material. Component [c] is a rod similar to component [b] which is modified to form a piston. This construct functions in a very similar way to the construct in Figure 4 with the piston and the gas/fluid environment inside it allowing for much greater increases in the effective length thus resulting in a larger extent of the negative compressibility. (Note that the piston shown in. Fig. 5-I is for illustration purpose only and different types and forms of pistons' or piston-type units' which function in the same nrnnner may be used.) Furthermore, as mentioned in Claim 4, the systems constructed in Figure 5-Il also exhibit negative compressibility irrespective of the shape of the rigid units. This system is constructed in the same way as the one shown in Fig. 4 with the difference that the rods forming the sides of the triangles are of a more generic nature such as but not limited to squares, hexagons, etc. As described in Claim 5, the units exhibiting negative linear compressibility described in Claims 3 and 4 (Figures 4 and 5) may be used as building blocks' to construct larger two or three dimensional systems which will also exhibit negative compressibility in one, two and/or three dimensions as illustrated but not limited to the systems in Figures 6-8. For example, figures 6 and 8 show systems which are networked structures composed of components [a] and [b]. Component [a] and component [b] must have different compressibilities, Young's moduli and / or different Poisson's ratios. Component [a] and component [b] are connected by means of pin joints or other types of connectors. This structure may exhibit negative compressibility in a number of directions. Note that it is also possible to make the three sides of the triangles from three different materials and there is no constraint on the lengths of the rods provided that the combinations of materials and lengths used permit triangle formations and permit the triangle to become shorter when subjected to a reduction in external pressure.

As described in Claim 6 the systems shown in Figure 9, hereafter referred to as chiral systems' (singular: chiral system') may be regarded as structures built from units hereafter referred to as basic unit' (plural basic units'). The basic unit (some examples of which are shown in Figure 9-I) may be described as systems having a central node [a] with bi-material ligaments, [b] and [c], hereafter referred to as ligaments' (singular ligament') attached to it. More specifically, a basic unit may be defined as having: * A central node [a] (which may be cylindrical, spherical, square, oblong or of any other geometrical form, and which may be of any size), * A number (one, two, three, four, five, six or more) of bi-material ligaments made up of at least different two materials [b] and [ci which are fused, glued or riveted to the central node, where the bi-material ligaments are constructed as described in the first embodiment, * The material of the node [a] may be the same material used for of one moiety ([b] or [c]) of the bi-material ligament. Alternatively, the material of the node [a] may be different from the materials used for the moieties ([b] or [ci) of the bi-material ligament.

More complex systems may be built using two or more basic units. The basic units used may have the same number of ligaments, in which case they will result in structures such as those shown in Figure 9-Il or the nodes may have a different number of ligaments in which case they will result in structures such as those shown in Figure 9-Ill. Some of the structures, for example those shown in Figure 9-Il, may be regarded as the unit cell of a larger system. The basic unit may be tessellated in more than one way, examples of which are illustrated in Figure 9-IV. Three-dimensional systems having similar characteristics may also be constructed.

To explain the behaviour of such systems let us take the chiral sytem made up from square nodes having four ligaments attached to each node (see Figure 9-V). Let us first consider a simplified version of it where the system is only constructed from one material (i.e. referring to Figure 9-V. material [d] = material Eel = material [fi). When this simplified structure is subjected to a change in pressure, it behaves in a conventional manner, in the sense that an increase in the applied hydrostatic pressure will result in a shrinkage of all the components of the system, and vice versa if the system is subjected to a decrease in the applied hydrostatic pressure (i.e. positive compressibility which is equal to the intrinsic compressibility of the material).

However, if the system is constructed from two different materials having different properties (i.e. referring to Figure 9-V material [d] = or material Eel!= material [fl) the ligaments in the systems will also bend as a result of the change in pressure, a property which results in a rotation of the nodes' (which in this case are squares). As a result of this, if the component materials are such that a reduction in pressure results in Material [e] expanding more than Material [1] (for example, by having the Young's modulus of Material [e] is smaller than that of Material En), a reduction in pressure will result in bending of the bi-material ligament in such a way that the centres of the nodes Ed] approach each other and vice versa for an increase in pressure (i.e. contribute to negative compressibility). In such cases, an overall negative compressibility will be observed if the negative contribution' to the compressibility which results from these rotations is larger than the positive contribution' which results from the conventional behaviour of the individual components.

