Expandable sheet with slits having nonterminal vertical distal end portions, roll, rotary die

Abstract

A sheet includes a plurality of expandable slits formed in a substrate in a repeating pattern including at least two adjacent rows of slits. Each slit has four vertical distal end portions. At least one of the vertical distal end portions has a non-terminal end and at least two of the vertical distal end portions have terminal ends. A plurality of the vertical distal end portions in the first row and a plurality of the vertical distal end portions in the second row are aligned to intersect a horizontal line. The slits are configured to open in response to a minimum tension applied to the substrate along the vertical axis to form a plurality of folding walls and a plurality of nonrotating beams.

Description

EXPANDABLE SHEET WITH SLITS HAVING NONTERMINAL VERTICAL DISTAL END PORTIONS, ROLL, ROTARY DIE

[0001] The present disclosure relates to sheets and, in particular, to expandable sheets with a plurality of slits configured to expand into a three-dimensional structure.

[0002] Tension-activated, expandable sheets are sheets, for example of paper or plastic, that are cut with a slit pattern enabling them to be expanded when tension is applied along a tensioning axis of the sheet. An exemplary tension-activated, expandable sheet is SCOTCH™ CUSHION LOCK™ protective wrap available from 3M Company (St. Paul, Minnesota, USA), a paper-based, tension-activated, expandable sheet. Upon application of tension to expand such a sheet, portions of the sheet rotate to create an interlocking folded-wall structure that absorbs energy and can be used, for example, to cushion and protect objects during shipping.SUMMARY

[0003] In one aspect, the present disclosure relates to a sheet defining a vertical axis and a horizontal axis along a major surface. The sheet includes a substrate of sheet material defining the major surface. The sheet also includes a plurality of expandable slits formed in the substrate in a repeating pattern having at least a first row of the slits and a second row of the slits adjacent to the first row. Each slit defines a slit height along the vertical axis and a slit width along the horizontal axis. Each slit has four vertical distal end portions. At least one of the vertical distal end portions has a non-terminal end and at least two of the vertical distal end portions have terminal ends. A plurality of the vertical distal end portions in the first row and a plurality of the vertical distal end portions in the second row are aligned to intersect a horizontal line. The slits are configured to open in response to a minimum tension applied to the substrate along the vertical axis to form a plurality of folding walls and a plurality of nonrotating beams.

[0004] In one aspect, the present disclosure relates to a roll having the expandable sheet.

[0005] In one aspect, the present disclosure relates to a rotary die having cutting surfaces configured to form the expandable sheet.BRIEF DESCRIPTION OF VIEWS OF THE DRAWINGS

[0006] To easily identify the discussion of any particular element or act, the most significant digit or digits in a reference number refer to the figure number in which that element is first introduced.

[0007] FIG. 1A and FIG. IB are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet in accordance with one embodiment.

[0008] FIG. 2 is an elevation view of one example of forming an expandable sheet using a rotary die in accordance with one embodiment.

[0009] FIG. 3A is a front view of a flat configuration of a portion of one example of an expandable sheet in accordance with one embodiment, and FIG. 3B is an enlarged view of a slit of FIG. 3A.

[0010] FIG. 4A and FIG. 4B are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet having non-terminal ends in accordance with one embodiment.

[0011] FIG. 5A and FIG. 5B are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet having non-terminal ends and slit inversions in accordance with one embodiment.

[0012] FIG. 6A and FIG. 6B are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet having sharp non-terminal ends in accordance with one embodiment.

[0013] FIG. 7A and FIG. 7B are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet having sharp non-terminal ends and slit inversions in accordance with one embodiment.

[0014] FIG. 8A and FIG. 8B are a front view of a flat configuration and a perspective view of an expanded configuration, respectively, of a portion of one example of an expandable sheet having gradual non-terminal ends and slit inversions in accordance with one embodiment.DESCRIPTION

[0015] The present disclosure relates to an expandable sheet having a plurality of slits. Each slit has at least one vertical distal end portion being a non-terminal end. In general, use of a nonterminal segment as a vertical distal end portion facilitates a wide variety of slit shapes that may have various benefits in the structure of the expandable sheet in an expanded configuration or in manufacturing the expandable sheet. In particular, use of the nonterminal segment may facilitate creating new arrangements of folded walls in the expanded configuration that may vary in loft, energy absorption, and visual appearance. Use of the nonterminal segment may also facilitate use of simpler and less expensive manufacturing techniques, particularly when using a rotary die, to form the slits in a sheet material substrate compared to some existing slit patterns having segment intersections.

