Strain sensing model, establishment and prediction method of flexible piezoresistive sensor

Abstract

The application belongs to the field of strain sensing, and discloses a strain sensing model of a flexible piezoresistive sensor based on a contact effect, a building method and a strain prediction method. R c The contact resistance between the two stacked conductive sheets in the piezoresistive sensor is calculated R c An equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistance, and the resistance of the equivalent circuit is calculated as the total resistance of the piezoresistive sensor R Total The relationship between the total resistance change rate of the piezoresistive sensor and the number of contact points is obtained n The relationship between the contact area between the two stacked conductive sheets and the number of contact points n , and the relationship between the contact area and the change after the piezoresistive sensor is strained are substituted into the above relationship to construct the strain sensing model. The application establishes a quantitative relationship model between the resistance change rate of the piezoresistive sensor and the strain, realizes the quantification and visualization of the sensing process, significantly improves the measurement accuracy, and has good engineering applicability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of flexible electronic strain sensing, and more particularly relates to a strain sensing model of a flexible piezoresistive sensor based on contact effect, a building method and a strain prediction method. BACKGROUND

[0002] Steel structures have the characteristics of light weight, high strength, large span, fast construction speed, etc., and are widely used in global civil infrastructure such as bridges, factories, airports and railway stations. Fatigue damage such as local yielding and weld cracking is crucial to the performance and safety of steel structures, and has become a challenge faced by global steel structure maintenance. Real-time monitoring of yield strain and weld cracking is crucial to the evaluation of the structural health of important components in steel structures. However, the deformation range of commonly used metal strain gauges and fiber Bragg grating sensors is limited, and they are prone to failure before yielding and cracking occur; and their flexibility is poor, and they cannot be attached to irregular surfaces such as welds and hole edges, thereby hindering effective monitoring of large strains and crack propagation in challenging situations. Therefore, there is an urgent need to develop flexible strain sensors with high sensitivity, wide range, easy installation and strong adhesion for steel structure monitoring.

[0003] At present, compared with other sensing mechanisms, contact effect is easier to prepare high-performance flexible sensors than tunneling effect and two-dimensional piezoresistive effect. The sensor based on tunneling effect has high sensitivity but poor stability; the sensor based on two-dimensional piezoresistive effect has high sensitivity but low range; the sensor based on contact effect has relatively balanced sensitivity, range and stability.

[0004] In recent years, domestic and foreign scholars have deduced and analyzed the sensing mechanism of sensors based on contact effect, considering the influence of stacking mode, shape, sliding and interruption in the sensor mechanism, but few have considered the interlayer contact resistance. In addition, in the stacked conductive sheet sensor, the contact resistance is significantly higher than the intrinsic resistance of the conductive sheet, and the resistance change of the sensor is mainly caused by the change of the contact resistance, which plays an important role in sensing. However, the existing theoretical model does not consider this influence, resulting in a large error in the resistance calculation of the sensor based on contact effect, so that the relative resistance change and sensitivity calculated by the current research theoretical derivation are small.

[0005] Therefore, most of the current stacked conductive sheet sensors are used for qualitative measurement of certain dynamic characteristics of the structure, and the lack of accuracy is one of the main problems that prevent them from being applied to actual engineering strain measurement. SUMMARY

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a strain sensing model of a flexible piezoresistive sensor based on contact effect, a building method and a strain prediction method, which aims to calculate the contact resistance between two stacked conductive sheets R c The contact resistance characteristics between the conductive sheet layers are determined by constructing an equivalent circuit and by the change of the contact area when strain occurs, and then the strain sensing model of the sensor is constructed depending on the relationship between the resistance change rate of the piezoresistive sensor and the strain, which can solve the technical problem of insufficient strain measurement accuracy of the existing stacked conductive sheet sensor.

[0007] To achieve the above-mentioned purpose, according to the first aspect of the present application, a building method of a strain sensing model based on contact effect is provided, comprising the following steps:

[0008] S1: calculating the contact resistance between the two stacked conductive sheets in the piezoresistive sensor R c ; wherein the contact resistance is the contact resistance of the contact surface between the two stacked conductive sheets composed of a plurality of circular contact points with a diameter of n ; a

[0009] S2: ignoring the intrinsic resistance of the conductive sheet in the piezoresistive sensor, taking the contact resistance R c as the equivalent resistance to construct the equivalent circuit of the piezoresistive sensor, calculating the resistance of the equivalent circuit as the total resistance of the piezoresistive sensor R Total ; calculating the total resistance change rate of the piezoresistive sensor after strain occurs, obtaining the relationship between the total resistance change rate of the piezoresistive sensor and the number of contact points n ;

[0010] S3: substituting the relationship between the contact area between the two stacked conductive sheets and the number of contact points n , and the relationship between the contact area and the change after the piezoresistive sensor is strained into the relationship between the total resistance change rate of the piezoresistive sensor and the number of contact points n , to obtain the relationship between the total resistance change rate of the piezoresistive sensor and the strain.