This counterintuitive negative behaviour will not be observed if Material Eel is replaced by Material [fl as in this case the curvature of the ligament will result in the centres of the squares moving further away from each other when the system is subjected to a reduction in pressure (i.e. positive compressibility). However, such systems are also of interest in view of the fact that the overall positive compressibility of the structure nmy in fact be larger than that of the constituent materials.

The same effect may also be obtained if the nodes Ed], are of the same or different material from the ligament material [e]. In all cases negative compressibility will be obtained if the negative contribution' to the compressibility is larger than the positive contribution'.

Note that the materials in the above systems may be metals (for example, but not limited to iron and copper). plastics or other naturally occurring / synthetic materials Third Embodiment The system referred to in Claim 7, illustrated in Figure 10, is a finite system composed of strip-like components [a], components [b] and component [c]. Components [a] and components [b] are joined together such that they form a bimaterial strip as explained in the first embodiment. The material for components [a] has a higher expansivity (as a result of an increase in temperature and/or a decrease in pressure) than the material of component [b]. Component [c] is perpendicular to components [a] and components [b] and connects parallel components [b]. This will cause the bi-material strip made from components [a] and [b] to bend in the manner illustrated in Fig. 10 when there is a pressure decrease (given that the compressibility, Poisson's ratio and / or Young's moduli of components [a] and [b] are sufficiently different) or if there is a temperature increase (0 (given that the thermal expansion of components [a] and [b] are sufticiently different) so that the unit becomes re-entrant' or more re-entrant'. Note that the ligaments made from materials [a] and [b] will bend in the opposite manner to form a non re-entrant unit if materials [a] and [b] are swopped.

The systems in Figure 11 are examples of structures built from the building block' presented in Figure 10. These systems may be 2-dimensional or 3-dimensional and their Poisson's ratios are dependent on the external temperature and pressure such that a change in these external conditions will result in a variation of the systems' Poisson's ratios. In this sense, a carefully applied change in temperature and / or pressure may convert a non re-entrant conventional system into a re-entrant auxetic system.

The mechanism of how these systems operate will be explained using Figure 11-1 as reference. When there is an increase temperature change of sufficient magnitude (considering that thermal expansion of components [a] are also sufficiently larger from that of components [b]), they will bend in a manner such that the initial grid structure will form a re-entrant honeycomb system where the former is a conventional system and the latter is auxetic. In a similar way, when a pressure change is applied, given that components [a] and [b] have sufficiently different compressibility and Poisson's ratios or Young's moduli, the initial conventional grid structure will form an auxetic re-entrant honeycomb system. The other systems in this group behave in a similar way with the exception of forming auxetic re-entrant (star-shaped) systems instead of the auxetic re-entrant honeycomb systems.

General notes The exact properties of the system so constructed may be adjusted and fine-tuned by monitoring and varying the geometric parameters of the systems or the materials properties. Further variation may be obtained by introducing more material types.

These mechanisms which result in negative compressibility result in negative thermal expansion when subjected to a change in temperature, provided that the different rod elements have different thermal expansion coefficients. Also, systems based on the same principles designed to exhibit negative thermal expansion will also exhibit negative compressibility when subjected to a change in pressure, provided that the different rod elements have different compressibility properties.

Furthermore, the re-entrant systems generated by the application of external pressures / temperature changes on systems such as the one illustrated in Fig. 11 can exhibit negative Poisson's ratio, the extent of which depends, amongst other things, on the extent of re-entrancy, whilst the non re-entrant honeycomb exhibits positive Poisson's ratio. The extent of re-entrancy is in turn dependent on the external pressure and/or temperature that the system is subjected to. This provides a mechanism which allows for adjustable Poisson's ratios which can be varied and controlled through the application of externally applied pressure and/or temperature changes.

