JPWO2017179716A1 - Method for adjusting elasticity of sheet material, force sensor, and sheet material - Google Patents

Abstract

The desired elastic modulus is designed with a sheet material having a cut paper structure cut. Based on the relational expression K1 = (α / 2N) × E × d3h / w3 or E1 = α (d / w) 4 × E in the initial deformation region where in-plane deformation is maintained in the sheet material, the first Incision of staggered cut paper structure in which the width in the direction of w is w, the arrangement pitch in the second direction orthogonal to the first direction is d, and the number of repeating units of the incision in the second direction is N And the stiffness constant K1 or Young's modulus E1 is adjusted to a desired value by appropriately selecting the values of the cut width w, the pitch d, and the number of repeating units N. Here, E is the Young's modulus before the cutting of the constituent material of the sheet material, h is the thickness of the sheet material, and α is a numerical coefficient.

Description

  The present invention relates to a sheet material elasticity adjusting method, a force sensor, and a sheet material.

  Many applications focusing on the elasticity of the cut paper structure have been studied, and an elastic electrode (for example, Non-Patent Document 1) in which a sheet-like material called a nanocomposite is cut, and an elastic graphene (for example, a non-composite material). Patent Document 2), a stretchable lithium ion battery (for example, see Non-Patent Document 3), and the like have been proposed. Moreover, the application to the solar tracker which makes the panel surface of a solar panel track the sun is proposed (for example, refer nonpatent literature 4). All of them utilize a three-dimensional displacement or deformation (displacement / deformation including rotation) of the cut paper structure, and the flatness of the sheet is lost due to the displacement.

  On the other hand, a configuration is known in which a displacement induced on the center axis of a strain measurement plate with a cut is enlarged and detected as a shear stress (see, for example, Patent Document 1).

JP-A-57-124203

T.C.Shyu, et.al., “A kirigami approach to engineering elasticity in nanocomposites through patterned defects” Nature Materials, 14 (2015) 785 M.K.Blees, et al., “Graphene kirigami”, Nature 524 (2015) 204 Z. Song et al., Kirigami-based stretchable lithiumion batteries ”, Scientific Reports 5 (2015) 10988 A. Lamoureux et al. “Dynamic kirigami structures for integrated solar tracking”, Nature Communications 6 (2015) 8092

  In the prior art, when using the stretchability of the cut paper structure, the elastic modulus could not be predicted without actually making a prototype. Then, this invention aims at providing the application example of the method of controlling the elasticity modulus of arbitrary sheet-like raw materials based on simple numerical formula, and the cut sheet | seat adjusted to the desired elasticity modulus.

  In order to achieve the above object, the present invention focuses on the initial deformation region where the flatness of the sheet is maintained, and realizes the design of a desired elastic modulus with an arbitrary material based on a simple mathematical formula. To do.

In one aspect of the present invention, the method of adjusting the elasticity of the sheet material is:
Prepare the sheet material,
Relational expression K1 = (α / 2N) × E × d ³ h / w ³ or E1 = α (d / w) ⁴ × E applied to the sheet material in an initial deformation region where in-plane deformation is maintained.
Based on the above, staggered cut sheets whose width in the first direction is w, the arrangement pitch in the second direction orthogonal to the first direction is d, and the number of repeating units in the second direction is N Forming a cut in the structure, where K1 is a stiffness constant, E is a Young's modulus before the cut of the material constituting the sheet material, h is a thickness of the sheet material, α is a numerical coefficient,
The stiffness constant K1 or Young's modulus E1 is adjusted to a target value by selecting the values of w, d, and N.
It is characterized by that.

  The elastic modulus of an arbitrary sheet material can be adjusted and controlled by a simple method.

It is a figure which defines the parameter of a cut sheet structure. It is a figure which defines the parameter of a cut sheet structure. It is a figure explaining the principle of this invention. It is a figure explaining in-plane displacement and three-dimensional displacement. It is a figure which shows the relationship between the stiffness constant (spring constant) of a sheet | seat, and sheet | seat thickness. It is a figure which shows the relationship between the stiffness constant (spring constant) of a sheet | seat, and parameter d / w. It is the schematic of the force sensor of embodiment. 2 is an image of a force sensor of Example 1. It is an image of the force sensor of Example 2. It is a figure which shows the modification of a force sensor. It is a figure which shows that the force sensor of embodiment does not ask | require material. It is a figure which shows the cut paper structure in which the cutting row | line | column was formed in multiple numbers by the horizontal direction. It is a figure which shows that the design of the elasticity modulus in the initial region of this invention is applicable also to the structure of FIG. It is a figure which shows application of invention to a medical reproduction | regeneration sheet | seat. It is a figure which shows application to mounting tools, such as a supporter, a corset, and a low back pain belt.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
<Principle explanation>
FIG. 1A and FIG. 1B are diagrams for explaining the definition of parameters of the cut paper structure used in the present invention, and FIG. 2 is a diagram for explaining the principle of the present invention. In the embodiment, a desired elastic modulus is designed by using a displacement in an initial region where the flatness of a sheet having a cut paper structure is maintained.