[0011] As a preferred embodiment of the present application, in step S1, the contact resistance of the circular contact point with a diameter of a is represented as: , and the contact resistance of the contact surface between the two stacked conductive sheets is represented as: R c . ​

[0012] ;

[0013] wherein, ρ is the conductivity of the conductive sheet material.

[0014] As a preferred embodiment of the present application, in step S2, the contact resistance R c The equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistance, including:

[0015] The contact resistance R c The equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistance, in combination with the distribution of conductive sheets in the piezoresistive sensor, including:

[0016] The piezoresistive sensor contains an odd number of layers of k conductive sheets, and an even number of layers of k -1 conductive sheets, in total m layers of conductive sheets; the equivalent circuit of the piezoresistive sensor is composed of 2( k -1) series resistances along the length direction of the conductive sheets, each of which includes ( m -1) contact resistances R c in parallel.

[0017] As a preferred embodiment of the present application, in step S2, the total resistance change rate of the piezoresistive sensor and the number of contact points n before and after the strain, specifically includes:

[0018] The contact resistance R c between the two stacked conductive sheets is represented by n the contact resistance of a circular contact points with a diameter of R c , and is substituted into the total resistance change rate of the piezoresistive sensor, which is represented as:

[0019] ;

[0020] wherein, is the total resistance change value of the piezoresistive sensor after the strain, is the contact resistance after the strain, is the number of contact points after the strain.

[0021] As a preferred embodiment of the present application, in step S3, the number of contact points nproportional to the contact area, denoted as:

[0022] ;

[0023] wherein, S is the contact area between the two stacked conductive sheets, b is the number of contact points per unit area.

[0024] As a preferred embodiment of the present application, in step S3, the relationship between the contact area and the change of the piezoresistive sensor after being strained, including the state of zero strain and the change of the contact area and the piezoresistive sensor after being strained, is as follows:

[0025] In the state of zero strain, the initial contact area between the two stacked conductive sheets S 0is denoted as:

[0026] ;

[0027] Under the action of an external force that generates strain, the contact area between the two stacked conductive sheets changes due to the increase in the distance between the conductive sheets on the even layers, and is denoted as:

[0028] ;

[0029] wherein, L is the length of the conductive sheet, d is the distance between the conductive sheets in the same layer, is the strain, k is the number of conductive sheets on the odd layers.

[0030] As a preferred embodiment of the present application, in step S3, the relationship between the total resistance change rate of the piezoresistive sensor and the strain is denoted as follows:

[0031] ;

[0032] wherein, is the total resistance change rate of the piezoresistive sensor, k is the number of conductive sheets on the odd layers, is the strain, L is the length of the conductive sheet, d is the distance between the conductive sheets in the same layer.

[0033] As a preferred embodiment of the present application, considering the non-uniformity of the size of the conductive sheets in the piezoresistive sensor, three sizes of conductive sheets are defined, with lengths of L 1, L 2, L 3, wherein, , and odd layers of conductive sheets L 1 、L 2 two lengths are alternately distributed, and the length of the conductive sheet on the even layer is L 3, and contact surfaces of two sizes are formed;

[0034] After the strain occurs, the contact area and the number of contact points on the two types of contact surfaces are respectively represented as:

[0035] ;

[0036] ;

[0037] After the strain occurs, the total resistance change rate of the piezoresistive sensor and the strain are related as:

[0038] ;

[0039] wherein, and the number of contact points on the first type of contact surface, the number of contact points on the second type of contact surface, k the number of conductive sheets on the odd layer, the strain, d the pitch of the conductive sheets in the same layer.

[0040] According to a second aspect of the present application, a strain sensing model of a flexible piezoresistive sensor based on contact effect is provided, which is determined by the method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to the first aspect of the present application.

[0041] According to a third aspect of the present application, a strain prediction method of a flexible piezoresistive sensor based on contact effect is provided, which is used for strain prediction by the strain sensing model of a flexible piezoresistive sensor based on contact effect according to the second aspect of the present application, and includes: determining the strain of the piezoresistive sensor based on the total resistance of the piezoresistive sensor measured before and after the strain.

