Patent Application: US-87612710-A

Abstract:
the invention described herein relates to structured porous materials , where the porous structure provides a tailored poisson &# 39 ; s ratio behavior . in particular , the structures of this invention are tailored to provide a range in poisson &# 39 ; s ratio ranging from a negative poisson &# 39 ; s ratio to a zero poisson &# 39 ; s . two exemplar structures , each consisting of a pattern of elliptical or elliptical - like voids in an elastomeric sheet , are presented . the poisson &# 39 ; s ratios are imparted to the substrate via the mechanics of the deformation of the voids and the mechanics of the material . the geometry of the voids and the remaining substrate are not limited to those presented in the models and experiments of the exemplars , but can vary over a wide range of sizes and shapes . the invention applies to both two - dimensional structured materials as well as three dimensionally structured materials .

Description:
the invention provides a structured material , providing isotropic or anisotropic poisson &# 39 ; s ratios including zero or even a negative poisson &# 39 ; s ratio . the structured material includes a strain - permitting matrix material and a patterned porous conformation that allows the control of the poisson &# 39 ; s ratio of the structured material . the resulting poisson &# 39 ; s ratio is controlled at small strain ( strains less than 1 %) and may also be robust to larger strain ( strains up to and greater than 10 %). the material is patterned with a repeating pattern of voids , which can be cut , molded , printed , or otherwise imparted into the material ( 2 - d sheets or 3 - d solids ). the material can be polymeric ( including , but not limited to , unfilled or filled vulcanized rubber , natural or synthetic rubber , crosslinked elastomer , thermoplastic vulcanizate , thermoplastic elastomer , block copolymer , segmented copolymer , crosslinked polymer , thermoplastic polymer , filled or unfilled polymer , or epoxy ) but may also be non - polymeric ( including , but not limited to , metallic and ceramic and composite materials ). several exemplar patterned structures are used to illustrate the invention : the exemplar structures in fig1 through 12 consist of two - dimensional patterns of ellipsoidal pores in elastomeric sheets . in the exemplar application , the sheets are loaded uniaxially , and the in - plane strain transverse to the loading direction is controlled by the patterned porous conformation . the first pattern in fig1 ( oep and variations of this pattern ) results in lateral expansion when the patterned sheet is pulled in uniaxial tension , or lateral contraction when the patterned sheet is shortened in uniaxial compression . variations in the bias of the pore patterning , shown in fig8 , allow the control of the in - plane poisson &# 39 ; s ratio in a range from 0 to large negative values . an example is shown in fig7 , demonstrating that this phenomenon enables a sheet , patterned with the oep pattern , to conform smoothly to double curvature surfaces , highlighting the ability to tailor these patterns to allow conformability to double and more complex curvature surfaces . a second exemplar two - dimensional pattern is shown in fig2 ( sep and variations of this pattern ). variations in the pitch of the pore patterning , shown in fig1 , allow the control of the in - plane poisson &# 39 ; s ratios in a range from 0 to − 1 . exemplar patterned structures that illustrate the invention in its full three - dimensional embodiment are shown in fig1 , 14 , and 15 . the patterned structures in fig1 through 15 demonstrate the application of the invention to create patterned materials with negative poisson &# 39 ; s ratio three - dimensionally ( i . e . in both lateral directions ). similarly to the two dimensional applications , the poisson &# 39 ; s ratios in the two transverse directions can be controlled by varying the bias in the pore dimensions , or by staggering the pores with variable pitch . the nature of this invention avoids limitations that have hampered the development of auxetics to - date , as a wide variety of materials , polymeric and non - polymeric , can be used . the fabrication of the 2 - d structures is straightforward , and can be achieved by a number of manufacturing approaches e . g . via water jet cutting , laser cutting , die cutting , stamping , injection molding , compression molding , vulcanization , or a combination of these or other processes , depending on the particular material . similarly , the fabrication of 3 - d structures is straightforward , and can be achieved by a number of processes including 3d printing and sintering . finally , manufacturing processes such as microfabrication techniques and interference lithography enable the fabrication of such porous structures at the lengthscale of micrometers . the two illustrative patterns shown in fig1 and 2 consist of repeating units of ellipsoidal pores , surrounding large square - like or rectangular - like domains of matrix material . note that in other embodiments of this invention repeating