Expandable sheet

Abstract

The present disclosure provides 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 further includes a pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration. Each slit is configured to open in response to a minimum tension applied to the substrate along one or more axes. Each slit has curvature and a bounding box whose aspect ratio is in the range of 1:1 to 10: 1. The slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a same gap between the parallel slits.

Description

EXPANDABLE SHEETTechnical Field

[0001] The present disclosure relates generally to sheets and, in particular, to expandable sheets with a plurality of slits configured to expand into a three-dimensional structure. 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 one or more axes of the sheet.Background

[0002] Many applications require bundling of objects. Some mechanisms are often required to hold objects together in groups during the process of manufacturing, sorting, transporting, or selling items. For example, many retailers will group multiple items together or bundle them, to be sold as a single item. In warehouses, it may be helpful to group objects together for storage or transport. Even putting items on a pallet generally requires some form of bundling wrap to hold the items together.

[0003] Traditionally, bundling is achieved using plastic stretch wraps or adhesive tapes. Stretch wraps, which are widely used to secure palletized goods, rely on the elastic properties of thin plastic films to tightly hold items in place. Adhesive tapes are commonly used to bind smaller item sets. However, both methods typically involve single-use plastic materials, raising environmental sustainability concerns. In particular, adhesive-based bundling solutions may also leave behind sticky residues, which can damage surfaces or degrade the appearance and usability of the items being bundled.Summary

[0004] In a first aspect, the present disclosure provides 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 further includes a pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration. Each slit is configured to open in response to a minimum tension applied to the substrate along one or more axes. Each slit has curvature and a bounding box whose aspect ratio is in the range of 1: 1 to 10: 1. The slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a same gap between the parallel slits.

[0005] In a second aspect, the present disclosure provides 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 further includes a pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration. The sheet between the slits is in an expanded state in an angle in the range of 5 degrees to 85 degrees in response to a minimum tension applied to the substrate along one or more axes. Each slit has curvature and a bounding box whose aspect ratio is in the range of 1: 1 to 10: 1. The expanded slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a similar gap between the parallel slits.

[0006] In a third aspect, the present disclosure provides a method of manufacturing a sheet defining a vertical axis and a horizontal axis along a major surface. The method includes providing a substrate of sheet material defining the major surface. The method further includes creating a pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration. Each slit opens in response to a minimum tension applied to the substrate along one or more axes. Each slit has curvature and a bounding box whose aspect ratio is in the range of 1: 1 to 10: 1. The slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a similar gap between the parallel slits.

[0007] The details of one or more examples of the disclosure are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the disclosure will be apparent from the description and drawings, and from the claims.Brief Description of the Drawings

[0008] Exemplary embodiments disclosed herein may be more completely understood in consideration of the following detailed description in connection with the following figures. The figures are not necessarily drawn to scale. Like numbers used in the figures refer to like components. However, it will be understood that the use of a number to refer to a component in a given figure is not intended to limit the component in another figure labeled with the same number.

[0009] FIG. 1A is an illustration of a sheet depicting a kirigami pattern of slits;

[0010] FIG. IB is an illustration of a sheet depicting another kirigami pattern of slits;

[0011] FIG. 1C is an illustration of a sheet depicting another kirigami pattern of slits;

[0012] FIG. ID is a top view schematic drawing of a compound slit pattern named as folding -wall pattern with fingers;

[0013] FIG. IE is an illustration of a sheet depicting a non-reversing hook single slit pattern;

[0014] FIG. IF is an illustration of a sheet depicting a non-reversing hook double slit pattern;

[0015] FIG. 1G is an illustration of a sheet depicting a basic single slit pattern;

[0016] FIG. 2A is a schematic diagram depicting different design alternatives for reversing hooks, in accordance with an embodiment of the present disclosure;

[0017] FIG. 2B is an illustration of a sheet depicting a pattern of reversing hook double slit pattern with a multi -beam, in accordance with an embodiment of the present disclosure.

[0018] FIG. 3 A is an illustration of a sheet depicting dual -axis dual-slit geometry, in accordance with an embodiment of the present disclosure;

[0019] FIG. 3B is an illustration of the sheet of FIG. 3A when the sheet is subjected to a strain in horizontal and vertical axes equally to obtain a one-degree rotation, in accordance with an embodiment of the present disclosure;

[0020] FIG. 3 C is an illustration of the sheet of FIG. 3 A when the sheet is subjected to a strain in horizontal and vertical axes equally to obtain a ten-degree rotation, in accordance with an embodimentof the present disclosure;

[0021] FIG. 3D is an illustration of the sheet of FIG. 3A when the sheet is subjected to a strain in horizontal and vertical axes equally to obtain a twenty-degree rotation, in accordance with an embodiment of the present disclosure;

[0022] FIG. 3E is illustration of the sheet of FIG. 3A when the sheet is subjected to a strain in horizontal and vertical axes equally to obtain a forty-five-degree rotation, in accordance with an embodiment of the present disclosure;

[0023] FIG. 3F is an illustration depicting a sheet having a first dual-axis dual-slit orthogonal pattern that marginally allows force to be transmitted along with horizontal and vertical axes, in accordance with an embodiment of the present disclosure;

[0024] FIG. 3G is an illustration depicting a sheet having a second dual-axis dual-slit orthogonal pattern that allows force to be transmitted along with horizontal and vertical axes, in accordance with an embodiment of the present disclosure;

[0025] FIG. 4A is an illustration depicting a sheet having a dual-axis dual-slit non-orthogonal pattern, in accordance with an embodiment of the present disclosure;

[0026] FIG. 4B is an illustration depicting a sheet having a dual-axis dual-slit parallel slit non- orthogonal pattern, in accordance with an embodiment of the present disclosure;

[0027] FIG. 4C is an illustration depicting a sheet having a dual-axis dual-slit non-orthogonal pattern with slits having terminal ends along the primary axes with no direct path for the axes, in accordance with an embodiment of the present disclosure;

[0028] FIG. 4D is an illustration depicting a sheet having a dual-axis dual non-orthogonal pattern with slits having terminal ends along the primary axes, in accordance with an embodiment of the present disclosure;

[0029] FIG. 5A is an illustration depicting a sheet having rectangular dual-axis dual-slit patterns and fat slits, in accordance with an embodiment of the present disclosure;

[0030] FIG. 5B is an illustration depicting a sheet having rectangular dual-axis dual-slit patterns and fat slits and wings, in accordance with another embodiment of the present disclosure;

[0031] FIG. 6A is an illustration depicting a sheet having a dual -axis dual-slit hook 60-degree pattern in accordance with an embodiment of the present disclosure;

[0032] FIG. 6B is an illustration depicting a close-up view of the pattern depicted in FIG. 6A in accordance with an embodiment of the present disclosure;

[0033] FIG. 7A is an illustration depicting a sheet having a dual-axis hook 60-degree pattern in which terminal ends are not on the axes, in accordance with an embodiment of the present disclosure;

[0034] FIG. 7B is an illustration depicting a close-up view of a dual-axis hook 60-degree pattern of FIG. 7A in which terminal ends are not on the axes, in accordance with an embodiment of the present disclosure;

[0035] FIG. 8A is an illustration depicting a sheet having dual-axis dual-slit hook 90-degree patternwith terminal ends aligned along the axes, in accordance with an embodiment of the present disclosure;

[0036] FIG. 8B is a front view of the pattern of FIG. 8A being deployed along one axis in accordance with an embodiment of the present disclosure;

[0037] FIG. 8C is a side view of the pattern of FIG. 8A being deployed in accordance with an embodiment of the present disclosure;

[0038] FIG. 8D is a perspective view of the pattern of FIG. 8 A being deployed in accordance with an embodiment of the present disclosure;

[0039] FIG. 8E is another side view of the pattern of FIG. 8A being deployed in accordance with an embodiment of the present disclosure;

[0040] FIG. 9A is an illustration depicting a sheet having a dual-axis hook 75 -degree angle pattern in which terminal ends are shifted slightly, in accordance with an embodiment of the present disclosure;

[0041] FIG. 9B is an illustration depicting a close-up view of the dual-slit, dual -axis, long hook of FIG. 9A, in accordance with an embodiment of the present disclosure;

[0042] FIG. 10A is an illustration depicting a sheet having a dual -axis hook 60-degree angle pattern in a non-deployed state with splines to create uniform gaps, in accordance with an embodiment of the present disclosure;

[0043] FIG. 10B is a front view of the pattern depicted in FIG. 10A as deployed, in accordance with an embodiment of the present disclosure;

[0044] FIG. 10C is a side view of the pattern FIG. 10A as deployed, in accordance with an embodiment of the present disclosure;

[0045] FIG. 10D is another side view of the pattern FIG. 10A as deployed, in accordance with an embodiment of the present disclosure;

[0046] FIG. 10E is a perspective view of the pattern FIG. 10A as deployed, in accordance with an embodiment of the present disclosure;

[0047] FIG. 11 A is an illustration depicting a sheet having a dual-slit, dual-axis, dual-hook pattern in a non-deployed state, in accordance with an embodiment of the present disclosure;

[0048] FIG. 1 IB is a front view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11 A deployed in accordance with an embodiment of the present disclosure;

[0049] FIG. 11C is a side view of the dual-slit, dual -axis, dual -hook pattern of FIG. 11A deployed in accordance with an embodiment of the present disclosure;

[0050] FIG. 11D is another side view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11A deployed in accordance with an embodiment of the present disclosure;

[0051] FIG. HE is a perspective view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11A deployed in accordance with an embodiment of the present disclosure;

[0052] FIG. 1 IF is another side view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11A deployed in accordance with an embodiment of the present disclosure;

[0053] FIG. 12A is an illustration depicting a sheet having a dual-slit, dual-axis, long hook with wingsin a non-deployed state, in accordance with an embodiment of the present disclosure;

[0054] FIG. 12B is an illustration of the sheet of FIG. 12A in a deployed state, in accordance with an embodiment of the present disclosure;

[0055] FIG. 13A is an illustration depicting a sheet having a dual-axis single slit pattern of slits in a non-deployed state, in accordance with an embodiment of the present disclosure;

[0056] FIG. 13B is a perspective view of the pattern of FIG. 13A as deployed, in accordance with an embodiment of the present disclosure;

[0057] FIG. 14A is an illustration depicting a sheet having dual -hook dual-axis multi-slit pattern with shifting, in accordance with an embodiment of the present disclosure;

[0058] FIG. 14B is an illustration depicting the pattern of FIG. 14A in a zoomed-out view.