[0042] Overall, compared with the prior art, the above technical solutions conceived by the present application mainly have the following technical advantages:

[0043] (1) The method for establishing a strain sensing model provided by the present application transmits the current between every two stacked conductive sheets through n contact points with a diameter of a , the contact resistance of the n contact points forms a parallel path, and the resistance of the parallel circuit is calculated to obtain the contact resistance between every two stacked conductive sheets R cThe existing model ignores the roughness of the contact surface, and directly regards the contact surface as a conductor for resistance calculation, and in the application, the form of the contact point between the contact surfaces and the calculation of the contact resistance are quantified, which is convenient to combine with the subsequent quantifiable strain change, improves the calculation precision and reduces the model design error; further, the contact resistance R c As an equivalent circuit for constructing a piezoresistive sensor, the resistance of the equivalent circuit is calculated as the total resistance of the piezoresistive sensor R Total Therefore, the existing stacked conductive sheet sensor sensing model establishment process only considers the intrinsic resistance of the conductive sheet, and the contact resistance much larger than the intrinsic resistance of the conductive sheet is substituted, which improves the accuracy of the strain sensing model prediction; at the same time, combining the relationship between the contact area and the number of contact points in the piezoresistive sensor n , the finally established sensor sensing model is related to the area change after the strain, eliminating the influence of other factors in the model, and the strain sensing process of the stacked conductive sheet sensor is quantized and visualized. Therefore, the force sensing model constructed by relying on the relationship between the resistance change rate of the piezoresistive sensor and the strain improves the measurement accuracy of the piezoresistive sensor.

[0044] (2) Compared with ignoring the influence of contact resistance on the overall resistance, the application quantitatively calculates the resistance of each conductive point, and then determines the contact resistance between each two stacked conductive sheets based on n the parallel connection of the contact points, which is more in line with the actual situation of the sensor contact interface and has higher calculation accuracy.

[0045] (3) Compared with the existing model, the equivalent circuit constructed based on the electrical contact theory includes the contact resistance, and since the change of the contact resistance is a more important factor affecting the overall resistance change than the change of the intrinsic resistance of the conductive sheet, the consideration of the application reduces the model calculation error. At the same time, the application R c As an equivalent resistance to construct an equivalent circuit, the relationship between the total resistance change rate of the piezoresistive sensor and the number of contact points n is obtained, that is, the resistance change rate is converted into the change of the number of contact points in the contact resistance n , which simplifies the calculation method and improves the calculation efficiency.

[0046] (4) Before and after the strain occurs, the number of contact points on each contact surface is proportional to the contact area, and therefore, the sensor sensing model is related to the area change after the strain.

[0047] (5) The method is suitable for the differences in different sensor designs, deeply understands the influence mechanism of different factors on the resistance characteristics of the flexible sensor based on the contact effect, can optimize the material size and the preparation process, accurately analyzes the contact effect, adopts a more effective stacking distribution technology, and promotes the customized development of the flexible sensor based on the contact effect under different requirements.

[0048] (6) The method considers the influence of the conductive sheet stacking structure, the conductive sheet size, the conductive sheet spacing and the non-uniformity of the conductive sheet size on the resistance change rate, and provides more detailed theoretical support for the design and strain monitoring of the flexible sensor based on the contact effect.

[0049] To sum up, the method for establishing a strain sensing model provided by the application improves the measurement accuracy of the flexible sensor and solves the problem of low strain measurement accuracy of the flexible sensor. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The structure layer schematic diagram of a flexible piezoresistive sensor based on the contact effect is shown.

[0051] Figure 2 The flowchart of the establishment of a sensing model of a flexible piezoresistive sensor based on the contact effect is shown.

[0052] Figure 3 The structure schematic diagram of a uniform stacking piezoresistive sensor with graphene conductive sheets is shown.

[0053] Figure 4 The equivalent circuit diagram of a uniform stacking piezoresistive sensor with graphene conductive sheets is shown.

[0054] Figure 5 The structure schematic diagrams of a piezoresistive sensor with two types of contact surfaces before and after strain are shown. Figure 5 (a) is the structure schematic diagram of the piezoresistive sensor before strain, and (b) is the structure schematic diagram of the piezoresistive sensor after strain.

[0055] Figure 6 The relative resistance change comparison diagram of the traditional model, the model of the embodiment of the application and the simulation experiment under the condition that the number of conductive sheets is different is shown.

[0056] Figure 7 The relative resistance change comparison diagram of the traditional model and the model of the embodiment of the application is shown.

[0057] Figure 8 The relative resistance change comparison diagram of the model of the embodiment of the application and the simulation experiment under the condition that the spacing between the conductive sheets is different is shown.