  The cut paper structure in FIG. 1A has cuts 102e and cuts 102c that are alternately formed on the sheet 101 at regular intervals. The material of the sheet 101 is not limited, and paper, plastic, rubber, metal, or the like can be used.

  A notch 102c having a width w is formed along the length direction of the sheet 101 (y direction in FIG. 1). The cuts 102e extend from both ends of the sheet 101 alternately with the cuts 102c. The notch 102c has a width w in the x direction. The alternating cuts 102c and 102e are arranged at intervals or pitches d in the y direction. A region including the notch 102c having a width w between the notch 102e and the notch 102e adjacent in the y direction (the length in the y direction is 2d) is defined as one unit of the notch repetition. The number N of repeating units coincides with the number N in the y direction of the cuts 102c. In the example of FIG. 1, 10 units of cuts are formed. The entire length of the cut area is 2Nd, and the width of the sheet 101 is set to w + 2d. In FIG. 1A, for ease of explanation, the distance between the notches 102c and 102e in the x direction is also set to d, but the parameter d defined in the present invention is the pitch of the notches in the y direction.

In FIG. 1B, the cut pitch d in the y direction and the width w in the x direction of the cut 102c are the same as in FIG. 1A. Unlike FIG. 1A, the width of the sheet 101 is set to w + d ″, and the interval in the x direction of the notch 102e is set to d ′. If the value of d ′ is equal to or less than d, the elastic modulus described later is set. The desired elastic modulus can be designed, and the distance d ′ in the x direction of the notch 102e has a certain width so as not to be cut when the sheet 101 is stretched. Specifically, when the breaking stress of the sheet 101 is σ _f , the threshold load applied to the sheet at that time is Fc, and the thickness of the sheet 101 is h,
Fc / (d ′ × h) <σ _f , ie
d ′> Fc / (h × σ _f )
Design to meet If the value of d ″ is equal to or greater than d, the elastic modulus formula described later holds, and a desired elastic modulus can be designed.

  FIG. 2 shows the relationship between the force F applied to the sheet 101 and the elongation Δ. 2A is an overall view of a change when the cut of FIG. 1 is formed using Kent paper as the sheet 101, and FIG. 2B is an enlarged view of the initial region of FIG. As shown in FIG. 2A, when a force F [N] is applied in a direction orthogonal to the cut width of the sheet 101, the sheet 101 is displaced by an elongation Δ [mm]. At this time, in the initial region, a clear linear response is observed while the flatness of the sheet 101 is maintained. The linear characteristic continues until a certain force is reached, and a sudden change occurs when moving to the second region, and the flatness of the sheet 101 is lost. This change point is called a transition point.

  In the second region, the notches 102c and 102e of the sheet 101 are greatly opened, and the sheet 101 is deformed three-dimensionally. In this region, the sheet 101 is greatly extended with a slight force. When the sheet 101 extends to a certain extent, the sheet 101 cannot be extended unless a large force is applied thereafter. This area is the final area. If more force is applied in the final region, the sheet 101 will break.

  The application example of the conventional cut paper structure uses the second region. The inventors have found that the stiffness constant representing the elasticity of the sheet in the initial region and the elongation (strain) at the transition point from the initial region to the second region can be easily predicted with a simple mathematical formula. When transitioning from the initial region to the second region, the sheet 101 loses its flatness due to abrupt elongation, making it easy to see the change and easily detecting the force corresponding to the transition point. it can. Based on this knowledge, an application example using the initial region is provided.

Here, the difference between the in-plane displacement and the three-dimensional displacement will be described with reference to FIG. 3A shows in-plane deformation (elongation), and FIG. 3B shows three-dimensional deformation (bending). When attention is paid to the surface 105 including the notch 102c at the edge, in FIG. 3A, the notch 102c is deformed by δ _{1 in} the y direction while maintaining the planarity in the xy plane. In contrast, in FIG. 3B, when the notch 102c is opened, the surface of the sheet 101 is twisted in the z direction at an angle θ and deformed beyond the xy plane. This displacement including rotation in the out-of-plane direction is referred to as three-dimensional deformation or bending.

  In the transition from the initial region that undergoes in-plane deformation to the second region that undergoes three-dimensional deformation, in-plane strain energy and out-of-plane strain energy compete. When these two energies are equal, a transition occurs between the two regions.

In FIG. 3A, when the critical elongation amount that can deform the surface 105 while maintaining the planarity in the xy plane is δ _c , the critical elongation amount δ _c is the critical elongation amount Δc (Δc = 2Nδ _c ) or critical strain ε _c (ε _c = δ _c / d), given by equation (1).

Here, h is the thickness of the sheet 101, d is the pitch of cutting in the y direction, and β is a numerical coefficient described later. In the initial region, the extension amount Δ of the sheet 101 is proportional to the number N of repeating units in the y direction. On the other hand, the strain ε does not depend on N. These amounts are expressed as a function of the cutting pitch d when the thickness h of the sheet 101 is determined for a given force F or stress σ. The critical elongation amount Δ _c and the critical strain ε _c of one notch 102c can be designed by the notch pitch d. This will be described in more detail below.