[0059] FIG. 14C is a side view of the pattern of FIG. 14A as deployed in accordance with an embodiment of the present disclosure.

[0060] FIG. 14D is a perspective view of the pattern of FIG. 14A as deployed in accordance with an embodiment of the present disclosure

[0061] FIG. 15A is an illustration depicting a sheet having a single-slit hook pattern;

[0062] FIG. 15B is a top view of the dual-slit hook pattern of FIG. 15A as deployed;

[0063] FIG. 15C is a perspective view of the dual-slit hook pattern of FIG. 15A as deployed;

[0064] FIG. 15D is another perspective view of the dual-slit hook pattern of FIG. 15A as deployed;

[0065] FIG. 15E is another top view of the dual-slit hook pattern of FIG. 15A as deployed;

[0066] FIG. 16A is an illustration depicting a sheet having a dual -axis dual-slit first rectangular pattern of hooks, in accordance with an embodiment of the present disclosure;

[0067] FIG. 16B is an illustration depicting a sheet having dual -axis dual-slit second rectangular pattern of hooks, in accordance with another embodiment of the present disclosure;

[0068] FIG. 17A is an illustration depicting a sheet having dual-slit dual -axis dual -hook pattern, in accordance with an embodiment of the present disclosure;

[0069] FIG. 17B is an illustration depicting a close-up view of the pattern of FIG. 17A, in accordance with an embodiment of the present disclosure;

[0070] FIG. 18A is an illustration depicting a sheet having a dual-axis dual-slit pattern with wings, in accordance with an embodiment of the present disclosure;

[0071] FIG. 18B is a front view of the entire pattern of FIG. 18A as deployed, in accordance with an embodiment of the present disclosure;

[0072] FIG. 18C is a side view of the pattern of FIG. 18A as deployed, in accordance with an embodiment of the present disclosure;

[0073] FIG. 18D is a perspective view of the pattern of FIG. 18A as deployed, in accordance with an embodiment of the present disclosure;

[0074] FIG. 19 is an illustration depicting a sheet having a dual-axis dual -hook triple-slit pattern, in accordance with an embodiment of the present disclosure;

[0075] FIG. 20A is a photograph depicting an expanded sheet utilizing a deployed pattern wrapped around objects, in accordance with an embodiment of the present disclosure;

[0076] FIG. 20B is a photograph depicting an expanded sheet utilizing a deployed pattern to securely bundle several objects together, in accordance with another embodiment of the present disclosure;

[0077] FIG. 20C is a graph depicting comparison of overlap grip strength and tear strength of different sheets;

[0078] FIGS. 21A to 21F illustrate an exemplary application of a sheet having reversing hook slit patterns to bundle a collection of books, in accordance with an embodiment of the present disclosure;

[0079] FIGS. 22A to 22E illustrate an exemplary application of a sheet to secure closure of a bag containing a plurality of items, in accordance with an embodiment of the present disclosure;

[0080] FIGS. 23A to 23D illustrate a multi-layer overlapping phenomenon, in accordance with an embodiment of the present disclosure;

[0081] FIG. 24 illustrates an exemplary application of a sheet to secure a wearable object, in accordance with an embodiment of the present disclosure;

[0082] FIGS. 25A to 25C illustrate a user wearing a face mask secured by utilizing a sheet, in accordance with an embodiment of the present disclosure;

[0083] FIGS. 26A to 26C illustrate a user wearing a shirt having an arm cuff secured by utilizing a sheet, in accordance with an embodiment of the present disclosure;

[0084] FIGS. 27A to 27C illustrate a diaper secured by utilizing a sheet, in accordance with an embodiment of the present disclosure; and

[0085] FIG. 28 is a flow chart of a method for manufacturing a sheet defining a vertical axis Y-Y and a horizontal axis X-X along the major surface.Detailed Description

[0086] In the following description, reference is made to the accompanying FIG. s that form a part thereof and in which various embodiments are shown by way of illustration. It is to be understood that other embodiments are contemplated and may be made without departing from the scope or spirit of the present disclosure. The following detailed description, therefore, is not to be taken in a limiting sense.

[0087] In the following disclosure, the following definitions are adopted.

[0088] As used herein, all numbers should be considered modified by the term “about”. As used herein, “a,” “an,” “the,” “at least one,” and “one or more” are used interchangeably.

[0089] The term “about”, unless otherwise specifically defined, means to a high degree of approximation (e.g., within + / - 5% for quantifiable properties) but again without requiring absolute precision or a perfect match.

[0090] As used herein as a modifier to a property or attribute, the term “generally”, unless otherwise specifically defined, means that the property or attribute would be readily recognizable by a person ofordinary skill but without requiring absolute precision or a perfect match (e.g., within + / - 20 % for quantifiable properties).

[0091] As used herein, “at least one of A and B” should be understood to mean “only A, only B, or both A and B”.

[0092] As used herein, “substantially” means “for the most part” relevant to the term being modified as would be understood by one of ordinary skill in the art.

[0093] As used herein, “corresponding” indicates that two structural components are sized and shaped similar to each other and can be coupled with a minimum amount of friction. Thus, an opening “corresponding” to a member is sized slightly larger than the member so that the member can pass through the opening with a minimum amount of friction. This definition is changed when the two components are said to “snugly” fit together or “just correspond”. In that situation, the difference between the sizes of those components is even smaller, thereby increasing the amount of friction.

[0094] 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 nonlinear, 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 a surface 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 inches (approximately 0.18 mm) thick might have slits with a gap that is approximately 0.007 inches 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.

[0095] As used herein, the term “compound slit” refers to a slit with more than two terminal ends, which is distinguished from a “simple slit,” which is defined herein as a slit with exactly two terminal ends. Compound slits have at least two slit segments with at least one segment intersection. As such, a “compound slit pattern” is a pattern including a plurality of individual slits at least some of which are compound slits. In some embodiments, the pattern includes a plurality of rows of slits that are phase offset from one another. In some embodiments, the slits are substantially perpendicular to the tension axis.

[0096] 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.

[0097] “Kirigami” is a name for cuting and folding paper and is used to describe the technology where slits are added to flat sheets of material to create some new functionality in those sheets. 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. Tension-activated, expandable sheets are sheets, for example of paper or plastic, that are cut with a slit patern enabling them to be expanded when tension is applied along one or more axes of the sheet. Rows of paterns may be at any orientation with respect to the sheet in various embodiments. The plurality of slits deploy in an expanded state in response to a minimum tension applied to the substrate along one or more axes.

[0098] The present disclosure provides 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 further includes a patern of slits formed in the substrate in a repeating patern based on the sheet being in a flat configuration. Each slit is configured to open in response to a minimum tension applied to the substrate along one or more axes. Each slit has curvature and a bounding box whose aspect ratio is in the range of 1: 1 to 10: 1. The slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a similar gap between the parallel slits.

[0099] The sheet of the present disclosure may be used as cushioning material or a filler material to protect fragile or sensitive objects during transit into shipping containers. Presence of the curvature and the bounding box in the slits may advantageously reduce the deployment force and allow the patern to stretch out farther (i.e., increased maximum strain). This may also create more springiness to the patern.

[0100] The paterns disclosed herein are useful for creating a deployable self-gripping tape, or a mechanical tape. The paterns can be cut into any appropriate material and then provided in a sheet or roll form. The material then deploys (or expands) when tension is applied, such as when pulling off the roll. Two or more layers of the material can be wrapped around any object, a set of objects, or the material itself as one might normally use adhesive tape. The material in its deployed form will stick to itself strongly without the need for adhesives. This can be advantageous for applications where adhesive is undesirable, such as with sensitive items, or human skin. In addition, because the adhesion is achieved mechanically, the material properties of the substrate (sheet material) can be adjusted to include a range of materials that are not normally used, such as more sustainable options or biocompatibility. Since the paterns disclosed herein also increase the extensibility and modify the stiffness (or stretchiness) of the material, the substrate (sheet material) can have an even wider range of properties that can be tailored with these paterns.

[0101] Some embodiments herein utilize exemplary, non-adhesive, tension-activated expandable sheets having a substrate of sheet material defining the major surface into which a kirigami patern of non-deployed kirigami paterns may be cut. The sheet may be stored in a roll or any other suitable manner. In some embodiments, non-adhesive, tension-activated expandable sheets may have a substrate of sheet material defining the major surface into which a kirigami patern of non-deployed single slit rows may be cut. In some embodiments, one or more of the slits include a curvilinear portion, and inother embodiments one or more of the slits comprise a hook portion. The hook portion can be reversing or non-reversing. The sheet may be stored in a roll or any other suitable manner. Tension may be applied lengthwise, for example. The sheet may comprise any suitable paper or plastic material(s). Any thin fdm sheet material may also be used in some embodiments, including metal foils, foams, woven or knit materials, multi-layered materials or any other sheet material. Upon application of tension to expand the sheet, portions of the sheet rotate to create a structure that deploys in a three-dimensional manner and can be used, for example, to bundle objects together during shipping. By way of non-limiting example, a range of rotation for sheet portions may be 5 degrees to 85 degrees, although any suitable range may be utilized in various embodiments.