[0058] Figure 9 This is a comparison diagram of relative resistance changes under conditions of different conductive sheet lengths in the model and simulation experiments of an embodiment of the present invention.

[0059] Figure 10 This is a comparison diagram of relative resistance changes in a model and a sensor stretching experiment considering size non-uniformity conditions according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0061] See also Figure 1 , which is a schematic diagram of the structural layers of a piezoresistive sensor based on the contact effect provided by the present invention. The sensor is simplified into a layered structure. The flexible sensor includes, from top to bottom, a sensitive layer formed by stacking conductive sheets and a base layer; the sensitive layer is directly adhered to the base layer to reduce strain transmission loss, and the materials of each layer are linear elastic materials and are isotropic.

[0062] Specifically, Figure 1 The sensitive layer is formed by stacked conductive sheets in the same contact state. Its main function is to convert the mechanical behavior it receives into an electrical signal. When the structural layer is strained, the stacked conductive sheets in the sensitive layer slide relative to each other, changing the resistance of the two contacting conductive sheets and causing the total resistance of the sensitive layer to change. Based on this, by monitoring the resistance change of the sensitive layer, the strain of the stacked conductive sheet sensor structure can be measured.

[0063] based on Figure 1 The present invention provides a method for establishing a sensing model of a piezoresistive sensor based on a contact effect, such as Figure 2 As shown, the following steps are included:

[0064] S1: Based on R.Holm's electrical contact theory, the contact surface between two stacked conductive sheets is n The diameter is a The circular contact point transmits current, n The contact resistance of the circular contact points forms a parallel path. The resistance of the parallel path is calculated to obtain the contact resistance between the two stacked conductive sheets. R c ;

[0065] S2: ignoring the intrinsic resistance of the conductive sheet in the piezoresistor, the contact resistance R c The equivalent circuit of the piezoresistor is constructed as an equivalent resistance, and the resistance of the equivalent circuit is calculated as the total resistance of the piezoresistor R Total The total resistance change rate of the piezoresistor after strain occurs is calculated, and the relationship between the total resistance change rate of the piezoresistor and the number of contact points n

[0066] S3: the relationship between the contact area between the two stacked conductive sheets and the number of contact points n , and the relationship between the contact area and the change after the piezoresistor is strained, is substituted into the relationship between the total resistance change rate of the piezoresistor and the number of contact points n , and the relationship between the total resistance change rate of the piezoresistor and the strain is constructed.

[0067] In the design concept of the present application, since the contact resistance between the two stacked conductive sheets is much larger than the intrinsic resistance of the conductive sheet, the resistance change of the piezoresistor is mainly caused by the contact resistance change, and the contact resistance between the two stacked conductive sheets R c can reflect the electrical contact performance of the sensitive layer of the conductive sheet stack.

[0068] In step S1 of the present application, the contact resistance R c is represented by means of the R.Holm electrical contact theory, the conductivity of the conductive sheet in the piezoresistor is ρ , the contact point is considered to be circular, the diameter is a , the number of contact points per unit area is b , and the total number of contact points on the contact surface is n .

[0069] Therefore, based on the R.Holm electrical contact theory, the essence of the contact resistance is the resistance of the conductor, which is proportional to the resistivity of the contact conductive material and inversely proportional to the diameter of the conductive contact point, and the contact resistance of each contact point in the sensitive layer of the conductive sheet stack is The calculation formula is represented as:

[0070] ;

[0071] The contact resistance between the two stacked conductive sheets is calculated by Cooper-Mikic-Yovanovich correlation, and the contact resistance of each contact point is in parallel relationship on the contact surface, that is n The contact point resistance is in parallel relationship on the contact surface, that is

[0072] .​

[0073] In step S2 of the present invention, in a stacked sensitive layer sensing model, the contact resistance between two stacked conductive sheets is converted to R c The total resistance is calculated by the equivalent circuit design based on the stacking method of the sensitive layer. That is, the conductive sheets stacked between each layer are in parallel, and the conductive sheets arranged in each layer are in series. The resistance of the sensitive layer is obtained by the equivalent circuit. Then, the contact resistance between the two stacked conductive sheets is calculated. R c Introduced into the resistance calculation of the piezoresistive sensor, the total resistance of the piezoresistive sensor and the number of contact points are established n Similarly, the relationship between the total resistance change rate of the piezoresistive sensor after strain and the number of contact points can be confirmed. n relationship.