  First, in the initial region where in-plane deformation occurs, the response characteristic of the sheet 101 is expressed by the relationship between the force F applied to the sheet 101 and the elongation Δ of the sheet 101, or the relationship between stress (stress σ) and strain (strain ε). Given in A).

F = K1 × Δ or σ = E1 × ε (A)
Here, K1 is the stiffness constant of the sheet 101 in the initial region, E1 is the Young's modulus of the sheet 101 in the initial region,
K1 = k1 / 2N
E1 = k1 × d / hw
k1∝E × d ³ h / w ³ (A) ′
It is. E is the original Young's modulus of the material of the sheet 101 (before cutting). K1 represents an amount corresponding to the spring constant in the initial region in the cut paper structure, and is referred to as “spring constant” for convenience in the following description. k1 is a stiffness constant (spring constant) per notch. From equation (A) ′, K1 and E1 are given by equation (B).

K1 = (α / 2N) × E × d ³ h / w ³
E1 = α (d / w) ⁴ × E (B)
As described above, d is the pitch of the cut in the y direction, h is the thickness of the sheet 101, w is the width of the cut 102c, and N is the number of repeating units in the direction (y direction) orthogonal to the cut width (or the cut 102c). Number). α is a numerical coefficient and is about 7.0. More precisely, α is about 6.92, but in the following, α = 7.0 is set for ease of explanation. In the present specification and claims, “α = 7.0” includes an error.

  Expression (B) is a basic expression for adjusting the elasticity of the sheet, and it can be seen that the spring constant, that is, the elastic modulus of the sheet 101 can be adjusted and changed in a very wide range by the combination of E, d, h, and w. . In order to reduce the influence of the end portion in the y direction of the sheet 101 (the region without the cut), it is desirable that the number N of repeated cut repeated units is larger, for example, 10 or more.

  The range in which the formula (A) is satisfied is the initial region, and the elongation Δ of the sheet 101 in the initial region must be smaller than the critical elongation amount Δc (Δ <Δc). The critical elongation amount Δc is represented by the formula (C).

Δc = β × 2N × h ² / d (C)
Expression (C) is a basic expression that gives a threshold value of applied elongation. β is a numerical coefficient obtained experimentally and is about 3.02. The value of β includes an error due to rounding. In this specification and claims, when “β = 3.02”, the error is also included. The sheet 101 transitions from the initial region to the second region when Δ = Δc.

The applicable range of Formula (1) and Formula (A)-(C) is as follows. First, regarding the length parameter,
h <d <w (D)
It is more desirable if h <d << w. When discriminating d, d ′, and d ″ as in FIG. 1B, it is not the d ′ and d ″ but the pitch “d” in the y direction that enters these inequalities. Actually, if w / d> 4, Equation (1) and Equations (A) to (C) are established. Regardless of the thickness h of the sheet 101, the thickness is 1 μm or 1 m as long as the condition of the expression (D) is satisfied.

The Young's modulus E of the material of the sheet 101 is not limited. When the stress is σ and the strain is ε, the Young's modulus E is expressed by E = σ / ε. There is no problem even if it is 1 MPa, which is a typical value of Young's modulus of a soft gel, or 1000 times that value. However, it is important to show linear elasticity against minute deformation. From this point, it is only necessary that the strain [Δc / (2N × d)] at the transition point of the sheet 101 is in an initial region showing a linear elastic response. Note that the strain ε _c at the transition point is _calculated from the equation (C) as follows: ε _c = Δc / (2N × d) = β × h ² / d ²
Is described.

  In the case of gel or rubber, d / h of 1 or more is sufficient. Actually, the formulas (A) and (B) hold even when h> d, but in the case of a sheet material, it can be said that h <d is realistic from the viewpoint of workability.

  FIG. 4 shows K1 as a function of thickness h with various combinations of notch pitch d and notch 102c width w. Here, the number N of repeating units is N = 10. It can be seen that even if the thickness h is constant, the elasticity of the sheet 101 can be controlled by changing d and w.

  FIG. 5 shows K1 / (E × h) as a function of the parameter d / w (the ratio of the pitch d to the cut width w) with N = 10 and various combinations of d and w. FIG. 5 confirms that the spring constant K1 and the Young's modulus E1 of the sheet having the cuts are accurately defined by (d / w), as represented by the formula (B).

  In the present invention, a desired stiffness or elastic modulus can be designed for any material by appropriately selecting the number of repeating units N, the width w of the cut, and the pitch d.