[0102] Referring now to figures, FIG. 1A is an illustration of a sheet 100 depicting a kirigami pattern of slits 106. In FIG. 1A, the sheet 100 is shown in a pretensioned state SI. The “pretensioned state SI” is interchangeably referred as “flat configuration” or “non deployed state”. The sheet 100 is a nonadhesive, tension-activated expandable sheet. The sheet 100 may be made of paper. The sheet 100 may be made of plastic. The sheet 100 may be made of a woven or nonwoven fabric of natural fiber, for example, hemp / bamboo / coir etc. for sustainability.

[0103] As shown in FIG. 1A, the sheet 100 defines a vertical axis Y-Y and a horizontal axis X-X along a major surface 102. The sheet 100 includes a substrate 104 of sheet material defining the major surface 102. The sheet 100 further includes a pattern of slits 106 or a plurality of slits 106 formed in the substrate 104 in a repeating pattern based on the sheet 100 being in a flat configuration. The slits 106 are arranged in a plurality of rows 108. The plurality of rows 108 may be arrayed along the vertical axis Y-Y. The slits 106 in FIG. 1A are shown with some as a physical opening in the sheet 100 to illustrate the fact that some material may have been removed to create the slit 106. The pattern of slits 106 includes a plurality of solid regions 114 separated by the slits 106. The solid regions 114 include islands 116 of a substantially square shape and long rectangular bridges 118. Each island 116 is connected to each adjacent island 116 by one bridge 118 respectively.

[0104] FIG. IB is an illustration of a sheet 100’ depicting another kirigami pattern of slits 106’. The sheet 100’ is substantially similar to that of the sheet 100 of FIG. 1A, with common components being referred to by the same numerals. However, the sheet 100’ includes a pattern of slits 106’ different from the pattern of slits 106 in the sheet 100 of FIG. 1A.

[0105] As shown in FIG. IB, the pattern of slits 106’ includes a plurality of open slits 106’ and a plurality of solid regions 114’. The plurality of solid regions 114’ includes islands 116’. Each island 116’ is connected to each adjacent island 116’ by one bridge 118’ respectively. Moreover, in the sheet 100’, the islands 116’ formed by the slits 106’ are arranged in a hexagonally-packed arrangement with a repeat unit having six triangular islands 116’ arranged into a hexagon and a portion of the bridges 118’ extending therefrom to adjacent islands 116’.

[0106] FIG. 1C is an illustration of a sheet 100” depicting another kirigami pattern of slits 106”. The sheet 100” is substantially similar to that of the sheet 100 of FIG. 1A, with common components beingreferred to by the same numerals. However, the sheet 100” includes a pattern of slits 106” different from the pattern of slits 106 in the sheet 100 of FIG. 1A.

[0107] As shown in FIG. 1C, the pattern of slits 106” creates a plurality of solid regions 114”. The plurality of solid regions 114” includes islands 116” of a substantially square shape. Each island 116” is connected to each adjacent island 116” by one bridge 118” respectively.

[0108] FIGS. 1A to 1C show kirigami patterns that generally have conformability and easily extend in multiple axes, but they do not have regions that rotate out of the original plane very far to create 3D structures that might interlock with adjacent features. However, these slit patterns also do not contain any hooks to create excellent interlocking.

[0109] FIG. ID is a top view schematic drawing of a compound slit pattern of slits 206, named as folding -wall pattern with fingers. As shown, the slit 206 is a compound slit with more than two terminal ends. In the illustrated embodiment of FIG. ID, the slit 206 has four terminal ends 117. It should be noted that a sheet 100 may include multiple slits 206 similar to the slits 106 shown in FIG. 1A. Further, the multiple slits 206 may be arranged in a plurality of rows (not shown). The slit pattern of FIG. ID and in particular the oscillations or fingers have been shown to create some enhancement to the interlocking strength over straight lines without the oscillations or fingers.

[0110] FIG. IE is an illustration of a sheet 200 depicting a non-reversing hook single slit pattern. FIG. IF is an illustration of a sheet 200’ depicting a non-reversing hook double slit pattern. The sheet 200 (shown in FIG. IE) includes a pattern of slits 206’, and the sheet 200’ (shown in FIG. IF) includes a pattern of slits 206” different from the pattern of slits 206’. Referring to FIGS. IE and IF, each slit 206’, 206” is oriented along a horizontal midline path MP. Each slit 206’, 206” includes a hook. Specifically, each slit 206’, 206” includes a non-reversing hook 120. In FIG. IE, the non-reversing hook slits 206’ are arranged in single slit rows. However, in FIG. IF, the non-reversing hook slits 206” are arranged in double slit rows. Further, each non-reversing hook 120 (shown in FIGS. IE and IF) includes a stem region 122, a cap region 124, and at least one horizontal non-reversing region 128.

[0111] The patterns of FIGS . 1 E and 1 F have been shown to exhibit improvement in interlocking when compared to similar patterns with smooth continuous lines. An additional improvement in the interlocking of such patterns can be achieved by converting the non-reversing hooks 120 into reversing hooks 120’ (will be described with reference to FIG. 2A), where the flat non-reversing region 128 is replaced by a reversing region 126.

[0112] FIG. 1G is an illustration of a sheet 210 depicting a basic single slit pattern. The sheet 210 includes the basic single slit pattern including slits 212.

[0113] FIG. 2A is a schematic diagram depicting different design alternatives for reversing hooks 120’, in accordance with an embodiment of the present disclosure. As shown, the reversing hook 120’ includes a cap region 124, a stem region 122, and at least one reversing region 126. As shown in FIG. 2A, the reversing region 126 moves away from the cap region 124, reverses direction, and joins the stem region 122. Accordingly, the cap region 124 is disposed between both reversing regions 126. Thenon-reversing region 128 (shown in FIGS. IE and IF) by comparison does not move away from the cap region 124. Each of the cap region 124, the stem region 122, and the reversing region 126 may have different shapes which are shown in different rows of FIG. 2A.

[0114] First row R1 depicts various shapes for the cap regions 124. It is shown and contemplated that the cap region 124 may have different shapes, such as, round, orthogonal point, sharp point, and rectangular, by way of non-limiting example, although any other suitable type of cap region 124 may also be utilized. Second row R2 depicts various shapes for the reversing region 126. As shown, the reversing region 126 may take any suitable shape / style that protrudes downward past the top of the stem region 122. In various embodiments, the reversing region 126 generally moves away from the cap region 124, and then reverses direction towards the cap region 124 before joining the stem region 122.

[0115] Third row R3 depicts various shapes for the stem region 122. The stem region 122 may also take any suitable shape / design as shown in the third row R3. Fourth row R4 depicts different shapes for reversing hooks 120’ as per different cap regions 124, reversing regions 126, and stem regions 122 in the above three rows. It should be noted that the design of each of the cap region 124, the reversing region 126, and the stem region 122 may be interchangeable in various embodiments and any other suitable shape(s) / design(s) may be utilized.

[0116] FIG. 2B is an illustration of a sheet 220 depicting a pattern of reversing hook double slit pattern with a multi -beam, in accordance with an embodiment of the present disclosure. As shown, the sheet 220 includes the multi -beam, double slit pattern of the plurality of reversing hooks 120’ formed by slits 222.

[0117] The kirigami designs described in the following description may include hooks that are of the reversing or non-reversing type. In general, the reversing hooks 120’ have superior interlocking performance to non-reversing hooks 120. However, non-reversing hooks 120 may also have advantages such as requiring a lower force to deploy the pattern via tension activation.

[0118] FIG. 3A is an illustration of a sheet 300 depicting dual-axis dual-slit geometry, in accordance with an embodiment of the present disclosure. The sheet 300 includes a pattern of slits 306. The dualaxis dual-slit geometry is characterized by the presence of three independent design variables. By way of non-limiting example, the selection of design variables for the configuration depicted in FIG. 3A may comprise W, L, R and H as defined by in FIG. 3A. R is the gap between two parallel slits 306, H is the offset distance between parallel adjacent sets of parallel slits 306, L is the overlap distance between parallel adjacent sets of parallel slits 306, and W is gap width between adjacent colinear slits 306. There is an inherent relationship between these variables, so only 3 free choices exist. For example, if W, L and R are chosen, then H is defined by the relationship H=L+W-R. Alternatively, the selection of design variables may comprise H, W, and R, wherein L is defined by the relationship L=H-W+R. This exemplary pattern creates a pattern of square regions 308 with dimensions of H by H and rectangular regions 310 with dimensions of R by (W+2*L). In FIG. 3A, one square region 308 and one rectangular region 310 are shown as shaded portions for illustrative purposes. This exemplary patternin which W>L>0 and R>0 may create undulations of the rectangular regions 310 with respect to two axes when force is applied in one or both axes (horizontal axis X-X and vertical axis Y-Y) or some combination thereof.

[0119] FIG. 3B is an illustration of the sheet 300 when the sheet 300 is subjected to a strain in any axis to obtain a one-degree rotation of the square regions 308, in accordance with an embodiment of the present disclosure. FIG. 3 C is an illustration of the sheet 300 when the sheet 300 is subjected to a strain to obtain a ten-degree rotation of the square regions 308, in accordance with an embodiment of the present disclosure. FIG. 3D is an illustration of the sheet 300 when the sheet 300 is subjected to a strain to obtain a twenty-degree rotation of the square regions 308, in accordance with an embodiment of the present disclosure. FIG. 3E is an illustration of the sheet 300 when the sheet 300 is subjected to a strain to obtain a forty-five-degree rotation of the square regions 308, in accordance with an embodiment of the present disclosure. In FIG. 3E, the sheet 300 is shown in a maximum expanded state S2 (interchangeably called the maximally deployed state S2).