Claims (1)

  1. C.LAftAS (I) A system consisting of a bi-material rod i.e. a rod made from two materials, each of which has different material properties from the other and which respond differently to pressure changes joined or attached together as in Fig 1 will bend when subjected to a change in the external pressure where the extent of change in curvature is dependent on the extent of change in pressure and the compressibility, Young's moduli and/or Possion's ratios of the materials used.
    (2) The system described in claim 1 consisting of sheets, structures or gilds instead of rods as in Fig. 2 -3, i.e. bi-material sheets, structures or grids made from two sheets, two structures or two grids of different materials which respond differently to pressures, joined or attached together from the side of maximum surface area as in Figure 2 that will dome when subjected to a change in pressure where the extent of change curvature is dependent on the extent of change in pressure and the compressibility, Young's moduli and/or Possion's ratios of the materials used.
    (3) A system constructed from two or three different materials which respond differently to pressure changes as a result of having different mechanical properties which are connected together as a triangular system as shown in Figure 4 will change shape when subjected to a change in pressure and may exhibit the property of negative compressibility in at least one dimension (i.e. get smaller in at least one direction when subjected to a decrease in pressure, and vice-versa when subjected to an increase in pressure) where the extent of the compressibility can be controlled by varying the geometric features of the systems or the materials used.
    (4) Systems constructed in accordance with claims 3 further comprising of either pistons instead of at least one of the rods in the triangles (such as the ones shown in Fig 5-I), or different rigid units of any shapes such as polygons (such as the ones shown in Fig 5-I!) will also exhibit the properties claimed in claim 3.
    (5) Two or three dimensional systems (examples shown in Figures 5 -8) constructed from triangular building blocks built in accordance with claims 3 and 4 exhibit negative compressibility in one or more dimensions.
    (6) System constructed from bi-material rods constructed in accordance to those described in Claim 1 which are connected together via nodes so as to obtain systems similar but not limited to those shown in Fig 9 exhibit negative compressibility.
    (7) Systems based on the systems illustrated in Fig. 10 -11 can be made re-entrant or non re-entrant by varying the external pressure and/or temperature. These systems can exhibit different values of the Poisson's ratios. the magnitude of which will depend on the degree of re-entrancy and thus these systems may exhibit either positive or negative Poisson's (auxetic) where the degree of auxeticity will be dependent on the degree of re-entrancy which is in turn dependent on the external pressure and/or temperature. All this is in addition to their potential to exhibit negative thermal expansion and / or negative compressibility.
    (8) Other systems constructed from components made from more than one material which exhibit negative thermal expansion as a result of having the two components exhibiting different thermal expansion coefficients will exhibit negative compressibility if the material properties (compressibility, Poisson's ratio and / or Young's moduli) of the constituting materials are sufficiently different and connected in line to what is described in the claims above, and vice-versa.
    (9) Systems constructed in accordance with claims 1 to 7 which are made from building blocks described in claims 1 to 7 either by repeating (tessellating) the systems or otherwise exhibit the same properties claimed.
    (10) All the systems identified in this document and systems in accordance to claims I to 9 based on systems defined in this document which include more material types or additional components.
GB0816016A 2007-09-04 2008-09-03 Bimetallic or bimaterial members and systems which exhibit negative Poisson's ratio Withdrawn GB2455167A (en)

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Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9402439B2 (en) 2013-09-18 2016-08-02 Nike, Inc. Auxetic structures and footwear with soles having auxetic structures
US9456656B2 (en) 2013-09-18 2016-10-04 Nike, Inc. Midsole component and outer sole members with auxetic structure
US9474326B2 (en) 2014-07-11 2016-10-25 Nike, Inc. Footwear having auxetic structures with controlled properties
US9538811B2 (en) 2013-09-18 2017-01-10 Nike, Inc. Sole structure with holes arranged in auxetic configuration
US9549590B2 (en) 2013-09-18 2017-01-24 Nike, Inc. Auxetic structures and footwear with soles having auxetic structures
US9554622B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Multi-component sole structure having an auxetic configuration
US9554620B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Auxetic soles with corresponding inner or outer liners
US9554624B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Footwear soles with auxetic material
US9635903B2 (en) 2015-08-14 2017-05-02 Nike, Inc. Sole structure having auxetic structures and sipes
US9668542B2 (en) 2015-08-14 2017-06-06 Nike, Inc. Sole structure including sipes
US9681703B2 (en) 2014-12-09 2017-06-20 Nike, Inc. Footwear with flexible auxetic sole structure
US9775408B2 (en) 2014-12-09 2017-10-03 Nike, Inc. Footwear with auxetic ground engaging members
US9854869B2 (en) 2014-10-01 2018-01-02 Nike, Inc. Article of footwear with one or more auxetic bladders
US9861161B2 (en) 2014-04-08 2018-01-09 Nike, Inc. Components for articles of footwear including lightweight, selectively supported textile components
US9901135B2 (en) 2014-12-09 2018-02-27 Nike, Inc. Footwear with flexible auxetic ground engaging members
US10064448B2 (en) 2014-08-27 2018-09-04 Nike, Inc. Auxetic sole with upper cabling
US10070688B2 (en) 2015-08-14 2018-09-11 Nike, Inc. Sole structures with regionally applied auxetic openings and siping

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GB553079A (en) * 1941-12-17 1943-05-06 Sidney Arthur Leader A clamping device, for use particularly in clamping together two parts of a mould
GB1238567A (en) * 1968-11-05 1971-07-07
GB1411096A (en) * 1971-10-04 1975-10-22 Dresser Ind Condition responsive gauge instrument
SU1065700A1 (en) * 1980-04-28 1984-01-07 Предприятие П/Я А-1097 Pressure converter tensile sensing element

Cited By (19)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9820532B2 (en) 2013-09-18 2017-11-21 Nike, Inc. Auxetic structures and footwear with soles having auxetic structures
US9456656B2 (en) 2013-09-18 2016-10-04 Nike, Inc. Midsole component and outer sole members with auxetic structure
US9538811B2 (en) 2013-09-18 2017-01-10 Nike, Inc. Sole structure with holes arranged in auxetic configuration
US9549590B2 (en) 2013-09-18 2017-01-24 Nike, Inc. Auxetic structures and footwear with soles having auxetic structures
US9554622B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Multi-component sole structure having an auxetic configuration
US9554620B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Auxetic soles with corresponding inner or outer liners
US9554624B2 (en) 2013-09-18 2017-01-31 Nike, Inc. Footwear soles with auxetic material
US9402439B2 (en) 2013-09-18 2016-08-02 Nike, Inc. Auxetic structures and footwear with soles having auxetic structures
US9872537B2 (en) 2014-04-08 2018-01-23 Nike, Inc. Components for articles of footwear including lightweight, selectively supported textile components
US9861161B2 (en) 2014-04-08 2018-01-09 Nike, Inc. Components for articles of footwear including lightweight, selectively supported textile components
US9474326B2 (en) 2014-07-11 2016-10-25 Nike, Inc. Footwear having auxetic structures with controlled properties
US10064448B2 (en) 2014-08-27 2018-09-04 Nike, Inc. Auxetic sole with upper cabling
US9854869B2 (en) 2014-10-01 2018-01-02 Nike, Inc. Article of footwear with one or more auxetic bladders
US9775408B2 (en) 2014-12-09 2017-10-03 Nike, Inc. Footwear with auxetic ground engaging members
US9681703B2 (en) 2014-12-09 2017-06-20 Nike, Inc. Footwear with flexible auxetic sole structure
US9901135B2 (en) 2014-12-09 2018-02-27 Nike, Inc. Footwear with flexible auxetic ground engaging members
US9668542B2 (en) 2015-08-14 2017-06-06 Nike, Inc. Sole structure including sipes
US9635903B2 (en) 2015-08-14 2017-05-02 Nike, Inc. Sole structure having auxetic structures and sipes
US10070688B2 (en) 2015-08-14 2018-09-11 Nike, Inc. Sole structures with regionally applied auxetic openings and siping

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