Here, a more preferable range realized by the design of FIG. 1 will be described. First, examples of usable materials, realistic thicknesses, and typical tensile elastic modulus (Young's modulus) are shown.
Paper: Thickness h = 0.05 to 0.5 [mm], Young's modulus E is about 100 [MPa]
Plastic material (acrylic resin, etc.): thickness h = 0.2-5 [mm], Young's modulus E is approximately 1 [GPa]
Rubber gel material: thickness h = 0.01 to 10 [mm], Young's modulus E is about 1 [MPa]
Considering these ranges and conditional expression (D), a range satisfying d> 10h and w> 4d is considered. From equation (B), K1 and E1 are
K1≈ (7.0 / 2N) × E × h × d ³ / w ³
E1≈7.0 × E × (d / w) ⁴
It is. Since K1 and E1 are correlated (K1 = E1 × h × w / (2N × d)), K1 will be described below. When N is a constant value, the value of K1 can be reduced as much as possible by increasing the value of w. In order to increase the value of K1, the value of w may be decreased, but the minimum w is about w = 4d from the above assumption. If it is further reduced, the application limit of the formula (B) is reached. Therefore, the maximum value K1 _max that K1 can take is
K1 _max = (7.0 / 2N) × E × h × d ³ / (4d) ³
= (7.0 / (2N × 64)) × E × h
Degree. If N = 10,
When using paper with a thickness h = 0.5 [mm] and Young's modulus E = 100 [MPa], K1 _max is about E × h / 180 = 2.8 × 10 ² [N / m]. .
When a plastic material having a thickness h = 5 [mm] and a Young's modulus E = 100 [MPa] is used, K1 _max is about E × h / 180 = 2.8 × 10 ³ [N / m].
When a rubber gel having a thickness h = 10 [mm] and a Young's modulus E = 1 [MPa] is used, K1 _max is about E × h / 180 = 5.5 × 10 [N / m].

Next, consider Δc. As shown in the formula (C), there is a relationship of Δc = β × 2N × h ² / d, Δc is proportional to the number of repeating units N, and the value of β is about 3.02 from the experiment. For simplicity of explanation, β = 3. Assuming that the number of repeating units N is constant, the value of Δc can be increased by decreasing the value of d, but the minimum d is set to d = 10 h from the above premise range. When N = 10, the maximum Δc _max is
Δc _max = 3 × 2 × 10 × h ² / 10h = 6h
Degree. Since d and h can be made equal if the thickness h is large, it may be larger than the following value. If N = 10,
When using paper with a thickness h = 0.5 [mm], Δc _max = 3 [mm]
When a plastic material having a thickness h = 5 [mm] is used, Δc _max = 30 [mm]
・ Thickness h = 10 [mm], when rubber gel material is used, Δc _max = 60 [mm]
Thus, in the embodiment, the elasticity in the initial region is represented by K1 = (α / 2N) × E × d ³ h / w ³ in the formula (B), and the critical elongation amount that loses flatness is Δc = β Any sheet-like material determined by × 2N × h ² / d (formula (C)) is provided.

Based on these findings, specific application examples will be described below.
<Application to force sensor>
FIG. 6 is a schematic diagram of a force sensor 10A to which the present invention is applied. Since the transition point from the initial region to the second region is clear in the sheet of the cut paper structure, a force sensor or a weight checker using a force at the transition point as a threshold value can be manufactured.

  The force sensor 10 </ b> A includes a sheet 11 and notches 12 c and 12 e formed in the sheet 11. In this example, the number of repeating units of alternating cuts (or the number of repeating units of the central cut 12e) N is 7 (N = 7). A hole 15 for holding the measurement target is formed at the lower end of the force sensor 10A. A hook for hooking the measurement object may be attached to the lower end of the sheet 11 instead of the hole 15, or a hook for holding the measurement object may be hooked in the hole 15. Any form of measured object holding means may be employed. When a hook or a holder with a hook is used, its weight is measured in advance, and the threshold value, that is, the width w and the pitch d of the notch 12c are designed in consideration of the load of the hook or the holder.

  When the load to be measured is less than the threshold value, as shown in FIG. 6A, the sheet 11 of the sensor 10A is displaced while maintaining flatness. When the load of the sample exceeds the threshold value, as shown in FIG. 6B, the notches 12c and 12e are suddenly opened, and the structure is greatly extended with rotation.

  Normally, the threshold value can be determined visually by the rapid elongation of the sheet 11 or the opening of the cut. Depending on the shape, the cut may open to some extent while maintaining the flatness. For example, when the pitch d and the thickness h are approximately the same, the cuts 12c and 12e are opened while maintaining the flatness in the initial region. Even in such a case, when the transition point is exceeded, the entire sheet 11 is suddenly extended with rotation in the out-of-plane direction, so that visual observation is possible. When precision is required, the sheet 11 may be accommodated in a casing with a touch sensor. A conductive thin film may be formed on a part of the surface of the sheet 11, and the LED or the like may be turned on when the sheet 11 is three-dimensionally deformed and comes into contact with the transparent electrode formed on the inner wall of the casing.

  In order to obtain the load threshold value Fc measurable by the force sensor 10A, Fc = K1 × Δc may be roughly estimated based on the equation (A). As above-mentioned, K1 and (DELTA) c are each represented by Formula (B) and Formula (C).