[0120] In an embodiment, the sheet 300 between the slits 306 is in the expanded state S2 in an angle in the range of 5 degrees to 85 degrees in response to a minimum tension applied to the substrate 104 along one or more axes (i.e., X-X and Y-Y). The sheet 300 further includes a deployed region of slits 306 in the expanded state S2. In some embodiments, the sheet 300 further includes two deployed regions that grip each other. In some embodiments, the sheet 300 further includes a non-pattemed region between the two deployed regions. In some embodiments, the sheet 300 further includes a second sheet having a deployed region configured to grip one of the two deployed regions. In some embodiments, the sheet 300 further includes conformability of the sheet 300 in the deployed state S2.

[0121] FIGS. 3B to 3D show the basic pattern of the sheet 300 pulled in horizontal axis X-X and vertical axis Y-Y equally, with the undulations starting to emerge. In other words, in FIGS. 3B to 3D, the sheet 300 is neither in pretensioned state SI nor in the maximally deployed state S2, it is transitioning from the pretensioned state SI to the maximally deployed state S2 (i.e., it is in a partially deployed state S3). Specifically, FIG. 3B depicts the geometry pattern of the sheet 300 under application of a strain to obtain a one-degree rotation of the square region 308 with nominal dimensions of H by H. FIG. 3C depicts the geometry pattern of the sheet 300 under application of a strain to obtain a ten-degree rotation. FIG. 3D depicts the geometry pattern of the sheet 300 under application of a strain to obtain a twenty-degree rotation.

[0122] FIG. 3E depicts the geometry pattern of the sheet 300 reaching a full forty-five-degree rotation of the square elements, such that maximum undulation is reached, and there are straight paths 312 in both axes along which the force can act. Such straight paths 312 are illustrated as double arrow lines which are not a part of the slit pattern. Hence, the sheet is in its maximally deployed state S2 in FIG. 3E. In some embodiments, the undulations do not support tension forces, they are only in compression which is why they undulate.

[0123] FIG. 3F is an illustration depicting a sheet 300’ having a first dual-axis dual-slit orthogonalpatern of slits 306’ that have a value of L=0 that marginally allows force to be transmited along with the horizontal axis X-X and the vertical axis Y-Y, in accordance with an embodiment of the present disclosure. There are straight paths 312’ in both axes along which the force can act. Such straight paths 312’ are illustrated as double arrow lines which are not a part of the slit patern.

[0124] FIG. 3G is an illustration depicting a sheet 300” having a second dual-axis dual-slit orthogonal patern of slits 306” that has a value of L<0 that allows force to be transmited along with the horizontal axis X-X and the vertical axis Y-Y, in accordance with an embodiment of the present disclosure. There are straight paths 312” in both axes along which the force can act. Such straight paths 312” are illustrated as double arrow lines which are not a part of the slit patern

[0125] FIGS. 3F and 3G depict dual-axis dual-slit orthogonal paterns having slits 306’, 306” that allow force to be transmited along the horizontal axis X-X and vertical axis Y-Y. These paterns still have some extensibility in axes that are not aligned with the horizontal axis X-X and the vertical axis Y-Y. Additionally, using non-straight (curved or multi-segmented) lines for the slits, enables in embodiments a larger design space, where L=0 or even L<0 may be utilized, as shown in FIG. 7A for example. Designs in which L<0 have smaller undulations, or they tend to buckle rather than undulate, because there are already paths in the horizontal axis X-X and the vertical axis Y -Y that allow force to be transmited in those axes, as shown in FIGS. 3F to 3G. Even though the paterns in FIGS. 3F and 3G undulate less, they still have significant mobility in the diagonal axis. The lack of undulation can increase the amount of material transmiting forces and increase the tear strength of the embodiment.

[0126] FIG. 4A is an illustration depicting a sheet 400 having a dual-axis dual-slit non-orthogonal patern of slits 406, in accordance with an embodiment of the present disclosure. FIG. 4B is an illustration depicting a sheet 400’ having a dual -axis dual-slit parallel slit non-orthogonal patern 406’, in accordance with an embodiment of the present disclosure. FIG. 4C is an illustration depicting a sheet 400” having a dual -axis dual-slit non-orthogonal patern of slits 406”, in accordance with an embodiment of the present disclosure. The slits 406’ ’ include terminal ends along the primary axes with no direct path for the axes. FIG. 4D is an illustration depicting a sheet 400’” having a dual -axis dual non-orthogonal patern of slits 406 ” ’ , in accordance with an embodiment of the present disclosure . The slits 406’” include terminal ends along the primary axes.

[0127] FIGS. 4A to 4D depict non-orthogonal dual-axis dual-slit paterns, given that the two primary axes of the dual -axis dual-slit patern do not have to be orthogonal. Specifically, FIG. 4A depicts a non- orthogonal dual-axis dual-slit patern with a 60-degree angle (instead of 90-degrees) and shows the basic variable definitions as well as the values in which L=0 inches, R=0.1 inches (2.54 millimeters), W=0.2 inches (5.08 mm), H=0.1 inches (2.54 mm). There are straight paths 412 in both axes along which the force can act. Such straight paths 412 are illustrated as double arrow lines which are not a part of the slit patern.

[0128] FIG. 4B depicts an embodiment having a non-orthogonal dual-axis dual-slit patern with a 60- degree angle (instead of 90-degrees), wherein slits 406’ are shifted so that ends do not he on the sameaxis line. In the illustrated embodiment of FIG. 4B, L is around zero. In this embodiment, the definition of variables is not clear when shifted as shown in FIG. 4B, which is useful to show a small reasonable break from the pattem / formula. There are straight paths 412’ in both axes along which the force can act. Such straight paths 412’ are illustrated as double arrow lines which are not a part of the slit pattern.

[0129] FIG. 4C depicts a non-orthogonal dual-axis dual-slit pattern with a 60-degree angle in which the slits 406” have terminal ends along the primary axes. In FIG. 4C, L is positive so there is no direct force path for the axes. There are straight paths 412” in both axes along which the force can act. Such straight paths 412” are illustrated as double arrow lines which are not a part of the slit pattern. FIG. 4D depicts a non-orthogonal dual -axis dual-slit pattern with a 60-degree angle in which the slits 406” ’ have terminal ends along the primary axes and L is zero. There are straight paths 412”’ in both axes along which the force can act. Such straight paths 412”’ are illustrated as double arrow lines which are not a part of the slit pattern.

[0130] FIG. 5 A is an illustration depicting a sheet 500 having rectangular dual-axis dual-slit patterns and fat slits 506, in accordance with an embodiment of the present disclosure. The fat slits 506 comprise slits of normal or minimal width (or kerf) but they occupy a wider region by having non straight regions (hooks for example) the wider region being shown by the rectangles of dimensions t by B in FIG. 5A. The regions between the slits 506 (shown as Hl by H2 regions in FIG. 5A) may be squares or rectangular (i.e., so it is longer in one axis than the other). That means, for example, that H and L are now different in the two axes (Hl, H2 and LI, L2). In some embodiments, because the slits 506 can occupy a wider space. That width can be accounted for in the patterns to obtain consistent gaps and optimize other dimensions. Similar to the basic dual-slit dual-axis pattern shown in FIG. 3A, this enhanced pattern (with wide slit regions and rectangular rather than square rotating areas) has multiple variables of interest (W, L, R, Q, H, t) but one fewer free choice. We define the variable Q as the quotient of the different L and H variables (Q=H2 / H1=L2 / L1). All the variables and two choices of free variables are summarized in Table 1.Table 1

[0131] As shown, each slit 506 or expanded slit 506 has curvature and a bounding box 130 (interchangeably called as a slit bounding box 130) whose aspect ratio is in the range of 1: 1 to 10: 1. Inother words, each slit 506 is represented by the bounding box 130. In some embodiments, the bounding box 130 may be a geometric shape (e.g., a rectangle or square) that encloses / surrounds each slit 506 and may be regarded as a tightly-fitting perimeter. For example, the bounding box 130 might be the rectangles shown in FIG. 5A, each of which has a length along one axis equal to t, and a length along a second axis (orthogonal to the first axis) equal to B. In some embodiments, such one or more slits 506 include a curved portion (i.e., the curvature not shown) and the bounding box 130 may have an aspect ratio in the range 1 : 1 through 10: 1, with the larger dimension is listed first in the ratio. In the description, “the curvature” can be interchangeably referred to herein as “the curved portion”.

[0132] Further, as shown in FIG. 5A, the slits 506 or the expanded slits (represented by bounding boxes 130) are arranged in parallel groups 508 askew to adjacent parallel groups 510 of slits 506 with each group having an internal gap Rbetween adjacent slits 506 in the same group (510 or 508) and an external gap G between slits 506 in adjacent skewed groups 508, 510. In some embodiments, the gaps R and G throughout the pattern may be a similar gap rather than the same gap. By way of non-limiting example, similarity may mean a gap being 10% larger / smaller than another gap. In other embodiments, similarity may mean a 5% larger / smaller difference between gaps, although other values may be utilized in other embodiments. In some embodiments, at least a plurality of the groups 508, 510 each include three or more slits 506. In some embodiments, there is a gap G or R between all bounding boxes 130 on at least two sides. In some embodiments, there is a gap G or R between each side of each bounding box 130 on all sides.