[0016] As used herein, the term "slit" refers to a narrow cut through the article forming at least one line or segment, which may be straight or curved, or described as linear or non-linear, having at least two terminal ends. Slits described herein are discrete, meaning that individual slits do not intersect other slits. A slit is generally not a cut-out, where a "cut-out" is defined as asurface area of the sheet that is removed from the sheet when a slit intersects itself. However, in practice, many forming techniques result in the removal of some surface area of the sheet that is not considered a "cut-out" for the purposes of the present application. In particular, many cutting technologies produce a “kerf,” or a cut having some physical width. For example, a laser cutter will ablate some surface area of the sheet to create the slit, a router will cut away some surface area of the material to create the slit, and even crush cutting creates some deformation on the edges of the material that forms a physical gap across the surface area of the material. Furthermore, molding techniques require material between opposing faces of the slit, creating a gap or kerf at the slit. In various embodiments, the gap or kerf of the slit will be less than or equal to the thickness of the material. For example, a slit pattern cut into paper that is 0.007" (approximately 18 mm) thick might have slits with a gap that is approximately 0.007" or less. However, it is understood that the width of the slit could be increased to a factor that is many times larger than the thickness of the material and be consistent with the technology disclosed herein.

[0017] Slits can be characterized as "simple slits" or "compound slits," where a "simple slit" is defined as having exactly two terminal ends and a "compound slit" has more than two terminal ends. As used herein, the term "single slit pattern" refers to a pattern of individual slits that form individual rows each extending across the sheet transversely (e.g, along a horizontal axis), where the rows form a slit pattern of individual rows arranged along the axial length of the sheet (e.g., along a vertical axis), and the pattern of slits in each row is different than the pattern of slits in the directly adjacent rows. For example, the slits in one row may be axially offset or out of phase with the slits in the directly adjacent rows. Various slits described herein include simple slits having four vertical distal end portions, including at least one non-terminal vertical distal end portion.

[0018] The sheet includes a substrate of sheet material that defines a major surface. The major surface may be defined as extending along vertical axis and a horizontal axis, which is orthogonal to the vertical axis. The plurality of slits are formed in the substrate. In a flat configuration, or undeployed configuration, of the sheet, the slits are configured to open, or expand, in response to a minimum tension applied to the substrate along the vertical axis to form a plurality of folding walls and a plurality of nonrotating beams in an expanded configuration, or deployed configuration, of the sheet. As used herein, "opening" or "expanding" the slits means separating at least a portion of the sheet material on each side of the slit. In particular, when the expandable sheet is in a flat configuration and tension-activated (pulled along the vertical axis), portions of the substrate may move upward and downward from the substantially two- dimensional major surface and become a three-dimensional article as described herein in more detail.

[0019] The expandable sheet may be formed in any suitable manner. In some embodiments, a rotary die may be used, which has cutting surfaces configured to form slits in sheet material. After being formed, the expandable sheet may be used to form a roll. A user may unroll and deploy the expandable sheet, for example, using a dispenser.

[0020] The plurality of slits are arranged in a slit pattern, which is a repeating pattern including at least a first row of slits and a second row of slits adjacent to the first row. In general, each row is defined as extending along the horizontal axis, and the rows spaced from one another along the vertical axis. The slit pattern is arranged such that a plurality of vertical distal end portions in the first row and a plurality of vertical distal end portions in the second row are aligned to intersect a horizontal line, which is generally parallel to the horizontal axis.

[0021] Each slit defines a slit height measured along the vertical axis and defines a slit width defined along the horizontal axis. In general, each slit includes four vertical distal end portions. At least one of the vertical distal end portions has a non-terminal end. At least two of the vertical distal end portions each include a terminal end. In some embodiments, only two of the vertical distal end portions each include a terminal end. In some embodiments, only two of the vertical distal end portions have non-terminal ends. As used herein, "terminal end" means the end of a slit, or cut, in the substrate. As used herein, "non-terminal end" means the extremum of the slit, generally along the vertical axis, that is not a terminal end. Although a terminal end is generally a point, a non-terminal end may be represented by a portion of the slit that is relatively flat (see FIG. 3A, FIG. 3B, FIG. 4A, FIG. 4B, FIG. 5A, FIG. 5B), curved (see FIG. 8A), or sharp (see FIG. 6A, FIG. 6B, FIG. 7A, FIG. 7B), which can be a segment intersection in some cases.

[0022] A segment intersection 110 may be described as a point in the slit 102 where segments from two different segments come together and intersect.

[0023] Slits may be defined as having horizontal distal end portions. In some embodiments, each slit in the plurality of slits includes two horizontal distal end portions. Each horizontal distal end portion may include two of the vertical distal end portions of the slit, for example, including one non-terminal end and one terminal end.

[0024] One or more of the slits may formed without segment intersections. In some embodiments, at least one of the slits is free of sharp segment intersections. As used herein, the term "segment intersection" means an intersection between two segments of a slit, which may be gradual (e.g., smooth) or sharp (e.g., non-gradual or non-smooth). A sharp segment intersection is defined as having slopes, or tangents, on either side of the intersection that do not approach each other. Another term that may be used to described a sharp segment intersection is a comer.

[0025] The slit pattern of the plurality of slits may define a plurality of nonrotating beam regions. Each nonrotating beam region may be positioned between adjacent slits in the same row. Each nonrotating beam region may be defined at least partially between two vertical distalend portions of a first slit and two vertical distal end portions of a second slit adjacent to the first slit in the same row. In some embodiments, the non-terminal ends of adjacent slits may be aligned. For example, one vertical distal end portion of the first slit may be a non-terminal end aligned to intersect a horizontal line and one vertical distal end portion of the second slit may be a non-terminal end aligned to intersect the same horizontal line. In some embodiments, the nonterminal end of a slit is aligned with the terminal end of an adjacent slit. For example, one vertical distal end portion of the first slit may be a non-terminal end aligned to intersect a horizontal line and one vertical distal end portion of the second slit may be a terminal segment aligned to intersect the same horizontal line.

[0026] The rows of the slit pattern may be staggered. Each slit may include a connector portion extending at least partially along the horizontal axis between two of the vertical distal end portions of the slit. The connector portion may also be described as extending between two horizontal distal end portions of the slit. In a slit pattern having staggered rows, the connector portion of a slit and a nonrotating beam region between slits in an adjacent row may be aligned to intersect a vertical line, which is generally parallel to the vertical axis.

[0027] As used herein, the terms “vertical line” and “horizontal line” refer to imaginary lines that extend substantially parallel to a defined vertical axis or a defined horizontal axis, respectively.

[0028] As used herein, the term "staggered row" refers to the locations of substantially all the slits in a given row being out of phase, or phase offset, by a set amount or a minimum distance along the horizontal axis when compared to corresponding slits in a directly adjacent row. In general, the adjacent rows are out of phase by one half of the horizonal spacing between slits in the row, as measured by the geometric center-to-center distance between slits.

[0029] The repeating pattern of the slit pattern may define a repeating region within the repeating pattern. The repeating region includes at least two staggered rows of the slits. The repeating region may repeat at least two times along at least one row of the slits in the repeating pattern, at least two times along the vertical axis in the repeating pattern, or both.

[0030] The slits may have one or more orientations in the repeating region. In some embodiments, the repeating region includes at least two slits oriented in the same direction or includes each slit being oriented in the same direction. In some embodiments, the repeating region includes at least one inverted slit in the same row to at least one noninverted slit or includes at least one inverted slit in an adjacent row to at least one noninverted slit. The at least one inverted slit may be an inversion across a horizontal line, which is parallel to the horizontal axis. Such a slit pattern may be described as having slit inversions.

[0031] In general, expandable sheets having slit patterns can create strong three-dimensional structures from flat sheets of material when tension is applied. Such slit patterns may be described as folding -wall, tension-activated kirigami patterns.

[0032] FIG. 1A and FIG. IB show one example of an expandable sheet 100 having a plurality of slits 102 with a tension-activated kirigami slit pattern 104 in a flat configuration 114, or unexpanded configuration, in the form of a substantially flat sheet in the schematic plan view of FIG. 1A and in a tension-activated, expanded configuration 116 (and rotated 90 degrees) in the top perspective view of FIG. IB.

[0033] The expanded configuration 116 of the sheet 100 is a three-dimensional (3D) structure wherein portions of the sheet 100 extend along all three axes in space. As illustrated, the slit pattern 104 includes a plurality of slits 102 each having the shape of a capital "H" arranged to define a plurality of nonrotating beam regions 118 and folding wall regions 122 such that, when the sheet 100 is expanded, or deployed, the nonrotating beam regions 118 form nonrotating beams 120 between adjacent slits in the same row and folding wall regions 122 form folding walls 126 between slits in adjacent rows. The formation of the tension-activated expanded configuration 116 may be designed, for example, based on the thickness and elasticity of the sheet material.

[0034] Although the slits 102 may have various shapes, each slit may be described as being formed of various slit features, such as segments, segment intersections, and terminal ends.

[0035] In general, each slit 102 includes at least one segment. In the illustrated embodiment, each slit 102 includes three segments. The connector portion 106 is formed of one horizontal linear segment and each horizontal distal end portion 108 is formed of one vertical linear segment. A segment of a slit 102 may be described as continuous and linear (e.g., straight) or non-linear (e.g., curved). A segment may also be described relative to the tool used to form the segment. For example, each segment may be cut by a distinct cutting surface on a rotary die.

[0036] In general, each slit 102 includes at least two terminal ends 112. The slits 102 in the slit pattern 104 as illustrated may be described as compound slits. The compound slits 102 have at least two slit segments with at least one segment intersection.

[0037] In the illustrated embodiment, the segment intersection 110 is the intersection of the connector portion 106 and the horizontal distal end portion 108, and each slit 102 has two segment intersections 110. The segment intersection 110 may be described as a sharp segment intersection. As described herein in further detail, other slits may be designed to include at least one gradual segment intersection. In some embodiments, each slit may be free of sharp segment intersections.

[0038] The substrate of sheet material may be formed of various suitable materials. Some exemplary materials into which the slit patterns described herein can be formed include, forexample, paper (including cardboard, corrugated paper, coated or uncoated paper, kraft paper, cotton bond, recycled paper, extensible paper); plastic; woven and non-woven materials and / or fabrics; elastic materials (including rubber such as natural rubber, synthetic rubber, nitrile rubber, silicone rubber, urethane rubbers, chloroprene rubber, Ethylene Vinyl Acetate or EVA rubber); inelastic materials (including polyethylene and polycarbonate); polyesters; acrylics; and polysulfones. The article can be, for example, a material, sheet, film, or any similar construction.

[0039] Examples of thermoplastic materials that can be used include one or more of polyolefins (e.g., polyethylene (high density polyethylene (HDPE), medium density polyethylene (MDPE), low density polyethylene (LDPE), linear low density polyethylene (LLDPE)), metallocene polyethylene, and the like, and combinations thereof), polypropylene (e.g., atactic and syndiotactic polypropylene)), polyamides (e.g. nylon), polyurethane, polyacetal (such as Delrin), polyacrylates, and polyesters (such as polyethylene terephthalate (PET), polyethylene terephthalate glycol (PETG), and aliphatic polyesters such as polylactic acid), fluoroplastics (such as THV from 3M company, St. Paul, MN, US), and combinations thereof. Examples of thermoset materials can include one or more of polyurethanes, silicones, epoxies, melamine, phenol-formaldehyde resin, and combinations thereof. Examples of biodegradable polymers can include one or more of polylactic acid (PLA), polyglycolic acid (PGA), poly(caprolactone), copolymers of lactide and glycolide, polyethylene succinate), polyhydroxybutyrate, and combinations thereof.

[0040] "Paper" as used herein refers to woven or non-woven sheet-shaped products or fabrics (which may be folded, and may be of various thicknesses) made from cellulose (particularly fibers of cellulose, (whether naturally or artificially derived)) or otherwise derivable from the pulp of plant sources such as wood, com, grass, rice, and the like. Paper includes products made from both traditional and non-traditional paper making processes, as well as materials of the type described above that have other types of fibers embedded in the sheet, for example, reinforcement fibers. Paper may have coatings on the sheet or on the fibers themselves. Examples of non- traditional products that are "paper" within the context of this disclosure include the material available under the trade designation TRINGA from PAPTIC (Espoo, Finland), and sheet forms of the material available under the trade designation SULAPAC from SULAPAC (Helsinki, Finland).

[0041] The extensibility of paper can be defined as the ability of paper to increase its linear length under the action of external mechanical forces due to elastic, viscoelastic, and plastic deformations. One type of mechanical deformation in paper is tensile deformation, where extensibility is determined as the strain at break value of the stress-strain curve. Many papers, which may be described as non-extensible papers created by existing manufacturing techniques may have extensibility around 1% to 4% in a machine direction (MD) and 3% to 6% in a crossdirection (CD), or even greater values in the MD and CD. Various techniques that can achieve greater extensibility include mechanical treatments, as well as chemical treatments.

[0042] The material in which the single slit pattern is formed can be of any desired thickness. In some embodiments, the material has a thickness between about 0.001 inch (0.025 mm) and about 5 inches (127 mm). In some embodiments, the material has a thickness between about 0.01 inch (0.25 mm) and about 2 inches (51 mm). In some embodiments, the material has a thickness between about 0.1 inch (2.5 mm) and about 1 inch (25.4 mm). In some embodiments, the thickness is greater than 0.001 inch (.025 mm), or 0.01 inch (.25 mm), or 0.05 inch (1.3 mm), or 0.1 inch (2.5 mm), or 0.5 inch (13 mm), or 1 inch (25 mm), or 1.5 inches (38 mm), or 2 inches (51 mm), or 2.5 inches (64 mm), or 3 inches (76 mm). In some embodiments, the thickness is less than 5 inches (127 mm) or 4 inches (101 mm), or 3 inches (76 mm), or 2 inches (51 mm), or 1 inch (25 mm), or 0.5 inch (13 mm), or 0.25 inch (6.3 mm), or 0.1 inch (2.5 mm).