K1 = (α / 2N) × E × d ³ h / w ³ (B)
Δc = β × 2N × h ² / d (C)
Fc = K1 × Δc = α × β × E × d ² h ³ / w ³ (E)
Here, when α = 7.0, β = 3, and α × β = 20 for simplification,
Fc≈20 × E × d ² h ³ / w ³
Is obtained. In actual design, α × β may be set to 20 ± 1. From the equation (E), it can be seen that the threshold value Fc can be designed with the cut width w and the pitch d regardless of the value of N. In order to increase the threshold value Fc, w may be decreased. If w> 4d is considered as a realistic condition, the threshold value Fc is
Fc = 20 × E × d ² h ³ / (4d) ³ = 0.31 × E × h ³ / d
It becomes. In order to increase Fc, d should be reduced, but if d> 10h, the maximum threshold is
Fc _max = 0.31 × E × h ³ /10h=0.03×E×h ²
It will be about. In some cases, the cutting pitch d in the y-direction and the sheet thickness h can be made comparable, so that a larger threshold value can be set.
When paper having a thickness of h = 0.5 [mm] is used, the threshold Fc _max is about 0.03 × E × h ² = 0.75 [N] with Young's modulus E = 100 [MPa]. .
When a plastic material having a thickness h = 5 [mm] is used, the threshold value Fc _max is about 0.03 × E × h ² = 0.75 × 10 ³ [N] with Young's modulus E = 1 [GPa]. It is.
When the rubber gel material is used for the thickness h = 10 [mm], the Young's modulus E = 1 [MPa] and the maximum threshold value Fc _max is about 0.03 × E × h ² = 3 [N]. .

When these materials are used, the upper limit is 7.5 × 10 ² [N], or when d and h are made equal, a weight sensor having a threshold value about 10 times that can be made. The lower limit of the threshold value Fc _max can be arbitrarily reduced.

FIG. 7 is a first embodiment of the force sensor 10A using in-plane deformation and transition points. In Example 1, the force sensor 10A uses an acrylic resin having a Young's modulus E of about 3 GPa as the sheet 11, and parameters are set as follows.
w = 80 [mm],
d = 10 [mm],
h = 0.3 [mm]
Set to. This force sensor functions as a 0.3 [N] sensor. Note that 1 [N] weighs about 100 grams. FIG. 7A shows a case where a load of 0.26 [N] is applied. The sensor remains flat and the load does not exceed the threshold. FIG. 7B shows a case where a load of 0.32 [N] is applied. Since the load exceeds 0.3 [N], the notch is opened and the sheet 11 is deformed three-dimensionally.

FIG. 8 is a second embodiment of the force sensor 10A using in-plane deformation and transition points. In Example 2, the force sensor 10A uses an acrylic resin having a Young's modulus E of about 3 GPa, and parameters are set as follows.
w = 60 [mm],
d = 15 [mm],
h = 0.2 [mm]
Is set. This force sensor functions as a 0.6 [N] sensor. FIG. 8A shows a case where a load of 0.58 [N] is applied, and the sensor maintains flatness. FIG. 8B shows a case where a load of 0.69 [N] is applied. Since the load exceeds 0.6 [N], the cut is opened, and the sheet 11 is deformed and stretched three-dimensionally. In FIG. 8B, the light-colored portion indicates reflection due to the rotation of the sheet 11.

It can be seen that both Examples 1 and 2 function well as load threshold sensors. If it is satisfied that Δc _max is an elongation that does not exceed the elastic limit of the sheet material and that Fc _max does not break from the tip of the sheet, it can be applied to metals that exhibit plastic deformation with a small strain. is there. For example, an aluminum foil can be used to determine the threshold of a load of a very light substance with high sensitivity.

On the other hand, when the design is made of steel having a thickness h of 0.3 [mm], d = 2.3 [mm], w = 12 [mm], and N = 10, the Young's modulus E is 100 [GPa]. Then, from the formula (E) for obtaining the threshold value, that is, Fc = 20 × E × d ² h ³ / w ³ , the threshold value is about 200 [N], which exceeds the threshold value when a nearly 20 kilogram suitcase is suspended. It will be.

  When a sensor is realized with rubber instead of metal, it is as follows. The formula (B) for adjusting the spring constant K1, the formula (C) for obtaining the maximum critical elongation amount Δcmax, and the formula (E) for obtaining the threshold value Fc are approximately equal to the sheet thickness h and the notch pitch d. This is also true for

For example, when h = d = 10 [mm], the cutting width w = 40 [mm], and a rubber having a Young's modulus E of 10 [MPa], Fc = 20 × E × d ² h ³ / w ³ The threshold is 300 [N], and a sensor exceeding the threshold can be realized when a suitcase of approximately 30 kilograms is suspended. In other words, if a hard rubber is used, a suitcase weight checker that can be easily carried, for example, having a planar size of 5 [cm] × 20 [cm] and a thickness of 5 [mm] can be realized. This configuration is useful for simple checks such as when there is a limit on the weight of luggage.
<Modification of force sensor>
FIG. 9 shows a force sensor 10B that measures the load itself as a modification. 7 to 9, the load is determined based on whether or not the threshold value is exceeded. On the other hand, in the force sensor 10B of FIG. 9, the strain gauge 16 is built on the cut paper structure, and the resistance value of the strain gauge 16 is measured by the measuring instrument 17, thereby measuring the force applied to the cut paper structure. be able to. It can be used as a weight sensor that measures the weight of a sample by obtaining the relationship between the resistance change of the strain gauge and the force in advance.