[0133] In the illustrated embodiment of FIG. 5A, no slit bounding box 130 overlaps with another slit bounding box 130. However, in other embodiments / pattems overlap may exist. In some embodiments, the pattern is extensible while the sheet 500 includes a non-extensible material, or a significantly less extensible material that will deploy, creating openings where the slits exist before the material itself starts to significantly deform. By way of non-limiting example, non-extensible may mean extension at break is less than 30% in at least one axis, although other values may be utilized in other embodiments. In various embodiments, the expanded slits 506 may be arranged in parallel groups 508 askew to adjacent parallel groups 510 of slits 506 with each group having a same gap G between the parallel slits 506. In a deployed state, the sheet 500 may include a deployed region of slits 506 in an expanded state and may further include two deployed regions that grip each other based upon Overlap Grip Strength discussed further herein. In a deployed state, the sheet 500 may include a non-pattemed region between the two deployed regions and may further include a second sheet having a deployed region configured to grip one of the two deployed regions.

[0134] FIG. 5B is an illustration depicting a sheet 500’ having rectangular dual-axis dual-slit patterns and fat slits 506’, in accordance with another embodiment of the present disclosure. In the illustrated embodiment of FIG. 5B, each slit 506’ has awing 131 that extends off each end of the slit 506’. In other words, the slits 506’ include wings 131 that create spirals (i.e., utilizing wings on the ends of the patterns to create a spiral in the Hl by H2 region between the slits) with the most basic elements of the dual-slitdual-axis patern with fat slits 506’, and wings 131. The wings 131 may contain straight segments or curved segments, although only a single straight segment is shown in FIG. 5B for illustrative purposes. Such slits 506’ may advantageously reduce the deployment force and allow the patern to stretch out farther (i.e., increased maximum strain). This may also create more springiness to the patern. Other non-limiting examples are depicted later in the disclosure (in FIGS. 8A to 8E, 9A and 9B, and 12A and 12B, and 18A to 18D for example). In some embodiments, each slit 506’ extends at each end beyond its bounding box 130. In other words, one or more slits 506’ extend at each end beyond corresponding bounding boxes 130, due to the wings 131 (by way of non-limiting example) that extend beyond the bounding box 130 even though the non- winged portion(s) of the slit 506’ are within the bounding box 130.

[0135] FIG. 6A is an illustration depicting a sheet 600 having a dual-axis dual-slit hook 60-degree patern of slits 606, in accordance with an embodiment of the present disclosure. FIG. 6B is an illustration depicting a close-up view of the patern depicted in FIG. 6A, in accordance with an embodiment of the present disclosure. In tests, this patern had a strain at the point of tearing of 7.3% and a peak force at the point of tearing of 59 oz when cut into a 40# virgin Kraft paper.

[0136] FIG. 7A is an illustration depicting a sheet 700 having a dual -axis hook 60-degree patern of slits 706 in which terminal ends are not on the axes. FIG. 7B is an illustration depicting a close-up view of a dual-axis hook 60-degree patern of FIG. 7A in which terminal ends are not on the axes. In tests, this patern had a strain at the point of tearing of 4.8% and a peak force at the point of tearing of 110 oz when cut into a 40# virgin Kraft paper.

[0137] FIG. 8 A is an illustration depicting a sheet 800 having a dual-axis dual-slit hook 90-degree patern of slits 806 with terminal ends aligned along the axes, in accordance with an embodiment of the present disclosure. FIG. 8B is a front view of the patern of FIG. 8A being deployed along one axis, in accordance with an embodiment of the present disclosure. FIG. 8C is a side view of the patern of FIG. 8 A being deployed, in accordance with an embodiment of the present disclosure. FIG. 8D is a perspective view of the patern of FIG. 8A being deployed, in accordance with an embodiment of the present disclosure. FIG. 8E is another side view of the patern of FIG. 8 A being deployed, in accordance with an embodiment of the present disclosure.

[0138] FIGS. 8B to 8E depict the dual-axis hook 90-degree angle patern of FIG. 8A. In tests, this patern had a strain at the point of tearing of 18.9% and a peak force at the point of tearing of 32.7 oz when cut into a 40# virgin Kraft paper. Although depicted as being stretched in one axis, stretching may be performed along two axes, by way of non-limiting example. In some embodiments, the curvature of the non-deployed slits in the dual -axis hook 90-degree patern of FIG. 8A becomes their corresponding contour curvature as clearly visible in FIG. 8B in a deployed state. Similarly in some embodiments, the bounding box 130 (shown in FIGS. 5A and 5B) of each dual-axis hook slit can be extrapolated (regardless of the change to rotation) based on a side of the deployed portion that corresponds to the slit prior to deployment.

[0139] FIG. 9A is an illustration depicting a sheet 900 having a dual -axis hook 75 -degree angle pattern of slits 906 in which terminal ends are shifted slightly, in accordance with an embodiment of the present disclosure. FIG. 9B is an illustration depicting a close-up view of the dual-slit, dual -axis, long hook of FIG. 9A. As shown in FIGS. 9A and 9B, the dual axis long hook includes long wings that spiral towards a center point. In tests, this pattern had a strain at the point of tearing of 10.9% and a peak force at the point of tearing of 36 oz when cut into a 40# virgin Kraft paper.

[0140] FIG. 10A is an illustration depicting a sheet 1000 having a dual -axis hook 60-degree angle pattern of slits 1006 in a non-deployed state SI with splined curves that create more uniform gaps internally (gap R shown in FIG.5 A) between adjacent slits 1006 in the same group and externally (gap G shown in FIG. 5 A) between slits 1006 in adjacent skewed groups as described in FIG. 5 A, in accordance with an embodiment of the present disclosure. The uniform gap may be of 0.058 inches (1.4732 mm), 0.076 inches (1.9304 mm) by way of non-limiting example. FIG. 10B is a front view of the pattern depicted in FIG. 10A as deployed, in accordance with an embodiment of the present disclosure. FIG. 10C is a side view of the pattern depicted in FIG. 10A as deployed, in accordance with an embodiment of the present disclosure. FIG. 10D is another side view of the pattern depicted in FIG. lOA as deployed, in accordance with an embodiment ofthe present disclosure. FIG. 10E is a perspective view of the pattern depicted in FIG. 10A as deployed, in accordance with an embodiment of the present disclosure. FIGS. 10B to 10E depict the dual-axis hook 60-degree angle pattern of FIG. 10A with splines to create uniform gaps pattern in various deployed states. In tests, this pattern had a strain at the point of tearing of 6.3% and a peak force at the point of tearing of 65 oz when cut into a 40# virgin Kraft paper.

[0141] FIG. 11A is an illustration depicting a sheet 1100 having a dual-slit, dual-axis, dual-hook pattern of slits 1106 in a non-deployed state SI. FIG. 1 IB is a front view of the dual-slit, dual -axis, dual-hook pattern of FIG. 11A deployed, in accordance with an embodiment of the present disclosure. FIG. 11C is a side view of the dual-slit, dual-axis, dual -hook pattern of FIG. 11A deployed, in accordance with an embodiment of the present disclosure. FIG. 1 ID is another side view of the dualslit, dual-axis, dual-hook pattern of FIG. 11 A deployed, in accordance with an embodiment of the present disclosure. FIG. 1 IE is a perspective view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11A deployed, in accordance with an embodiment of the present disclosure. FIG. 1 IF is another side view of the dual-slit, dual-axis, dual-hook pattern of FIG. 11A deployed, in accordance with an embodiment of the present disclosure. FIGS. 11B to 1 IF depict the dual-slit, dual-axis, dual-hook pattern of FIG. 11A in various deployed states. In tests, this pattern had a strain at the point of tearing of 21.5% and a peak force at the point of tearing of 29.6 oz when cut into a 40# virgin Kraft paper.

[0142] FIG. 12A is an illustration depicting a sheet 1200 having a dual-slit, dual -axis, long hook pattern of slits 1206 in a non-deployed state SI. The slits 1206 include long wings that spiral towards a center point along with the dual-slit, dual -axis, long hook pattern. FIG. 12A also illustrates measurements associated with the pattern of slits 1206, in accordance with an embodiment of the present disclosure.In other words, the FIG. 12A depicts the dual-slit, dual -axis, long hook with long wings that spiral towards a center point with some exemplary dimensions. FIG. 12B is an illustration of the sheet 1200 in a deployed state.

[0143] FIG. 13A is an illustration depicting a sheet 1300 having a dual-axis single slit pattern of slits 1306 in a non-deployed state, in accordance with an embodiment of the present disclosure. The single slit pattern is distinguished from the dual slit pattern because each slit does not have an adjacent parallel slit. In this embodiment, all the adjacent slits 1306 are perpendicular to each other. FIG. 13B is a perspective view of the pattern of FIG. 13A as deployed, in accordance with an embodiment of the present disclosure. In other words, FIG. 13B depicts the dual-axis single slit pattern of reversing hook single slit rows in a deployed state.

[0144] FIG. 14A is an illustration depicting a sheet 1400 having dual -hook dual -axis multi-slit pattern of slits 1406 with shifting, according to various embodiments. In this embodiment, the two axes are perpendicular, or at 90 degrees to each other. FIG. 14B is an illustration depicting the pattern of FIG. 14A in a zoomed-out view. FIG. 14C is a side view of the pattern of FIG. 14A as deployed, in accordance with an embodiment of the present disclosure. FIG. 14D is a perspective view of the pattern of FIG. 14A as deployed, in accordance with an embodiment of the present disclosure. FIGS. 14C and 14D depict the dual -hook dual -axis multi-slit pattern with shifting oriented at 90 degrees in deployed states.

[0145] FIG. 15A is an illustration depicting a sheet 1500 having dual-slit hook pattern of slits 1506 in a non-deployed state S 1. FIG. 15B is a top view of the dual-slit hook pattern of FIG. 15 A as deployed. FIG. 15C is a perspective view of the dual-slit hook pattern of FIG. 15A as deployed, in accordance with an embodiment of the present disclosure. FIG. 15D is another perspective view of the dual-slit hook pattern of FIG. 15A as deployed. FIG. 15E is another top view of the dual-slit hook pattern of FIG. 15A as deployed. FIGS. 15B to 15E depict the dual-slit hook pattern of FIG. 15A in various deployed states. The sheet 1500 includes the non-reversing hooks 120.

[0146] FIG. 16A is an illustration depicting a sheet 1600 having dual-slit dual -axis first rectangular pattern of hooks formed by slits 1606, in accordance with an embodiment of the present disclosure. Following the general pattern described in FIG. 5 A, the driving variables are shown in FIG. 16A, where approximate values for those variables in the design shown are Hl=0.10 inches (2.54 mm), H2=0.90 inches (22.86 mm), B=1.25 inches (31.75 mm), G=0.10 inches (2.54 mm), R=0.10 inches (2.54 mm), t=0. 18 inches (4.57 mm).

[0147] FIG. 16B is an illustration depicting a sheet 1600’ having dual-slit dual-axis second rectangular pattern of hooks formed by slits 1606’, in accordance with an embodiment of the present disclosure. Following the general pattern described in FIG. 5A, the driving variables for the design shown are Hl=0.1 inches (2.54 mm), H2=0.59 inches (14.99 mm), B=0.94 inches (23.88 mm), G=0.1 inches (2.54 mm), t=0.018 inches (0.453 mm), R=0.1 inches (2.54 mm).

[0148] FIG. 17A is an illustration depicting a sheet 1700 having dual-slit dual-axis dual-hook patternof slits 1706, in accordance with an embodiment of the present disclosure. FIG. 17B depicts a close-up view of the dual-slit dual-axis dual-hook pattern of FIG. 17A.

[0149] FIG. 18A is an illustration depicting a sheet 1800 having a dual-axis dual-slit pattern of slits 1806 with wings in a non-deployed state SI, in accordance with an embodiment of the present disclosure. FIGS. 18B to 18D depict the dual -axis dual-slit hook pattern of FIG. 18A in various deployed states.

[0150] FIG. 19 is an illustration depicting a sheet 1900 having a dual-axis dual-hook triple-slit pattern of slits 1906, in accordance with an embodiment of the present disclosure. In this case, instead of only two parallel slits in the general case shown in FIG. 5A there are three parallel slits.

[0151] FIG. 20A is a photograph depicting an expanded sheet 2000 utilizing a deployed pattern wrapped around objects bundling them together, in accordance with an embodiment of the present disclosure. FIG. 20B is a photograph depicting an expanded sheet 2000’ utilizing a deployed pattern to securely bundle several objects together, in accordance with an embodiment of the present disclosure.

[0152] FIG. 20C is a graph 180 illustrating a comparison of overlap grip strength of different sheets. In the graph 180, the different sheets are presented in the abscissa, and the overlap grip strength and tear strength are presented in ounces. The top of the shaded bars represents the maximum tear strength, and the interface between the shaded and solid region represents the overlap grip strength.

[0153] The corresponding values in this illustration normalized by the width of the samples is presented in Table 2. Table 2 also summarizes the figures that correspond to the sample names in FIG. 20C.

[0154] Notably, the DSDADH patterns exhibits the highest overlap grip strength in the graph 180 with the maximum tear strength that is sufficiently above the overlap grip strength to advantageously help avoid inadvertent tearing (e.g., having the material tear before or at the point that the overlap grip is overcome), while also not being so hard to tear that it impacts the ability to intentionally tear the material (such as tearing off a portion once a sufficient amount of material has been wrapped around one or more objects).

[0155] Conformability is a feature that is valuable for many bundling or securing applications. Dualslit Dual -axis patterns in particular have exceptional conformability properties. Because these patterns can be expanded in two orthogonal axes, they can often expand as needed to conform around complex shapes. Pattern and material combinations that allow for a reasonable amount of maximum strain at tear, such as 20%-40%, have been found to conform around complex surfaces while still providing some force to hold objects in place. Many other ranges may be advantageous for some applications.

[0156] FIGS. 21A to 21F illustrate an exemplary application of four overlapping layers of deployed expandable sheets 300 with a plurality of slits 306 to bundle a collection of books 140, in accordance with an embodiment of the present disclosure. Although bundling of the books 140 is shown and contemplated, it should be noted that any suitable collection of objects may be bundled. Moreover, it should be noted that a sheet 300 having pattern of slits 306 is shown and contemplated, however, it maybe appreciated that any sheet (e.g., 220, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600 etc.) having any pattern of slits (222, 106”, 306’, 706, 806, 906, 1006, 1106, 1206, 1306, 1406, 1506, 1606 etc.) may be used / utilized. In the illustrated embodiment of FIGS. 21A to 21F, the sheet 300 has four layers 132, 134, 136, 138 of slits 306 of hook pattern (e.g., shown in FIG. 2A). Each of the layers 132, 134, 136, and 138 is configured to overlap each other. However, any suitable number of overlapping layers may be utilized.

[0157] Further, the slits 306 may be arranged into any number of patterns, such as single-slit, or doubleslit, reversing hook pattern, dual-axis dual-slit hook pattern, folding-wall, or the like to bundle the collection of books 140. However, it should be noted that the slits 306 in one part of the sheet 300 may be arranged such that their primary tension axes are different than the primary tension axes of the slits 306 in another part of the sheet 300. In other words, the tension axis TA of the layers 132, 134 is different from the tension axis TA of the layers 136, 138. Further, it should be noted that although the slits 306 are shown to get utilizing to bundle a collection of objects, however any sheet described above in the description may be used to bundle the collection of books 140.

[0158] Upon applying the tension, the sheet 300 is expanded with the deployed hook patterns (which may be reversing or non-reversing hooks but will be described for the reversing hook case), the expanded sheet 300 grips onto itself with overlap grip strength sufficient to hold objects together. Moreover, the reversing region 126 (shown in FIG. 2A) of each reversing hook 120’ of one layer (i.e., layer 132) add to the overlap grip strength by catching onto the reversing regions 126 of other reversing hooks 120’ of another layer (i.e., layer 134). Similarly, the reversing regions 126 of each reversing hook 120’ (shown in FIGS. 6A to 20B) of the layer 136 add to the overlap grip strength by catching onto the reversing regions 126 of other reversing hooks 120’ of the layer 138. Additionally, because of the random motion and dynamic nature of the hooks, adjacent layers that are not directly opposed to each other, such as layer 134 and layer 136, will still experience significant interlocking. Accordingly, the sheet 300 conforms to the books 140 without adding unnecessary bulk to the package, thereby making it suitable for securely bundling the different objects for shipping without making the overall package unnecessarily large. With the help of the sheet, cables, wires, draperies, may be organized or retained together by stretching the material and wrapping it around the objects with at least a portion of overlap.

[0159] In a related application, the sheet 300 having the pattern of slits 306 in the repeating manner may be used not just to bundle or hold objects together, but to cover one or more objects for aesthetic reasons. For example, sheets of material could be provided with any of the kirigami slit patterns disclosed here to function as a gift wrap or decorative covering of objects. Even single objects could be covered with the material which has an attractive appearance, a high level of conformability to cover any object, and strongly interlocks with itself to avoid the need for tape. The material can be sheets or rolls of any type of paper (such as kraft paper, extensible paper, recycled paper, etc) or any type of plastic (PET, recycled plastics, reclaimed plastics etc). The material could be colored or printed to include additional decorative elements.

[0160] Further, the sheet 300 having the pattern of slits 306 in the repeating manner may effectively and gently hold plant material in a configuration for transportation. Because trees and other plant materials are delicate but require some gentle control of branches and other plant material. Therefore, the plants and trees may be held or wrapped with the sheet 300 before being put in a box for example with or without additional cushioning material. In other words, before being loaded into a vehicle for transport from a nursery the plants and trees may be held or wrapped with the sheet 300. Furthermore, fragile gift items may be covered with the sheet 300 having the pattern of slits 306 to ensure safety during transportation.

[0161] FIGS. 21A to 21F illustrate a complete step-by-step process for bundling an object, (for example, books 140) by the sheet 300 having four overlapping layers 132, 134, 136, 138 each having the pattern of slits 306. Firstly, the sheet 300 is placed on a floor or any flat surface, as shown in FIG. 21A. Then, the objects, such as books 140, are placed onto the sheet 300, as shown in FIG. 21B. Upon placing the books 140 on the sheet 300, each layer 132, 134, 136, 138 of the sheet 300 is stretched by applying the minimum tension along the corresponding tension axis TA of each layer 132, 134, 136, 138. Upon applying the tension along the tension axis TA of each layer 132, 134, 136, 138, each slit 306 in the corresponding layer 132, 134, 136, 138 gets opened up and a three-dimensional structure is created. Then, each layer 132, 134, 136, 138 of the sheet 300 is wrapped around the books 140 one by one, as shown in FIGS. 21C to 21F.

[0162] As each layer 132, 134, 136, 138 is overlapped over one-another, for example, the layer 132 is overlapped with the layer 134 and the layer 136 is overlapped with the layer 138, the reversing hooks 120’ of each layer 132, 134, 136, 138 are interlocked with the overlapped layer. For example, the hooks 120 (e.g., shown in FIGS. IE and IF) of the layer 132 are interlocked with the hooks 120 (e.g., shown in FIGS. IE and IF) of the layer 134, similarly, the hooks 120 of the layer 136 are interlocked with the hooks 120 of the layer 138. For the case of reversing hooks 120’, the reversing regions 126 of each reversing hook 120’ of each layer (e.g., the layers 132, 134, 136, 138) interlock with the reversing region 126 of reversing hooks 120’ of another overlapping layer. For example, the reversing regions 126 of reversing hooks 120’ of layer 132 interlocks with the reversing regions 126 of reversing hooks 120’ of overlapping layer 134, similarly, the reversing regions 126 of each reversing hook 120’ of the layer 136 interlocks with the reversing regions 126 of the reversing hooks 120’ of overlapping layer 138. Accordingly, the bundle of books 140 is packed.

[0163] FIGS. 22A to 22E illustrate an exemplary application of the sheet 300 to secure closure of a bag 150 containing a plurality of items, in accordance with an embodiment of the present disclosure. It should be noted that the sheet 300 may be a region or a part of the bag 150 in this particular embodiment. The plurality of items is placed inside the bag 150 from an access opening 152 defined on top of the bag 150, as shown in FIG. 22A. The bag 150 further includes two regions 153 full of hook slits 306. As shown in FIG. 22A, each region 153 is positioned on either side ofthe access opening 152. Upon placing the plurality of items in the bag 150, the regions 153 full of hook slits 306 may be deployed through thetension and then brought into contact while deployed, as shown in FIG. 22B. It should be noted that a sheet 300 having pattern of slits 306 is shown and contemplated, however, it may be appreciated that any sheet (e.g., 220, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600 etc.) having any pattern of slits (222, 306’, 706, 806, 906, 1006, 1106, 1206, 1306, 1406, 1506, 1606 etc.) may be used / utilized. The deployed hook slits 306 then grip onto each other in a manner that the bag 150 keeps closed, as shown in FIG. 22C. The regions 153 with hooks may be part of the same material (e.g. paper) comprising the bag 150 itself, or they may be from a different or similar material added to the bag 150.

[0164] In some embodiments, the hook slit regions 153 may include a handle for carrying the bag 150. The hook slit regions 153 may be rolled to increase the amount of overlapped region and thereby the strength of the material. For example, FIG. 2 IE shows the case where the expanding reverse hook region 153 exists on the short side of the bag 150 and an expanded interlocked region has left an opening that can be used as a handle. Other embodiments may utilize expandable sheets of hook slit patterns to secure face masks at the back of the head, hats, scarfs, tight fitting clothing, pallet wrap, and / or serving as a produce holder.

[0165] Standard Testing Pattern: Test coupons were created for different patterns using a laser cutter. The patterns were cut into a 40# virgin Kraft paper available from Uline. Normally 0.5 inches (12.7 mm) edge with no pattern was created to engage with clips, and 9 inches (228.6 mm) long pattern area, samples were normally 3.5 inches (88.9 mm) wide. To distinguish the value of different designs, tests were performed. Table 2 provides performance data regarding certain slit patterns provided herein.

[0166] Tensile Testing: The samples were pulled apart while recording force versus displacement. Then the maximum force the sample can sustain (tear strength) was extracted and divided by the width of the sample to produce Tear Strength per width. The extension of the sample was measured when that maximum force (tearing) occurs, in order to calculate the strain at this point (strain at tear) based on the initial length of the sample (AL / L). a. Tear Strength per Width [N / m] b. Strain at Tear [%]

[0167] Overlap Tensile Grip: Overlap Grip Strength may be regarded generally as an expanding slit sheet pattern and sheet material producing a given amount of gripping to adjacent layers of that same pattern and material combination. In one non-limiting example, to evaluate the Overlap Grip Strength of an expanding slit sheet sample, two sections of that sample are produced. The first section is expanded and mounted onto a curved surface (for example, taping the ends around the circumference of 3 inches (76.2 mm) diameter tube). The second section is held by one end in the clamp of a tensile testing apparatus such that it is directly above the center of the curved surface (6 inches (152.4 mm) for example) and the axis of the curved surface is parallel to the pivot axis of the clamp in the tensile testing apparatus. The free end of the second section is then pulled to fully deploy the second section and then pulled around a portion of the first section that is mounted to the curved surface. The overlap betweenthe two sections is about 45 degrees of contact along the curved surface then the first section is released. If the sections do not interlock and stick to each other, then they have an Overlap Grip Strength of zero. If they do stick together, then the tensile testing apparatus will pull the fixed end of the second section vertically while recording the force and distance. The maximum force recorded as the second section is dragged across the first section is the Overlap Grip Strength. Other methods may be utilized in various embodiments.Table 2

[0168] In some embodiments, the sheet includes an overlap grip in the range of 75 N / m and 83 N / m and a tear strength in the range of 90 N / m and 103 N / m. Further, as shown in Table 2, the dual-slit dualaxis dual-hook pattern (FIG. 11A to 1 IF) performed the best given it exhibited the highest overlap grip strength, a tear strength that exceeds that highest grip strength by a reasonable amount without being too high (i.e., without being unreasonably difficult to tear off a piece of deployed material), a reasonable deploy force (i.e., does not require too much force to pull to cause the pattern to rotate sufficiently), and a reasonable strain at tear (i.e., the pattern will not tear prematurely and has good conformability). The second-best pattern was the dual-axis hook 90-degree pattern with terminal ends on the axes pattern (FIG. 8A to 8D), whose overlap grip strength was the next highest, with a tear strength, deploy force, and strain at tear values that were not too divergent from the values of the dual-slit dual-axis dual-hook pattern. It should be noted that the tear strength of the uncut paper itself was 4,833 N / m and the highest tear strength with a kirigami pattern is only 2% of the raw paper (75.5N / m). A strain at peak of 20-40% appeared to work best for application in some embodiments, such that the material does not tear without stretching and does not stretch out a long way. More specifically regarding the deploy force, it shouldbe fairly low. However, it depends on the application, because if the deploy force is almost zero, then the material cannot hold any force with partially deploying the material (which would be needed if conformability is needed / desired to hold oddly shaped items, i.e., there needs to be some strength in that undeployed material).

[0169] From practical tests, a deploy force of 27.8 N / m seemed too high for the tested material, but a deploy force of 11.5 seemed acceptable. To summarize the Maximum Tear Strength findings above, it should be higher than the Overlap Grip Strength, otherwise the material might tear instead of holding it together and it will likely rip apart when trying to unwrap it. Therefore, the DSH (dual-slit hook) and SSH (single slit hook) patterns were not great. More specifically, the dual-slit hook pattern actually showed a lower Tear Strength than Overlap Grip Strength. The BLC22 pattern (FIG. 10A to 10E) had the highest tear strength, but its strain at tear was very low (so it does not extend very far limiting its conformability) and its deploy force was high making it harder to use. In some applications, however, it might be a good solution.

[0170] FIGS. 23A to 23D illustrate a multi-layer overlapping phenomenon, in accordance with an embodiment of the present disclosure. It should be noted that two or more layers of the sheet 300 lock to adjacent layers above or below it. It should also be noted that the interlocking strength of a short region of material is often greater than the tensile strength (tear strength) of the material. In other words, if tension force Stl (interchangeably called as tear strength Stl) is applied to a layer of deployed material 154 shown in FIG. 23A until it tears, that value Stl will be the tear strength of that material. If two layers of the same deployed material 154 are overlapped as shown in FIG. 23B, the interlocking strength in the overlap region OR1 is often greater than the tear strength Stl, such that the samples in FIG. 23B will tear with a value of tension force St2 (interchangeably called as tear strength St2) that is similar to the tension force Stl instead of releasing from each other at a lower force. This case where the interlock strength is greater than the tear strength can be easily achieved with many materials and slit patterns that include reversing hooks.

[0171] As the number of locked layers increases, the total strength of bundling may also get increased. In the illustrated embodiment of FIG. 23C, a deployed or expanded layer 154 is wrapped in a loop such that a small portion overlaps itself. The small overlapping region OR1 is formed, which results in reduced strength of bundling because only a single layer of material exists for most of the loop, so only the tear strength of a single layer of material can resist forces to tear the loop apart. In other words, tension force St3 (interchangeably called as tear strength St3) will be similar to the tension force Stl and the tension force St2.

[0172] However, in FIG. 23D, the deployed, or expanded layer 154 forms more than two complete loops that are strongly interlocked such that a much larger force is required to tear apart this double loop. In other words, tension force St4 (interchangeably called as tear strength St4) will be significantly larger than the tension forces Stl, St2 or St3, often it will be approximately double those forces. Accordingly, the tear strength of the loop of material is increased. When at least 100% of the loop hasa second layer, as shown in FIG. 23D, then its strength will be about double the first scenario (St4~2*St3). In other words, the strength St4 of the sheet 300 increases two times as compared to the tear strength St3 in first scenario. Accordingly, increasing the overlap increases the hold strength. The user can apply more overlap to increase the hold strength. Because the interlocking is continuous across the surface of adjacent deployed layers, localized strength can also be added. In other words, a region with more layers of material can withstand a higher maximum force before tearing than another region with fewer layers interlocked.

[0173] Multiple layers of deployable interlocking (hooking) material can be wrapped around or added to increase the effective tear strength of a multi-layered construction. Patterns with a multitude of hooks are particularly effective since they can grip adjacent layers frequently to convey forces and lock the multi-layered construction into its wrapped shape, thereby preventing the bundled (or wrapped) objects from moving easily.

[0174] FIG. 24 illustrates an exemplary application of the sheet 300 to secure a wearable object 160, in accordance with an embodiment of the present disclosure. To secure the wearable object 160 to a desired or predefined location, the sheet 300 includes at least one securement portion 162. The at least one securement portion 162 is made of cloth, fabric or other sheet material is shown. In some cases, the wearable object 160 may be a face mask, hats, scarfs, tight fitting clothing (for example, shirt cuff), or a sensor. The wearable object 160 may be secured to the predefined location by using the at least one securement portion 162. In the illustrated embodiment of FIG. 24, two securement portions 162 each connected on either side of the wearable object 160 are shown. The securement portions 162 may be made from the same material as the wearable object 160, cut from a continuous input material, or they may be made from other materials that are bonded together.

[0175] As shown in FIG. 24, each securement portion 162 includes a locking region 164 having a pattern of slits 306 in a repeating pattern. Each slit 306 is configured to open (i.e., deployed) in response to a minimum tension applied along the tension axis TA. Each securement portion 162 further includes atab region 166 that can be easily grabbed and pulled to facilitate deployment (i.e., opening) of the slits 306. Each securement portion 162 further includes a stretch control region 168 to control the tension forces experienced by the wearer once the locking regions 164 are engaged and a loop has been formed around part of a user’s body, such as a head, arm or leg.

[0176] In some embodiments, the locking region 164 of each securement portion 162 includes the pattern of slits 306 configured to open (be deployed) in response to a minimum tension applied via the tab region 166 along the tension axis TA. In such cases, the locking region 164 of one securement portion 162 overlaps and strongly grips with the locking region 164 of another securement portion 162 which enables the interlocking of the securement portions 162 to each other, thereby facilitating securement of the wearable object 160.

[0177] In some embodiments, the locking region 164 of one of the securement portions 162 includes a pattern of slits 306 that is configured to open in response to the minimum tension applied along thetension axis TA and the locking region 164 of the another securement portion 162 includes a structure or device (not shown) configured to be locked with the pattern of slits 306 of the associated securement portion 162. Accordingly, the securement portions 162 may interlock with each other, and securement of the wearable object 160 is achieved.

[0178] In some embodiments, the tab portion 166 of the at least one securement portion 162 may be omitted, and the user directly grabs the locking region 164 and applies tension to it to facilitate securement of the wearable object 160 to the predefined location. In some embodiments, the stretch control region 168 may be omitted and the locking region 164 may be configured to achieve the desired stretch to hold it comfortably. In such cases, the length and scale of pattern may be adjusted to tune stiffness of the securement portion 162. In some embodiments, the securement portion 162 may further include additional regions (not shown) that have rounded patterns to remove sharp edges and increase comfort.

[0179] FIGS. 25 A to 25 C illustrate a user wearing a face mask 250 secured by utilizing the sheet 300, in accordance with an embodiment of the present disclosure. The face mask 250 includes the sheet 300 to secure the face mask 250 to a person. It should be noted that the face mask 250 is substantially similar to the wearable object 160 of FIG. 24 and is secured in the same manner with the help of the sheet 300 (i.e., the securement portion 162). Although, in this figure, the wearable object 160 is shown and contemplated as the face mask 250. However, it should be noted that the wearable object 160 may be a hat, a scarf, a watch, a sensor or a footwear. Further, similar to FIG. 24, two securement portions 162 of the sheet 300 are connected to either side of the face mask 250. The sheet 300 (i.e., the securement portion 162) is configured to hold and secure the face mask 250 in place on the user’s face. In some embodiments, the sheet 300 may be made from the same material as the rest of the facemask, for example, the filtration media.

[0180] In some embodiments, the wearable objects may be a footwear with the sheet 300 having two securement portions 162. In such cases, the sheet 300 or securement portions 162 may secure the footwear to a body with controlled tightness. In some embodiments, the wearable object 160 may be a body covering with two interacting securement portions. The body covering may be a surgical gown or dressing gown and the securement portions are used to close the gown (i.e., surgical or dressing) quickly with large size adjustment and controlled tightness. Accordingly, the fit of the body covering is adjusted by pulling and locking the securement portions. In some embodiments, the wearable object 160 is shirt, pants or other body covering and a single securement portion is used to control the tightness of fit and close gaps between the body covering and the body.

[0181] FIGS. 26A to 26C illustrate a user wearing a shirt having an arm cuff 350 secured by utilizing the sheet 300, in accordance with an embodiment of the present disclosure. The arm cuff 350 includes the sheet 300 to secure the arm cuff 350 to a person. It should be noted that the function and assembly of the sheet 300 with the arm cuff 350 is same as the face mask 250. The arm cuff 350 is also secured to a desired or predefined location by the sheet 300 similar to the face mask 250 of FIGS. 25A to 25C.As shown, the sheet 300 is configured to reduce a gap between the arm cuff 350 and the body (i.e., hand) of the user. As shown in FIGS. 26A and 26C, the securement portion 162 of the sheet 300 can be pulled and wrapped around itself to hold the arm cuff 350 against the body with a desired tightness.

[0182] FIGS. 27A to 27C illustrate a diaper 450 secured by utilizing the sheet 300, in accordance with an embodiment of the present disclosure. The diaper 450 is also secured to a desired or predefined location by the sheet 300 similar to the face mask 250 of FIGS. 25 A to 25 C and arm cuff 350 of FIGS. 26A to 26C. As shown, the at least one securement portion 162 may be integrated into the diaper 450 (e.g. made from the same material). As shown, in the illustrated embodiment of FIG. 27A, two securement portions 162 of the sheet 300 are integrated into the diaper 450 and are positioned on opposite sides to each other. As shown, each of the securement portions 162 of the sheet 300 may further include the tab portion 166 configured to be stretched and overlapped to secure the diaper 450 to the predefined location. The same securement method can also be used to hold the diaper tightly closed for disposal once it is soiled.

[0183] Further, the tightness of the securement portion 162 may also have medical advantages, such as pressure stockings to prevent blood clots, control swelling, manage circulation, reduce pain, etc. The securement portion 162 may be attached to other clothing (e.g. pants) so it is readily available.

[0184] FIG. 28 is a llow chart of a method 550 for manufacturing a sheet 300 (or sheet 300’, sheet 500, etc.) defining the vertical axis Y-Y and the horizontal axis X-X along the major surface 102. At step 552, the method 550 includes providing the substrate 104 of the sheet material defining the major surface 102. At step 554, the method 550 further includes creating the pattern of slits 306 formed in the substrate 104 in a repeating pattern based on the sheet 300 being in a flat configuration SI. Further, each slit 306 opens in response to the minimum tension applied to the substrate 104 along one or more axes. Further, with reference to FIG. 5 A, each slit has curvature and the bounding box 130 whose aspect ratio is in the range of 1: 1 to 10: 1. The slits 306 are arranged in parallel groups 508 askew to adjacent parallel groups 510 of slits 306 with each group having a similar gap G between the parallel slits 306.

[0185] Unless otherwise indicated, all numbers expressing feature sizes, amounts, and physical properties used in the specification and claims are to be understood as being modified by the term “about”. Accordingly, unless indicated to the contrary, the numerical parameters set forth in the foregoing specification and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by those skilled in the art utilizing the teachings disclosed herein.

[0186] Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and / or equivalent implementations can be substituted for the specific embodiments shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Therefore, it is intended that this disclosure be limited only by the claims and the equivalents thereof.

Claims

CLAIMS1. 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 pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration, wherein each slit is configured to open in response to a minimum tension applied to the substrate along one or more axes; each slit has curvature and a bounding box whose aspect ratio is in the range of 1 : 1 to 10: 1; and the slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a same gap between the parallel slits.

2. The sheet of claim 1, wherein each slit comprises a hook.

3. The sheet of claim 1, wherein each slit comprises a reversing hook.

4. The sheet of claim 1, wherein no slit bounding box overlaps with another slit bounding box.

5. The sheet of claim 1, wherein there is a gap between all bounding boxes on at least two sides.

6. The sheet of claim 1, wherein there is a gap between each side of each bounding box on all sides.

7. The sheet of claim 1, wherein the pattern is extensible and the sheet comprises a non-extensible material.

8. The sheet of claim 1, wherein the sheet comprises an overlap grip in the range of 75 N / m and 83 N / m and a tear strength in the range of 90 N / m and 103 N / m.

9. The sheet of claim 1, wherein at least a plurality of the groups each comprise three or more slits.

10. The sheet of claim 1, wherein each slit extends at each end beyond its bounding box.11 . The sheet of claim 1, wherein each slit has a wing that extends off each end of the slit.

12. 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 pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration, wherein the sheet between the slits is in an expanded state in an angle in the range of 5 degrees to 85 degrees in response to a minimum tension applied to the substrate along one or more axes; each expanded slit has curvature and a bounding box whose aspect ratio is in the range of 1: 1 to 10: 1; andthe expanded slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a similar gap between the parallel slits.

13. The sheet of claim 12, further comprising a deployed region of slits in an expanded state.

14. The sheet of claim 13, further comprising two deployed regions that grip each other.

15. The sheet of claim 14, further comprising a non-pattemed region between the two deployed regions.

16. The sheet of claim 15, further comprising a second sheet having a deployed region configured to grip one of the two deployed regions.

17. The sheet of claim 12, further comprising conformability of the sheet in a deployed state.

18. A method of manufacturing a sheet defining a vertical axis and a horizontal axis along a major surface comprising: providing a substrate of the sheet material defining the major surface; creating a pattern of slits formed in the substrate in a repeating pattern based on the sheet being in a flat configuration, wherein each slit opens in response to a minimum tension applied to the substrate along one or more axes, each slit has curvature and a bounding box whose aspect ratio is in the range of 1 : 1 to10: 1, and the slits are arranged in parallel groups askew to adjacent parallel groups of slits with each group having a similar gap between the parallel slits.

19. A gift wrap comprising the sheet of claim 1 configured to cover objects.

20. A face mask comprising the sheet of claim 1 configured to secure the face mask to a person.

21. An arm cuff comprising the sheet of claim 1 configured to secure the arm cuff to a person.

22. A diaper comprising the sheet of claim 1 configured to secure the diaper to a person.

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