[0043] In some embodiments, where the material is paper, the thickness is between about 0.003 inch (0.076 mm) and about 0.010 inch (0.25 mm). In some embodiments where the material is plastic, the thickness is between about 0.005 inch (0.13 mm) and about 0.125 inch (3.2 mm).

[0044] In some embodiments, the slit or cut pattern extends substantially to one or more of the edges of the sheet, film, or material. In some embodiments, this allows the material to be of unlimited length and also to be deployed by tension, particularly when made with non-extensible materials. The amount of edge material is the area of material surrounding and not including the single slit pattern. In some embodiments, the amount of edge material, or down-web border, can be defined as the width of the rectangle whose long axis is parallel to the tension axis and is infinitely long and can be drawn on the substrate without overlapping or touching any slits. In some embodiments, the amount of edge material is less than .010 inch (0.25 mm) or less than .001 inch (0.025 mm). In some embodiments, the width of the down-web border is less than .010 inch (0.25mm) or less than .001 inch (0.025mm). In some embodiments, the amount of edge material is less than 5 times the thickness of the substrate. In some embodiments, the width of the down-web border is less than 5 times the thickness of the substrate.

[0045] In general, expandable sheets having a slit patterns can be made in a number of different ways. For example, slit patterns can be formed by extrusion, molding, laser cutting, water jetting, machining, stereolithography or other 3D printing techniques, laser ablation, photolithography, chemical etching, rotary die cutting, stamping, other suitable negative or positive processing techniques, or combinations thereof.

[0046] Rotary die cutting uses a rotary die with cutting surfaces (e.g., blades) to form slits in sheet material according to the slit pattern. However, a rotary die for a slit pattern withcompound slits (see FIG. 1), or any other slits that have segment intersections, can take a long time to create due to the use of precision, intersecting cutting surfaces.

[0047] For illustrative purposes, FIG. 2 shows an example of using a rotary die 206 to process paper or other sheet material 202 to form an expandable sheet 204. In particular, paper or other sheet material 202 is fed into a nip consisting of a rotary die 206 and an anvil 208. In this example, uncut sheet material 202 may be stored in the form of a roll 212 where the material is rolled around a central axis that may include or may omit a central core and then unrolled to be fed into the nip. The rotary die 206 has cutting surfaces 210 on it that correspond to the slit pattern, such as the slit pattern 104 (FIG. 1A), to be cut into the sheet material 202. The rotary die 206 cuts through the sheet material 202 and forms an arrangement of slits along its major surface representing the slit pattern. In particular, the length of the slit pattern may correspond with the circumference of the rotary die 206 such that multiple revolutions of the rotary die 206 form a repeating slit pattern in the expandable sheet 204. The expandable sheet 204 may then be stored in the form of a roll 214 where the material is rolled around a central axis that may include or may omit a central core and then unrolled to be expanded by tension activation. The same process can be used with a flat die and flat anvil.

[0048] The present disclosure provides various slit patterns including non -terminal ends, that may facilitate the use of fewer segment intersections or eliminate segment intersections from the slit pattern that are particularly difficult to make, particularly using a rotary die or related techniques. In particular, the various slit patterns according to the present disclosure can be free of "T" shaped, sharp segment intersections, such as the segment intersections 110 shown in FIG. 1A. In some embodiments, at least one, at least some, or all of the slits in the slit pattern are free of sharp segment intersections. Such slit pattern may result in less expensive manufacturing, particularly when using dies to make expandable sheets, and can facilitate higher quality expandable sheets. Such slit patterns according to the present disclosure may also provide a wide variety of slit patterns, which may be used to vary characteristics, such as loft, energy absorption, and visual appearance, versus existing patterns.

[0049] FIG. 3 A shows one example of an expandable sheet 300 having a slit pattern 304 in a flat configuration in the schematic plan view. FIG. 3B shows one of the slits 306 of the slit pattern 304 in isolation in an enlarged view. In both views, a major surface of the substrate 302 of sheet material is shown having the slits 306 formed, or defined, in a slit pattern 304. The sheet 300 defines a vertical axis 314 (or expansion axis) and a horizontal axis 316 (or cross axis) orthogonal to the vertical axis along its major surface. The slit pattern 304 includes at least two staggered rows of the slits 306. In the illustrated embodiment, the all the slits 306 are free of sharp segment intersections. In general, the slit pattern may include each row having at least one slit free of sharp segment intersections, each slit in at least one row being free of sharp segment intersections, or each slit in a repeating pattern being free of sharp segment intersections.

[0050] Slit patterns may define one or more repeating regions that repeat along the horizontal axis, the vertical axis, or both in the slit pattern. The repeating region may repeat at least two, three, four, or more times along one or both axes. In the illustrated embodiment, the slit pattern 304 defines a repeating region 312 that repeats in both along the horizontal axis 316 and along the vertical axis 314. In general, each repeating region includes at least two staggered rows of the slits. As illustrated, the repeating region 312 includes a first slit and a second slit in an adjacent and staggered row. Both the first and second slit have the same shape and orientation.

[0051] The slits 306 of the sheet 300 are configured to expand in response to a minimum tension applied to the substrate 302 along the vertical axis 314 to provide an expanded configuration. In an expanded configuration, the folding wall regions 310 form folding walls and the nonrotating beam regions 308 form nonrotating beams. The folding wall regions 310 between slits 306 in adjacent rows at least partially define the folded walls in the expanded configuration. The sheet 300 also has one or more nonrotating beams in the expanded configuration. In particular, in the expanded configuration, at least one nonrotating beam of sheet material may be defined in at least one row between expanded slits. In the illustrated embodiment, the nonrotating beam regions 308 between adjacent slits in the same row at least partially define the nonrotating beams in the expanded configuration.

[0052] The slit pattern may include slits having one or more types of shapes. In the illustrated embodiment, all the slits 306 in the slit pattern 304 have the same, or substantially the same, shape. In particular, each slit 306 may be described as including a single segment 318 having multiple gradual bends (e.g., curves) and two terminal ends 320. Alternatively, each slit 306 may be described as including multiple segments connected by gradual segment intersections. For example, each slit 306 may be described as having four vertical linear segments and three horizontal linear segments connected by gradual segment intersections, such as segment intersection 336, segment intersection 338, and segment intersection 340, and two terminal ends 320. Slits having only two terminal ends 320 may be described as simple slits, such as slits 306.

[0053] Each slit 306 has at least four vertical distal end portions. As used herein, a "vertical distal end portion" means a portion along a slit within 33%, 25%, 20%, 15%, 10%, or even 5% of a slit height from a vertical extremum (e.g., maximum or minimum along the vertical axis) of the slit. As illustrated, one non-terminal vertical distal end portion 324 of the slit 306 is shown encircled by a dashed line and one terminal vertical distal end portion 322 of the slit 306 is shown encircled by a dashed line in FIG. 3B, each representing approximately 20% of the slit height 328.

[0054] As used herein, the term "slit height" means a total height of the slit measured from a lower extremum to an upper extremum along or parallel to the vertical axis. As illustrated, the slit height 328 of slit 306 is measured parallel to the vertical axis 314. In the illustratedembodiment, the vertical distal end portions 322, 324 are defined as any portion along the slit 306 within about 20% of the slit height 328 as illustrated by dashed line boxes each representing one type of vertical distal end portion.

[0055] At least one of the vertical distal end portions of each slit 306 has a nonterminal segment. In some embodiments, at least one of the vertical distal end portions of each slit 306 includes a terminal end, such as terminal end 320. In the illustrated embodiment, each slit 306 includes four vertical distal end portions with two terminal vertical distal end portions 322 and two non-terminal vertical distal end portions 324.

[0056] As illustrated, the slit 306 includes two non-terminal vertical distal end portions 324 and two terminal vertical distal end portions 322. In particular, the non-terminal vertical distal end portions 324 include upper extremums of the slit 306, and the terminal vertical distal end portions 322 include lower extremums of the slit 306. As used herein, the term "non-terminal vertical distal end portion" refers to a vertical distal end portion of the slit that does not include a terminal end, whereas a "terminal vertical distal end portion" includes a terminal end.

[0057] Vertical distal end portions of the slits in adjacent rows intersect a horizontal line. As perhaps best seen in FIG. 3A, the terminal vertical distal end portions in one row and the nonterminal vertical distal end portions in the adjacent row intersect the horizontal line 332. All slits in a first row and all the slits in a second, adjacent row may have vertical distal end portions that intersect a single horizontal line. In some embodiments, in particular, the vertical extremums of the slits intersect the horizontal line. However, in some embodiments, the adjacent rows of slits may overlap up to 1, 2, 5, or even 10%.

[0058] The slits may also be defined as including horizontal distal end portions. The slit 306 includes two horizontal distal end portions 326. As used herein, a "horizontal distal end portion" means a portion along a slit within 33%, 25%, 20%, 15%, 10%, or even 5% of a slit width from a horizontal extremum (e.g., maximum or minimum along the horizontal axis) of the slit. As illustrated, one horizontal distal end portion 326 of the slit 306 is shown encircled by a dashed line is shown encircled by a dashed line in FIG. 3B representing approximately 33% of the slit width 330.

[0059] As used herein, the term "slit width" means a total width of the slit measured from a first side extremum to a second, opposite side extremum measured along or parallel to the horizontal axis. As illustrated, the slit width 330 of the slit 306 is measured parallel to the horizontal axis 316. In the illustrated embodiment, the vertical distal end portions 322, 324 are defined as any portion along the slit 306 within about 20% of the slit height 328 as illustrated by dashed line boxes each representing one type of vertical distal end portion.

[0060] The width of each horizontal distal end portion may be defined relative to an overlap distance between slits in adjacent, staggered rows. In general, the width of each horizontal distalend portion is less than an overlap distance L (FIG. 3A) between the slit and a slit in an adjacent row. The overlap distance L is measured from a horizontal extremum of a slit in a direction along the horizontal axis 316 and horizontal extremum of the adjacent slit along the horizontal axis 316. In some embodiments, the width of each horizontal distal end portion 326 is approximately L / 2, such as L / 2 ± 30, 20, 15, 10, or 5% of L. In other words, the width of the horizontal distal end portion 326 can range from 20% to 80%, 30% to 70%, 35% to 65%, 40% to 60%, or 45% to 55% of L.

[0061] Each horizontal distal end portion may be described as having at least one vertical distal end portion. In the illustrated embodiment, each horizontal distal end portion 326 includes two vertical distal end portions. In particular, each horizontal distal end portion 326 includes a first vertically distal portion (e.g., terminal vertical distal end portion 322) and a second vertical distal end portion (e.g., non-terminal vertical distal end portion 324) opposite the first vertically distal portion.

[0062] The horizontal distal end portions 326 are connected by a connector portion 334 of the slit. Because the rows are staggered, the connector portion 334 of each slit 306 and a nonrotating beam region 308 in an adjacent row may be aligned to intersect a vertical line, which is generally parallel to the vertical axis.

[0063] Each slit 306 has at least one segment between distal portions. The segment may be linear or non-linear. In the illustrated embodiment, the slits 306 each include a vertical segment between two vertical distal end portions, such as vertical distal end portions 322, 324. The vertical segment may extend at least partially in along the vertical axis 314 more than the horizontal axis 316. Also, as illustrated, the slits 306 each include a horizontal segment (e.g., connector portion 334). The horizontal segment may extend at least partially along the horizontal axis 316 more than the vertical axis 314. In some embodiments, the slits include at least one nonlinear vertical segment, at least one nonlinear horizontal segment, or any combination of these (see FIG. 8A).

[0064] Slits may be oriented in various ways to align different types of vertical distal end portions. In the illustrated embodiment, all the terminal vertical distal end portions 322 in a row are aligned to intersect the horizontal line 332, and the non-terminal vertical distal end portions 324 of an adjacent row are aligned to intersect the same horizontal line.

[0065] FIG. 4A and FIG. 4B show a flat configuration 402 and an expanded configuration 406, respectively, of an expandable sheet having a slit pattern 404. The slit pattern 404 has a similar orientation of slits as slit pattern 304. However, each slit in the slit pattern 404 includes segment intersections with different curvatures. The segment intersections adjacent to the nonrotating beam regions are sharper, or tighter, than the other segment intersections.

[0066] FIG. 5A and FIG. 5B show a flat configuration 502 and an expanded configuration 506, respectively, of an expandable sheet having a slit pattern 504, in which the slits generally have an "N" or "Z" shape instead of the generally "H" or "M" shape of the slits in the slit pattern 304 and the slit pattern 404. In the illustrated embodiment, the slit pattern 504 has slits in a first row each having a non-terminal vertical distal end portion and a terminal vertical distal end portion aligned to a horizontal line 508, and the slits in an adjacent row also each have a non-terminal vertical distal end portion and a terminal vertical distal end portion aligned to the horizontal line 508. The slits within each row also have an alternating pattern of inverted and non-inverted slits. The inverted slits may be described as being inverted across a vertical line parallel to a vertical axis or across a horizontal line parallel to a horizontal axis (e.g., any horizontal line, not necessarily the horizontal line 508 depicted). The segment intersections of the slit pattern 504 are similar to the segment intersections of the slit pattern 404.

[0067] FIG. 6A and FIG. 6B show a flat configuration 602 and an expanded configuration 606, respectively, of an expandable sheet having a slit pattern 604, in which the slits generally have an "N" or "Z" shape. In the illustrated embodiment, the slits of the slit pattern 604 each have a connector portion that extends from an upper vertical extremum on a first side to a lower vertical extremum on a second side, whereas the slit pattern 504 has a generally horizontal connector portion. The connector portion is generally linear. Each slit of the slit pattern 604 may also be described as having sharper segment intersections than the slit pattern 304.

[0068] FIG. 7A and FIG. 7B show a flat configuration 702 and an expanded configuration 706, respectively, of an expandable sheet having a slit pattern 704, in which the slits generally have an "N" or "Z" shape. In the illustrated embodiment, the slits of the slit pattern 704 have the same shape as the slits of the slit pattern 604 but an alternating pattern within each row. The slits within each row have an alternating pattern of inverted and non-inverted slits. The inverted slits may be described as being inverted across a vertical line parallel to a vertical axis or across a horizontal line parallel to a horizontal axis.

[0069] FIG. 8A and FIG. 8B show a flat configuration 802 and an expanded configuration 806, respectively, of an expandable sheet having a slit pattern 804, in which the slits generally have an "H" or "M" shape. In the illustrated embodiment, the slits of the slit pattern 804 have nonlinear segments, including a nonlinear horizontal segment (e.g., connector portion) and nonlinear vertical segments between terminal ends. The rows of the slit pattern 804 have an alternating pattern of inverted and non-inverted rows of slits. The orientation of the slits in a first row are inverted relative to the orientation of slits in a second adjacent row. For example, as illustrated, the non-terminal vertical distal end portions of two rows intersect a same horizontal line.

Claims

CLAIMSWhat is claimed is:

1. A sheet defining a vertical axis and a horizontal axis along a major surface, the sheet comprising: a substrate of sheet material defining the major surface; and a plurality of expandable slits formed in the substrate in a repeating pattern comprising at least a first row of the slits and a second row of the slits adjacent to the first row, wherein each slit defines a slit height along the vertical axis and a slit width along the horizontal axis, wherein each slit comprises four vertical distal end portions, at least one of the vertical distal end portions has a non-terminal end and at least two of the vertical distal end portions have terminal ends, wherein a plurality of the vertical distal end portions in the first row and a plurality of the vertical distal end portions in the second row are aligned to intersect a horizontal line, wherein the slits are configured to open in response to a minimum tension applied to the substrate along the vertical axis to form a plurality of folding walls and a plurality of nonrotating beams.

2. The expandable sheet of claim 1, wherein each slit is free of sharp segment intersections.

3. The expandable sheet of claim 1 or 2, wherein each slit comprises a connector portion extending at least partially along the horizontal axis between two of the vertical distal end portions of the slit, wherein the connector portion and a nonrotating beam region in an adjacent row are aligned to intersect a vertical line .

4. The expandable sheet of any one of claims 1 to 3, wherein each slit has only two terminal ends.

5. The expandable sheet of any one of claims 1 to 4, wherein each slit comprises two horizontal distal end portions each comprising two of the vertical distal end portions of the slit.

6. The expandable sheet of any one of claims 1 to 5, wherein the plurality of slits defines a plurality of nonrotating beam regions, each nonrotating beam region positioned between adjacent slits in the same row.

7. The expandable sheet of claim 6, wherein each nonrotating beam region is defined at least partially between two vertical distal end portions of a first slit and two vertical distal end portions of a second slit adjacent to the first slit in the same row.

8. The expandable sheet of claim 7, wherein one vertical distal end portion of the first slit has a non-terminal end aligned to intersect a horizontal line and one vertical distal end portion of the second slit has a non-terminal end aligned to intersect the same horizontal line.

9. The expandable sheet of claim 7, wherein one vertical distal end portion of the first slit has a non-terminal end aligned to intersect a horizontal line and one vertical distal end portion of the second slit has a terminal segment aligned to intersect the same horizontal line.

10. The expandable sheet of any one of claims 1 to 9, wherein the repeating pattern comprises a repeating region within the repeating pattern, the repeating region comprising at least two staggered rows of the slits.

11. The expandable sheet of claim 10, wherein the repeating region includes at least one inverted slit in the same row or an adjacent row to at least one noninverted slit.

12. The expandable sheet of claim 11, wherein the at least one inverted slit is an inversion across a horizontal line.

13. The expandable sheet of any one of claims 10 to 12, wherein the repeating region repeats at least two times along at least one row of the slits in the repeating pattern, at least two times along the vertical axis in the repeating pattern, or both.

14. A roll comprising the expandable sheet according to any preceding claim.

15. A rotary die comprising cutting surfaces configured to form the expandable sheet according to any one of any one of any one of claims 1 to 13.

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