  As the strain gauge 16, an off-the-shelf strain gauge may be attached to the cut paper structure, or a strain gauge may be directly formed on the cut paper structure using a fine processing technique. A wide range of forces can be measured by designing the shape of the cut paper structure according to the order of the force to be measured.

  If the Young's modulus E and the thickness h of the sheet material to be used are given in both the force sensor 10A and the force sensor 10B, a desired width w and pitch d can be set from the formula (E). A sensor with a threshold value Fc can be produced.

FIG. 10 is a diagram demonstrating that a sensor having a desired threshold value Fc can be designed not only with paper but also with acrylic or rubber. The vertical axis represents the load threshold value Fc [N], and the horizontal axis represents the parameter Ed ² h ³ / w ³ [N] on the right side of the equation (E). A black circle is a threshold when acrylic is used for the sheet 11, and a black square is a threshold when rubber is used. With both acrylic and rubber, the number of repeating units of alternating incisions was N = 7, and five types of incision structures were produced manually. The parameters of each data point are as follows in order from the one closer to the origin.
1) E = 8 MPa rubber;
w = 30 [mm], d = 5 [mm], h = 1 [mm]
2) E = 3 GPa acrylic;
w = 80 [mm], d = 10 [mm], h = 0.3 [mm]
3) E = 3 GPa acrylic;
w = 60 [mm], d = 15 [mm], h = 0.2 [mm]
4) E = 3 GPa acrylic;
w = 60 [mm], d = 10 [mm], h = 0.4 [mm]
5) E = 3 GPa acrylic;
w = 60 [mm], d = 15 [mm], h = 0.4 [mm]
From the graph of FIG. 10, Fc and Ed ² h ³ / w ³ are linearly related to the slope 18, that is,
Fc = 18 × E × d ² h ³ / w ³
It can be seen that there is a relationship. The theoretical formula of the threshold value Fc is Fc = 20 × E × d ² h ³ / w ³ (E)
Therefore, it can be seen that it is in good agreement with the theory within the range of manufacturing errors. That is, the formula (E) is effective regardless of the material.

  FIG. 11 and FIG. 12 are diagrams showing that the elastic modulus design of the present invention is applied even when a plurality of repeated cutting units are arranged in the lateral direction (x direction in FIG. 1).

  11 shows three types of cut paper structures, and FIG. 12 shows the relationship between elongation (Δ) and force (F) in each configuration of FIG. The configurations (1) and (2) in FIG. 11 are a configuration in which a plurality of alternately repeated cuts in the vertical direction are continuously arranged in the horizontal direction. The configuration (3) in FIG. 11 is a configuration in which two cut paper structures are arranged independently.

As shown in the overall view of FIG. 12A, in the relationship between the elongation (Δ) and the force (F), all of the configurations (1) to (3) behave in the same tendency. FIG. 12B is an enlarged view of the initial region A in FIG. The linear characteristics in the initial regions of configurations (1) to (3), that is, the slopes of the displacement-force characteristics are substantially the same. This means that the spring constant of the initial region of the cut paper structure connected in the horizontal direction is expressed by the equation (B), that is, K1 = (α / 2N) × E × d ³ h / w ^{3 in} the case where the cuts are in a vertical line. It can be expressed by adding together. Even when a sheet having a plurality of cut rows in the horizontal direction is used, it is possible to apply the elastic design in the initial region and the sensor.

As shown in FIG. 12A, in the configuration (1) in which the rows of the cut paper structures are connected in the horizontal direction, the fracture occurs with a smaller displacement than in the configuration (3) separated from each other. However, in the case of the configuration (3) in which the displacement at which the breakage occurs is completely separated by previously separating the connecting portions of the cut paper near the upper end and the lower end of the cut paper structure as in the configuration (2). You can get closer. By connecting a plurality of incision rows in the horizontal direction, a large square meter cut paper structure is possible.
<Application example to medical sheet>
≪Description of sheet using biomaterial≫
To maintain or promote the function and state of organs by attaching or inserting a sheet based on biomaterials, such as polymer materials or ceramics or metal inorganic materials, to human organs be able to. For example, it is possible to support bone remodeling by being wound around a bone or being used as a joining member, or supporting movement of a hardened blood vessel by being inserted into a blood vessel. The elastic modulus of bone is about 30 GPa, while titanium, which is considered to have a low elastic modulus for metals, is about 110 GPa. The difference in elastic modulus is the cause of the stress shielding effect that is outside the living body. If the present invention is used, from the formula (B), the elastic modulus E1 when cutting into the metal sheet is
E1 = α × E × d ⁴ / w ⁴
Can be expressed as

Since α = 7.0 and titanium of E = 110 GPa is used, the elastic modulus can be tuned so that E1 = about 1 GPa if the slit is made to be d = 2 mm and w = 10 mm.
In addition, for example, by stretching outside the internal organs such as the heart and lungs, elasticity ideal for the internal organs can be supported. In this case, the elastic modulus of the biocompatible material sheet depends on the patient's current elasticity of the patient and the measured elasticity of the patient's current tissue, or the support elasticity value derived from the muscle mass and exercise strength of the organ. It can be obtained by customizing the cut paper structure. The elastic modulus can be adjusted over a wide range using a biomaterial sheet made of a unique material. In addition, since the elastic modulus is designed in a region where the in-plane displacement is maintained, that is, a region that does not reach a three-dimensional displacement with rotation, the compatibility with the tissue or organ of the patient to which the sheet is applied is good.
≪Example of cell culture sheet≫
Moreover, the optimal elasticity can be given to an application site | part to the cultured epidermis for skin transplantation of the patient who received the severe burn. FIG. 13 shows an application example of the cut paper structure to a medical recycled sheet. FIG. 13A is a schematic diagram of the medium 25 having the cuts 12c and 12e.