[0074] It should be noted that the piezoresistive sensor structure includes a base layer and a sensitive layer on structural layers stacked layer by layer, wherein the sensitive layer includes stacked conductive sheets and electrodes at both ends; the electrodes and the conductive sheets are assumed to have the same conductivity, and the contact resistance between the electrodes and the stacked conductive sheets is not considered; the base transfers the structural strain to the conductive sheets, ignoring the base layer and directly imparting strain to the conductive sheets.

[0075] In step S3 of the present invention, before and after the strain occurs, on the contact surface between the two stacked conductive sheets, the number of contact points on each contact surface is proportional to the contact area, which can be expressed as:

[0076] ;

[0077] in, S is the contact area between the two conductive sheets, b is the number of contact points per unit area.

[0078] Specifically, the changes in the contact area and the strain of the piezoresistive sensor include the following:

[0079] Initial contact area between two stacked conductive sheets at zero strain S 0 is represented by:

[0080] ;

[0081] Under the action of external force that generates strain, the contact area between the two stacked conductive sheets The change in is considered to be caused by the increase in the spacing between the conductive sheets on the even layers, which can be expressed as:

[0082] ;

[0083] in, L is the length of the conductive sheet,d is the spacing between conductive sheets in the same layer, For strain, k is the number of conductive sheets on odd layers.

[0084] Therefore, the total resistance change rate and the number of contact points of the piezoresistive sensor after strain established in step S2 are n In the relationship, the number of contact points on each contact surface is proportional to the contact area, and the change in the contact area and the strain of the piezoresistive sensor can be obtained. The relationship between the total resistance change rate of the piezoresistive sensor and the strain can be obtained.

[0085] In some embodiments, as Figure 3 , which is a schematic diagram of a uniformly stacked piezoresistive sensor structure in which the conductive sheet is graphene, provided in an embodiment of the present invention.

[0086] Specifically, the structure and composition of the piezoresistive sensor refer to Figure 1 As described above, the sensitive layer is a pure graphene sheet material; the base layer is a PDMS (polydimethylsiloxane) material; and the resistance of the sensitive layer is equivalent to the resistance of the piezoresistive sensor.

[0087] The conductivity of the conductive sheet in the sensitive layer is ρ , size is L , with a thickness of 1 μm and the conductive sheets have the same size and the spacing between the conductive sheets is set to the same. The number of layers stacked in the sensitive layer is m The number of conductive sheets arranged in odd layers is k , the number of conductive sheets arranged in even layers is ( k -1). Establish the coordinate system ( x , y ), x The axis is the length direction of the conductive sheet. y The axis is the thickness direction of the conductive sheet.

[0088] The method for establishing a strain sensing model for a flexible piezoresistive sensor based on contact effect specifically includes the following steps:

[0089] like Figure 4 As shown, in a uniform stacked sensitive layer sensing model, the contact resistance of the two-phase contact conductive sheet is R c According to the stacking method of the sensitive layer and the design of an equivalent circuit, specifically in a uniform stacking method, ignoring the wire resistance, the resistance of the sensitive layer is equivalent to the total resistance of the flexible piezoresistive sensor based on the contact effect.

[0090] The contact resistance is more than two orders of magnitude of the intrinsic resistance of the conductive sheet. The equivalent circuit is constructed by ignoring the intrinsic resistance, and the contact resistance between the electrode and the stacked conductive sheet is not considered. The total resistance of the sensor is R Total is expressed as:

[0091] .

[0092] The contact resistance between the two stacked conductive sheets is calculated according to the R. Holm theory as follows: R c ;

[0093] Further, before and after the strain occurs, the number of contact points on each contact surface is proportional to the contact area between the two stacked conductive sheets, which is expressed as:

[0094] ;

[0095] wherein, S is the contact area between the two conductive sheets, b is the number of contact points per unit area.

[0096] For the zero strain state, the initial number of conductive points of the model is expressed as:

[0097] ;

[0098] wherein L is the length of each conductive sheet, d is the spacing between the conductive sheets, b is a constant representing the relationship between the contact length and the number of contact points;

[0099] For the ɛ strain state, the total deformation is Since the elastic model of the conductive sheet is more than two orders of magnitude of the flexible substrate, the overall deformation during stretching is realized by the increase of k -1) spacing, then the number of contact points in each contact area is n' which can be defined by the following formula:

[0100] ;

[0101] and is: .

[0102] Then, the relative resistance change value ΔR / R is defined as:

[0103] .

[0104] i.e. to establish a relative resistance change rate-strain curve.