pores , slits , slots , notches , cuts , or other geometric shapes can surround matrix material domains of different shapes ( triangular , circular , oblong , irregular , etc .). fig1 shows the orthogonal ellipse pattern or oep . here , the ellipsoidal pores are offset such that the major axis of an ellipse runs through the center of the neighboring ellipse and a small “ bridge ” of polymer runs between each ellipse and its neighbor . this “ bridge ” is highlighted in fig3 ( 1 ). during macroscopic tension , this “ bridge ” acts as a hinge , opening the ellipsoidal pores and rotating the remaining matrix regions , shown in fig3 ( 2 - 5 ), outward . during macroscopic compression the “ bridge ” acts as a hinge in the opposite direction , closing the ellipsoidal pores and rotating the remaining matrix regions inward . fig3 further highlights this hinge mechanism in tension . as can be seen , the pores open , and the square matrix regions rotate outwards i . e . two of the square matrix regions ( 2 , 4 ) rotate clockwise , while the other two square matrix regions ( 3 , 5 ) rotate counterclockwise . this causes the sheet to expand laterally . fig4 ( 1 , 2 ) shows simulations of the sheet in the undeformed state and at a macroscopic tensile strain of 0 . 10 , as well as experiments ( 3 , 4 ) of a ⅛ ″ thick sheet of epdm , patterned with a variation of the oep , undeformed and at a macroscopic tensile strain of 0 . 10 . the simulation and experiment highlight the magnitude of the lateral expansion . the macroscopic poisson &# 39 ; s ratio for this pattern was measured to be approximately equal to − 1 . fig5 highlights this hinge mechanism in compression . here the pores close and the square matrix regions ( 1 - 4 ) rotate inwards , with matrix regions ( 2 , 4 ) rotating clockwise , and matrix regions ( 1 , 3 ) rotating counterclockwise . this causes the sheet to contract laterally . fig6 shows the sheet in the undeformed state and at a macroscopic compressive strain of 0 . 05 , highlighting the magnitude of the lateral contraction . an interesting result of the poisson &# 39 ; s ratio behavior of this pattern is that it can be used to construct 2d structures , which can deform differently in different regions . for example , a sheet patterned with this pattern can expand in the center , while contracting around the edges . this allows the sheet to conform smoothly to double and more complex curvatures surfaces , e . g . a dome . this phenomenon is shown in fig7 . this phenomenon is predictable , and similar patterns can be constructed , which allow for 2d structures that can conform smoothly to any arbitrary surface curvature . finally , the magnitude of the poisson &# 39 ; s ratio of the oep can be tailored by varying the aspect ratios of the ellipsoidal pores . fig8 shows the traditional oep undeformed ( 1 ) and deformed to 10 % macroscopic tensile strain ( 2 ), and a variation of the oep , made by increasing the length of the pore &# 39 ; s major axis in the direction parallel to loading , again shown undeformed ( 3 ), and deformed to 10 % macroscopic tensile strain ( 4 ). here , the major axis of vertical ellipsoidal pores is 50 % longer than the major axis of the horizontal ellipsoidal pores . as can be seen this pattern demonstrates a much larger negative poisson &# 39 ; s ratio . the plot in fig8 ( 5 ) shows the value of poisson &# 39 ; s ratio for different relative ellipse length , where 0 . 5 corresponds to the major axis of vertical ellipses being 50 % as long as the major axis of horizontal ellipses , and 1 . 5 corresponds to the major axis of vertical ellipses being 50 % longer than the major axis of horizontal ellipses . in the staggered ellipse pattern or sep pattern shown in fig2 the ellipsoidal pores are offset with alternating sets of side - by - side pores . the two pores of each side - by - side pair are offset such that the center of each pore is spaced some distance ( the magnitude of the offset can be varied ) in both the horizontal and vertical direction from its mate . two more sets of side - by - side pores run perpendicular to the first set , with one set at each tip of the first set . fig9 further highlights this geometry , where small “ bridges ” ( 1 ) exist between each pore and its nearest neighbor set . however , in this case , there are also “ bridges ” ( 2 ) between the two members of each side - by - side set . at the convergence of four sets , a small square “ island ” ( 3 ) of matrix material exists . during tensile loading , the pores open and deform . the pores that are oriented perpendicular to the direction of stretching open , as seen in fig9 ( 4 ), while the pores parallel to the direction of stretching deform ( the end bordering on the “ island ” region opens slightly ( 5 ), while the other end closes slightly ( 6 )). the “ island ” itself rotates ( 7 ), allowing the “ bridges ” between the two members of each side - by - side pair to rotate ( 8 ), which compensates for the behavior stated previously ( one end of the pore opening while the other closes ). a similar response is seen in compressive loading , though in this case the pores