  By culturing the cells in the medium 25 designed as shown in FIG. 13A, a cell sheet having a desired elastic modulus can be produced. The elastic modulus or stiffness constant of the cell tissue to which the cell sheet is applied is acquired in advance, and the cut width w and the direction perpendicular to the width w so as to obtain a desired elastic modulus in the cell sheet (in FIG. 1) The pitch (interval) d in the y direction) is designed.

  When the elastic modulus adjusting technique using the cut paper structure of the present invention is applied, it is possible to make a cell sheet having an elastic modulus of 0.1 MPa using a material of cells (elastic modulus of about 10 MPa).

From the formula (B), the elastic modulus E1 when the sheet is cut is
E1 = α × E × d ⁴ / w ⁴
Can be expressed as

  Since α = 7.0, when E = 10 MPa cells are used, if the medium shown in FIG. 13A is designed so that d = 2.4 mm and w = 12 mm, the cell sheet produced in the medium is E1. The elastic modulus can be tuned to be about 0.1 MPa. The elastic modulus of cells is described in E. Moeendarbary et al., “Cell mechanics: principles, practices, and prospects”, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, Volume 6, Issue 5, 2014, Pages 371-388. Has been.

By culturing the cells in a medium in which the cuts 12c and 12e have been put in advance, a cell sheet having a cut paper structure can be produced without mechanically damaging the cells. Such a cell sheet can be used as a medical regeneration sheet. In this case, the gap δ ₀ between the incisions 12c and 12e of the medium in a state where no force is applied needs to take an appropriate value other than zero. This is because when the gap between the cuts 12c and 12e is small, the cells may block the cuts 12c and 12e during the culture. When the gap δ ₀ between the medium cuts 12c and 12e has a finite value (δ ₀ ≠ 0), the resulting cut sheet structure of the cell sheet also has a finite cut width.
≪Explanation that the design rule holds even if there is a gap in the cuts≫
In the explanation of the principle of the present invention and the application example to the sensor, it is assumed that the notch gap δ ₀ formed in the sheet is extremely small (δ ₀ = 0), but as shown in FIG. 13B. Even when the notch gap is not zero (δ ₀ ≠ 0), the principles of the present invention apply. FIG. 13B is a diagram of displacement-force characteristics of a cut paper structure having a width where the notch gap is not zero, as in FIG. 13A. In the experiment, d = 2 mm, w = 20 mm, and the number of repeating units was N = 10. The material used is paper.

In FIG. 13B, samples were prepared with three different gaps δ, and the mechanical response of the cut paper structure was measured. Sample a has δ ₀ = 0 [mm], sample b has δ ₀ = 0.1 [mm], and sample c has δ ₀ = 0.5 [mm]. As can be seen from FIG. 13B, the inclinations of the initial regions of the three types of cut sheet structures are substantially the same. This indicates that the theoretical formulas (1) and (A) to (E) apply even when the notch gap has a certain size. That is, a cell sheet obtained by culturing cells in a medium having a notch gap can also predict the stiffness or elastic modulus using the above-described theoretical formula.

Instead of preparing a cell sheet having a gap δ ₀ in advance, immediately before using it as a cell sheet, a cell sheet having a cut paper structure is applied to the use site by cutting the cell membrane using the designed w and d. May be.
≪Example of designing the elastic modulus of human skin≫
It is known that the elastic modulus of human skin is about 1 MPa. The elastic modulus of the wound dressing using porcine dermis derived from the living body is comparable. Moreover, the elastic modulus of hydrogel is also comparable.

By applying the elastic adjustment technology using the cut paper structure of the present invention, it is possible to make a sheet with an elastic modulus of 1 MPa using a biodegradable PCL (poly ε-caprolactone; elastic modulus 0.4 GPa) material. is there. From the formula (B), the elastic modulus E1 when the sheet is cut is
E1 = α × E × d ⁴ / w ⁴
Can be expressed as Since α = 7.0, when PCL with E = 0.4 GPa is used, the elastic modulus can be tuned so that E1 = 4 MPa if the cut is made so that d = 2.4 mm and w = 12 mm. it can. In this design, the thickness h can be taken from the microscale to the order of submillimeters smaller than d. There is no restriction on the area.
<Other application examples>
FIG. 14 shows an application example to a wearer such as a supporter for sports or treatment, a corset, and a low back pain belt as still another application example. Here, the wearing tool 30 is taken as an example. The mounting tool 30 has a cut region 31 at least in part. The cut area 31 includes
K1 = (α / 2N) × E × d ³ h / w ³ , or
E1 = α (d / w) ⁴ × E (B)
A cut 32 is formed so as to satisfy the above. Here, α is a coefficient, and α = 7.0 experimentally. E is the Young's modulus of the material texture, and h is the thickness of the material texture. By appropriately designing the width w, the pitch d, and the number of repetitions N of the cuts 32, it is possible to give the optimal elasticity for the wearer.