[0105] In another embodiment, the influence of the size non-uniformity of the stacked conductive sheets on the resistance calculation is considered to improve the calculation accuracy. Three sizes of conductive sheets are defined, with lengths of L 1、 L 2、 L 3, wherein, , and the conductive sheets of the odd layers L 1 、L 2 are alternately distributed, and the conductive sheets of the even layers have a length of L 3, and the contact surfaces are formed in two sizes.

[0106] At this time, the sizes of the two types of contact surfaces in the piezoresistive sensor are as follows: the contact resistance and the number of contact points on the two types of contact surfaces are represented as:

[0107] , ; , ;

[0108] the number of contact points on the first type of contact surface is the number of contact points on the second type of contact surface is the contact resistance of the first type of contact surface is the contact resistance of the second type of contact surface is k the number of conductive sheets on the odd layers is the strain is d the pitch of the conductive sheets in the same layer is.

[0109] Further, the sizes of the two types of contact surfaces in the piezoresistive sensor are as follows: the total resistance of the stacked conductive sheet sensor considering the non-uniformity of the conductive sheets is R composed of 2( k -1) series resistances parallel to the sensitive layer direction, wherein each series resistance is formed by (( m -1) / 2) first type of contact resistances and (( m -1) / 2) second type of contact resistances in parallel, and the total resistance of the piezoresistive sensor is represented as:

[0110]

[0111]

[0112]

[0113] .

[0114] The number of contact points on the two types of contact surfaces after the strain occurs is:

[0115]

[0116] ;

[0117]

[0118] .

[0119] The changed contact resistance is:

[0120] ;

[0121] Referring to Figure 5 , the relationship between the resistance change rate and the strain after the strain occurs is:

[0122] .

[0123] That is, during the stretching process, when the sensor is strained, , the short conductive piece will be disconnected first, changing the relationship between the resistance change rate and the strain, corresponding to the segmented linear characteristics of the actual sensor.

[0124] In some other embodiments of the present application, a strain prediction method for a flexible piezoresistive sensor based on contact effect, uses the strain sensing model of the flexible piezoresistive sensor based on contact effect obtained in any one of the first aspect of the present application to predict the strain, including: determining the strain of the piezoresistive sensor based on the total resistance of the piezoresistive sensor measured before and after the strain.

[0125] Sensitivity is an important factor for evaluating the sensing performance of the flexible piezoresistive sensor based on contact effect, which represents the relative resistance ΔR / R per unit strain, and is defined by the following formula:

[0126] .

[0127] The strain sensing model of the flexible piezoresistive sensor based on contact effect described in the above embodiments is verified below in combination with the traditional model.

[0128] In the existing model, the contact resistance between the graphene layers is ignored, resulting in calculation errors. The existing model assumes that under the strain condition, the overall resistance is mainly affected by the change in the electron migration path length caused by the relative sliding of the overlapping graphene layers, and calculates the overall resistance as follows:

[0129] ;

[0130] wherein, sis the global stiffness matrix, m 1 is the number of odd layers, m 2 is the number of even layers, k is the number of graphene sheets per layer. Current models assume a linear relationship between resistance and strain, which means that the relative sliding between graphene layers will cause a linear change in the conductive path, which in turn causes a corresponding linear change in resistance. However, in practice, the sensor resistance does not change completely linearly, but tends to be linear under low strain conditions. Under zero strain conditions, the initial resistance of the current model is R 0 can be represented as

[0131] ;

[0132] Existing models assume m 1 and m 2 are roughly equal, the relative change in resistance can be simplified to

[0133] .

[0134] The model of the embodiment of the present invention is the strain electrical sensing model of the flexible piezoresistive sensor based on the contact effect in the above embodiment, specifically:

[0135] .

[0136] like Figure 3 As shown, this embodiment takes the finite element model of the flexible sensor as the object, the base layer material of the flexible sensor adopts PDMS, the sensitive layer material adopts graphene material, and the thickness of the graphene material is 1 μm.

[0137] The graphene flakes are considered as rigid flakes. In addition, when the overlapping areas of two adjacent graphene flakes in the sensor are naturally uneven, the sliding friction between the two contacting graphene flakes is almost zero. Therefore, when mechanical strain is applied to the sensor, the overlapping graphene will break or slide relative to each other due to the weak interface bonding, and the relative sliding between the graphene flakes and the substrate occurs due to the large stiffness mismatch. Based on the above facts, the sensor deforms uniformly under the action of strain. This means that the center of mass of each graphene flake remains unchanged relative to the substrate. During the deformation process, the center of mass of each graphene flake remains unchanged relative to the substrate. y The coordinates remain unchanged, while x The coordinates are calculated from Eq.

[0138] The simulation experiment was performed in Comsol. The displacement of the graphene sheets after applying strain in the finite element model was calculated using the Cooper-Mikic-Yovanovich (CMY) correlation hypothesis for the interface between the graphene sheets. The calculation method is as follows:

[0139] ;

[0140] ;

[0141] J 1, J 2 are the current at the upper and lower contact points, respectively, V 1, V 2 are the voltage at the upper and lower contact points, respectively, n is the number of contact points, is the electrical conductance at the interface due to incomplete contact caused by surface roughness:

[0142] ;

[0143] Here, H c is the microhardness of the softer material, p is the contact pressure, σ contact is the harmonic mean of the electrical conductivity of the contact surfaces, σ asp is the average roughness height, m asp is the average roughness slope:

[0144] ;

[0145] σ u , σ u is the electrical conductivity of the two contact surfaces, and is the harmonic mean of the electrical conductivity of the contact surfaces relative to the pressure p / H c can be evaluated by directly specifying H c or using the following relative pressure relationship of c 1 and c 2 (Vickers correlation coefficient and size index):

[0146] ;

[0147] The Brinell hardness is represented by H B , H 0 is equal to 3.178 GPa.

[0148] The rough surface is set to have an average roughness height of 1 pm, an average roughness slope of 0.4, a contact pressure of 100 KPa, and a microhardness of 3 GPa. A current of 1 A is applied to one end of the graphene sheet, and the other end is grounded, and the overall resistance is calculated.

[0149] To verify that the application is more suitable for flexible piezoresistive sensors based on contact effect, a comparison is made using traditional model calculation. Figure 6 The number of conductive sheets on odd layers is given as 5, 10, and 20 when the length of graphene sheets is 10 μm and the interval distance is 5 μm. k The relative resistance change values calculated by the traditional model, the model of the application, and the simulation experiment are compared under the conditions of 5, 10, and 20, respectively. Figure 7 The comparison chart of the relative change values of the resistance calculation of the traditional model and the model of the application is given. k The comparison chart of the relative change values of the resistance calculation of the traditional model and the model of the application is given. Figure 6 And Figure 7 It can be seen that the relative resistance change value calculated by the model of the application is greater than that of the traditional model, and the error is significantly smaller than the calculation result of the traditional model, which shows the effectiveness of the application in improving the accuracy of the force-electricity sensing model.

[0150] Further, to verify the wide applicability of the model establishment method of the application, different sizes of graphene sheets are used to compare the results. Figure 8 In the comparison, the length of the conductive sheet is 10 μm, the interval distance is 1 μm, 5 μm, and 7 μm, and the number of conductive sheets per layer is 10. Figure 9 In the comparison, the length of the conductive sheet is 6 μm, 8 μm, and 10 μm, the interval distance is 1 μm, and the number of conductive sheets per layer is 10. As can be seen from the chart, the results of the optimized model are well fitted with the finite element model under various conditions, which also shows the applicability of the application to various layered sensors.

[0151] Further, to improve the fitting degree of the application to the performance of the actual sensor, the non-uniformity of the graphene sheet is considered, as shown in Figure 2 .The length of the conductive sheet is L 1=8 μm, L 2=12 μm, L 3=10 μm, and the interval distance of the conductive sheet is d =7 μm. The comparison of the calculation results and the experimental results is shown in Figure 10 .The calculation method is well fitted with the experimental results and has high precision.

[0152] The improved flexible piezoresistive sensor force-electricity sensing model based on the contact effect in one of the embodiments shown in Figure 1 to Figure 10 combines the contact characteristics of the conductive sheet and the strain distribution relationship of the conductive sheet to obtain an improved strain sensing model, improves the accuracy of the strain sensing model, quantizes and visualizes the strain transmission process of the flexible sensor, improves the measurement accuracy of the flexible sensor, solves the problem of low strain measurement accuracy of the flexible sensor, is simple to calculate and has high precision, and has strong engineering applicability.

[0153] Obviously, various modifications and changes are possible in the present application without departing from the spirit and scope of the application. It is intended that the application encompass such modifications and changes as fall within the scope of the application, including its equivalents. The above-described embodiments are merely possible implementations of the present application, and the scope of protection is not limited thereto. Any equivalent substitutions or changes made by those skilled in the art based on the technical spirits and principles of the present application shall fall within the scope of protection of the present application.

Claims

1. A method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect, characterized in that: The steps include: S1: The contact resistance between the two stacked conductive sheets in the piezoresistive sensor R c Calculate; wherein, the contact resistance is the contact surface between the two stacked conductive sheets through n The diameter is a The contact resistance of the circular contact points is connected in parallel; S2: Ignore the intrinsic resistance of the conductive sheet in the piezoresistive sensor and use the contact resistance R c As an equivalent resistance, the equivalent circuit of the piezoresistive sensor is constructed in combination with the distribution of the conductive sheets in the piezoresistive sensor, and the resistance of the equivalent circuit is calculated as the total resistance of the piezoresistive sensor. R Total ; Calculate the total resistance change rate of the piezoresistive sensor after strain occurs, and obtain the total resistance change rate of the piezoresistive sensor and the number of contact points n wherein the piezoresistive sensor comprises an odd number of layers k Conductive sheets, on even layers k -1 conductive sheet, total m The equivalent circuit of the piezoresistive sensor is composed of 2 layers of conductive sheets. k -1) series resistors along the length direction of the conductive sheet, each of the series resistors includes ( m -1) The contact resistance along the thickness direction of the conductive sheet R c Parallel composition; S3: Compare the contact area between the two stacked conductive sheets and the number of contact points n The relationship between the contact area and the change after the piezoresistive sensor is strained is substituted into the relationship between the total resistance change rate of the piezoresistive sensor and the number of contact points. n In the relationship between the total resistance change rate and strain of the piezoresistive sensor, a relationship between the total resistance change rate and strain of the piezoresistive sensor is constructed.

2. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 1 is characterized in that: In step S1, the diameter is a The contact resistance of the circular contact point is expressed as: , then the contact resistance of the contact surface between the two stacked conductive sheets is R c , expressed as: ； in, ρ is the electrical conductivity of the conductive sheet material.

3. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 1, characterized in that: In step S2, the total resistance change rate of the piezoresistive sensor is proportional to the number of contact points. n The relationship includes: The contact resistance between the two stacked conductive sheets R c pass n The diameter is a Contact resistance of circular contact point R c It is expressed as follows, and substituted into the total resistance change rate of the piezoresistive sensor, which is expressed as: ； in, is the total resistance change of the piezoresistive sensor after strain occurs, is the contact resistance after strain occurs, is the number of contact points after strain occurs.

4. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 1, characterized in that: In step S3, before and after the strain occurs, the number of contact points on the contact surface between the two stacked conductive sheets is n is proportional to the contact area and is expressed as: ； in, S is the contact area between the two stacked conductive sheets, b is the number of contact points per unit area.

5. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 4, characterized in that: In step S3, the relationship between the contact area and the change of the piezoresistive sensor after the strain occurs, including the relationship between the contact area and the change of the piezoresistive sensor in the zero strain state and after the strain occurs, is as follows: The initial contact area between the two stacked conductive sheets in the zero strain state is S 0 is represented by: ； Under the action of an external force that generates strain, the contact area between the two stacked conductive sheets is The change in is considered to be caused by the increase in the spacing between the conductive sheets on the even layers, which can be expressed as: ； in, L is the length of the conductive sheet, d is the spacing between conductive sheets in the same layer, For strain, k is the number of conductive sheets on odd layers.

6. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 1, characterized in that: In step S3, the relationship between the total resistance change rate of the piezoresistive sensor and the strain is expressed as follows: ； in, is the total resistance change rate of the piezoresistive sensor, k is the number of conductive sheets on odd layers, For strain, L is the length of the conductive sheet, d is the spacing between conductive sheets in the same layer.

7. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 4, characterized in that: Considering the condition of the non-uniform size of the conductive sheet in the piezoresistive sensor, three sizes of conductive sheets are defined, with lengths of L 1. L 2. L 3, among which, ,and , odd-numbered conductive sheets L 1 、L 2 The two lengths are distributed alternately, and the length of the conductive sheet distributed in the even layers is L 3. and forming contact surfaces with two sizes; After strain occurs, the contact area and the number of contact points on the two types of contact surfaces are expressed as: ； ； After strain occurs, the relationship between the total resistance change rate of the piezoresistive sensor and the strain is: ； in, is the number of contact points on the first type of contact surface, is the number of contact points on the second type of contact surface, k is the number of conductive sheets on odd layers, For strain, d is the spacing between conductive sheets in the same layer.

8. A strain sensing model of a flexible piezoresistive sensor based on contact effect, characterized in that: The method is determined by using the method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect as described in any one of claims 1 to 7.

9. A method for predicting strain of a flexible piezoresistive sensor based on contact effect, using the strain sensing model of the flexible piezoresistive sensor based on contact effect as claimed in claim 8 to predict strain, comprising: The strain of the piezoresistive sensor is determined based on the total resistance of the flexible piezoresistive sensor measured before and after the strain.

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