perpendicular to the direction of loading close instead of opening . in both cases , the remaining matrix regions translate in the direction of loading . this mechanism is highlighted in fig9 . because the pores parallel to the direction of stretching do not significantly contract or expand laterally , and because the remaining matrix regions do not strain significantly , the overall pattern neither expands nor contracts laterally during deformation , giving an overall poisson &# 39 ; s ratio of near zero . fig1 and 11 show simulations and experiments of a sheet with the sep loaded in tension and compression respectively . as in the oep , the magnitude of the poisson &# 39 ; s ratio of the sep can be tailored by altering the pattern . here , the magnitude of the “ stagger distance ”, defined as the distance between parallel elliptical pores , relative to the distance between parallel elliptical pores in the oep , is varied , where a “ stagger distance ” of 0 corresponds to the oep pattern , and a “ stagger distance ” of 1 corresponds to the parallel ellipses almost touching . fig1 shows two stagger distances : 0 . 4 ( 1 and 2 ), and 0 . 7 ( 3 and 4 ). as can be seen , the magnitude of the negative poisson &# 39 ; s ratio is greater in the first case ( 1 and 2 ), as noted by the increased ( relative to 3 and 4 ) lateral expansion for the same macroscopic deformation . fig1 ( 5 ) plots the poisson &# 39 ; s ratio vs . the stagger distance , demonstrating that for this pattern , the poisson &# 39 ; s ratio can range in value from − 1 to 0 . because the remaining matrix regions , which account for a large percentage of the sheet surface , undergo very limited in - plane strain , they exhibit very small transverse strain in the direction normal to the plane of the sheet , so that these patterned sheets exhibit near - zero macroscopic poisson ratio in the out - of - plane direction . therefore the oep exhibits an anisotropic response , with a negative in - plane poisson &# 39 ; s ratio , and a zero out - of - plane poisson &# 39 ; s ratio , while the sep exhibits a near zero poisson &# 39 ; s ratio in both directions . the conceptual approach followed to obtain the two - dimensional ( 2d ) auxetic structures can be extended to obtain three - dimensional ( 3d ) auxetic structures , with tailored poisson &# 39 ; s ratio in both transverse directions . fig1 illustrates the 3d analog of the first exemplar pattern , termed the 3 - d orthogonal disk pattern , or 3dodp , where the three - dimensional patterned porous conformation consists of rounded disk - shaped pores , arranged perpendicular ( along 3 directions ) and offset , such that the major axis of one disk runs through the center of the neighboring disk , and a small “ bridge ” of the matrix material runs between each disk and its neighbor . the pores define cuboidal domains which rotate when the structure is loaded uniaxially , resulting in equal lateral expansion in both transverse directions . the 3dodp is co - continuous ( meaning that the void and the solid regions are both continuous ) and can be fabricated by a variety of processes , including , 3d printing , lithography , and high speed sintering . as an alternative approach to obtain 3d structures with biaxial tailored poisson &# 39 ; s ratios , the 2d porous conformations can be cut through cylindrical or prismatic structures . an example of this approach is illustrated in fig1 , where an axisymmetric sweep of the oep has been used to construct an auxetic cylinder . when the cylinder is extended in the axial direction , the wall of the cylinder thickens , so that the cylinder expands equally in all transverse directions ( a wedge of the cylinder has been cut in the picture to illustrate the transverse deformation ). this manifestation of the invention is particularly relevant to sealing and cork type applications . finally , in a third approach to obtaining 3d auxetic structures , a 2d patterned sheet can be wrapped around a cylinder . in this way , the negative poisson &# 39 ; s ratio of the sheet causes a transverse expansion , when loaded in macroscopic tension , or a transverse contraction , when loaded in macroscopic compression , leading to an expansion or constriction of the cylinder . this phenomenon is shown in fig1 . this manifestation of the invention is particularly relevant to surgical implants and stents , where a macroscopic stretching or shortening of the cylinder , easily controlled by coaxial cables and wires , can be used to increase and decrease the lumen of the stent . although the present invention has been shown and described with respect to several preferred embodiments thereof , various changes , omissions and additions to the form and detail thereof , may be made therein , without departing from the spirit and scope of the invention . 5 ) u . s . utility application ser . no . 12 / 822 , 609 boyce et al ., 2010 ( filing date : jun . 24 , 2010 ) 6 ) u . s . provisional patent application 61 , 240 , 248 boyce , et al ., 2009 other referenced publications 7 ) bertoldi , k ., boyce , m . c . ; 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