  The direction of incision can be appropriately set according to the application and site. For example, in the case of application to a bending / extending part such as a joint, an incision formed in the direction of FIG. If it is used for the purpose of compressing a cylindrical part (arm, leg, waist, etc.) of the body, an incision formed in the direction of FIG. 14B may be used.

  Moreover, it is good also as a structure which can temporarily peel each notch 32 with an adhesive tape etc., and a wearer can peel the adhesive tape of the notch 32 of a desired range. In this case, a comfortable wearing tool that provides desired elasticity at a desired site is realized. Even in the case of a cylindrical mounting tool, the displacement is only in the plane and does not include the displacement in the normal direction.

  As described above, according to the elastic design method of the present invention, the elastic modulus of the sheet-like material can be tuned in a wide range, and the elastic modulus can be predicted at the design stage.

  When the elastic modulus design is applied to a sensor, a wide range of force measurements can be achieved with a single sheet. A threshold determination type disposable force sensor is realized with an inexpensive material such as paper. Moreover, a weight measuring sensor is obtained by using together with calibration means, such as a strain gauge. The force sensor of the embodiment does not require a power source. In addition, since the sensor can be manufactured with a planar structure, it is small and space-saving.

Furthermore, application to the fields of regenerative medicine, sports equipment, and architecture is also expected. In the field of architecture, force sensors can be bridged, attached to pillars, horizontal members, etc., and used as strain sensors. Whether the building material has exceeded the stress limit or whether it complies with the building standards, depending on whether or not the force sensor has largely expanded beyond the elongation in the initial region (in-plane deformation region). It can be easily confirmed.
This application is based on patent application No. 2006-082472 filed with the Japan Patent Office on April 15, 2016, and includes the entire contents thereof.

10A, 10B Force sensors 11, 101 Sheets 12c, 12e, 32, 102c, 102e Cut 25 Medium 30 Mounting tool 31 Cut area w Cut width d Cut pitch d in the direction orthogonal to the cut width N h Sheet thickness

Claims (6)

Prepare the sheet material,
Relational expression K1 = (α / 2N) × E × d ³ h / w ³ or E1 = α (d / w) ⁴ × E applied to the sheet material in an initial deformation region where in-plane deformation is maintained.
Based on the above, staggered cut sheets whose width in the first direction is w, the arrangement pitch in the second direction orthogonal to the first direction is d, and the number of repeating units in the second direction is N Forming a cut in the structure, where K1 is a stiffness constant, E is a Young's modulus before the cut of the material constituting the sheet material, h is a thickness of the sheet material, α is a numerical coefficient,
The stiffness constant K1 or Young's modulus E1 is adjusted to a target value by selecting the values of w, d, and N.
An elastic adjustment method characterized by the above. The sheet material is a sheet of biocompatible material,
A notch is formed on the sheet based on the relational expression to produce a biological sheet having a desired elastic modulus.
The elastic adjustment method according to claim 1, wherein: Sheets having staggered cut paper structure cuts;
Holding means for holding the measurement object;
A force sensor having
In the initial deformation region where the in-plane deformation of the sheet is maintained,
Fc = α × β × E × d ² h ³ / w ³
Having a load threshold represented by
E is the Young's modulus before the cutting of the constituent material of the sheet, w is the width of the cutting in the first direction, and d is the cutting of the cut paper structure in the second direction orthogonal to the first direction. A force sensor, wherein pitch, h is the thickness of the sheet, and α × β is a numerical coefficient. A strain gauge formed on at least a part of the surface of the sheet;
A measuring instrument for measuring the resistance of the strain gauge;
The force sensor according to claim 3, further comprising: measuring a weight of a measurement object within a range of the load threshold. A sheet material having cuts of staggered cut paper structure,
The width of the notch in the first direction is w, the pitch of the notch in the second direction orthogonal to the first direction is d, the thickness of the sheet material is h, and the width in the second direction is When the number of repeating units of cutting is N and the Young's modulus before cutting of the constituent material of the sheet material is E, the elasticity of the sheet material uses a numerical coefficient α in an initial deformation region where in-plane deformation is maintained. K1 = (α / 2N) × E × d ³ h / w ³ , or E1 = α (d / w) ⁴ × E
A sheet material that is adjusted to have a stiffness constant K1 or a Young's modulus E1 determined by: The sheet material extends in the second direction in the initial displacement region where the in-plane displacement is maintained, and using a numerical coefficient β,
Δc = β × 2N × h ² / d
ε _c = Δc / (2N × d) = β × h ² / d ²
The sheet material according to claim 5, which has a critical elongation amount Δc or a critical strain ε _{c determined} by: