Strain sensing model of flexible piezoresistive sensor based on contact effect, establishment method and strain prediction method

Abstract

The invention belongs to the field of strain sensing, and discloses a strain sensing model of a flexible piezoresistive sensor based on a contact effect, an establishment method and a strain prediction method. The building method of the model comprises the following steps: calculating the contact resistance Rc between two stacked conducting strips in the piezoresistive sensor; constructing an equivalent circuit of the piezoresistive sensor by taking the contact resistance Rc as an equivalent resistance, calculating the resistance of the equivalent circuit as the total resistance RTotal of the piezoresistive sensor, and obtaining the relationship between the total resistance change rate of the piezoresistive sensor and the number n of the contact points; and substituting the relationship between the contact area between the two stacked conductive sheets and the number n of the contact points and the relationship between the contact area and the change of the piezoresistive sensor after strain into the relational expression to construct a strain sensing model. According to the method, the quantitative relation model of the resistance change rate and the strain of the piezoresistive sensor is established, quantification and visualization of the sensing process are achieved, the measurement precision is remarkably improved, and good engineering applicability is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to flexible electronic strain sensing, and more specifically, relates to a strain sensing model, establishment method and strain prediction method of a flexible piezoresistive sensor based on contact effect. Background Art

[0002] Steel structures are widely used in global civil infrastructure such as bridges, factories, airports, and railway stations due to their light weight, high strength, large spans, and fast construction speeds. Fatigue failures such as local yielding and weld cracking are crucial to the performance and structural safety of steel structures and have become a common challenge in global steel structure maintenance. Real-time monitoring of yield strain and weld cracking is essential for assessing the structural health of important components in steel structures. However, commonly used metal strain gauges and fiber Bragg grating sensors have a limited deformation range and are prone to failure before yielding and cracking occur. Furthermore, they have poor flexibility and cannot conform to irregular surfaces such as welds and hole edges, hindering the 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] Currently, compared with other sensing mechanisms, the contact effect is easier to fabricate high-performance flexible sensors than the tunneling effect and two-dimensional piezoresistive effect. Sensors based on the tunneling effect have high sensitivity but poor stability; sensors based on the two-dimensional piezoresistive effect have high sensitivity but a low range; sensors based on the contact effect have relatively balanced sensitivity, range, and stability.

[0004] In recent years, scholars at home and abroad have derived and analyzed the sensing mechanisms of sensors based on the contact effect, considering the effects of stacking pattern, shape, sliding, and interruptions on the sensor mechanism. However, few have considered interlayer contact resistance. Furthermore, in stacked conductive sheet sensors, the contact resistance is significantly higher than the intrinsic resistance of the conductive sheets. Changes in the sensor's resistance are primarily caused by changes in contact resistance, which plays a significant role in sensing. Existing theoretical models fail to account for this effect, resulting in large errors in resistance measurements for sensors based on the contact effect. Consequently, the relative resistance change and sensitivity calculated using current theoretical derivations are both understated.

[0005] Therefore, currently stacked conductive sheet sensors are mostly used to qualitatively measure certain dynamic characteristics of structures, and insufficient accuracy is one of the main problems that prevent them from being applied to actual engineering strain measurement. Summary of the Invention

[0006] In response to the above defects or improvement needs of the prior art, the present invention provides a strain sensing model, establishment method and strain prediction method of a flexible piezoresistive sensor based on contact effect, the purpose of which is to calculate the contact resistance between two stacked conductive sheets. R c The contact resistance characteristics between the conductive sheet layers are combined by constructing an equivalent circuit, and the relationship between the resistance change rate of the piezoresistive sensor and the strain is determined by combining the change in contact area when strain occurs. The strain sensing model of the sensor is constructed based 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 existing stacked conductive sheet sensors.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect is provided, comprising the following steps: 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 An equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistor, 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 relationship; 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.

[0008] As a preferred embodiment of the present invention, 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.

[0009] As a preferred embodiment of the present invention, in step S2, the contact resistance R c An equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistor, comprising: The contact resistance R c As an equivalent resistor, the equivalent circuit of the piezoresistive sensor is constructed in combination with the distribution of the conductive sheets in the piezoresistive sensor, including the following: 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.

[0010] As a preferred embodiment of the present invention, 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.

[0011] As a preferred embodiment of the present invention, 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.

[0012] As a preferred embodiment of the present invention, in step S3, the relationship between the contact area and the change of the piezoresistive sensor after strain, including the relationship between the contact area and the change of the piezoresistive sensor in the zero strain state and after strain, is as follows: The initial contact area between the two stacked conductive sheets in the zero strain state is S 0 Expressed as: ; 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.

[0013] As a preferred embodiment of the present invention, 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.

[0014] As a preferred embodiment of the present invention, considering the condition of uneven 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 ,in, ,and , odd-numbered conductive sheets L 1 、L 2 The two lengths are distributed alternately, and the length of the conductive sheets distributed in the even layers is L 3 , and forming contact surfaces with two types of 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, and 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.

[0015] According to the second aspect of the present invention, a strain sensing model of a flexible piezoresistive sensor based on contact effect is provided, which is determined using the method for establishing the strain sensing model of a flexible piezoresistive sensor based on contact effect as described in the first aspect of the present invention.

[0016] According to the third aspect of the present invention, a strain prediction method for a flexible piezoresistive sensor based on contact effect is provided, and strain prediction is performed using the strain sensing model of the flexible piezoresistive sensor based on contact effect as described in the second aspect of the present invention, including: determining the strain of the piezoresistive sensor based on the total resistance of the piezoresistive sensor measured before and after the strain.

[0017] In general, the above technical solutions conceived by the present invention have the following technical advantages compared with the existing technology: (1) The method for establishing the strain sensing model provided by the present invention is to establish the contact surface between each two stacked conductive sheets by n The diameter is a The contact points transmit current, n The contact resistance of each contact point forms a parallel path. The resistance of the parallel circuit is calculated to obtain the contact resistance between each two stacked conductive sheets. R c The existing model ignores the roughness of the contact surface and directly regards the entire contact surface as a conductor for resistance calculation. In the present invention, the shape of the contact points between the contact surfaces and the calculation of the contact resistance are quantified, which is convenient for combining with the subsequent quantifiable strain changes, thereby improving the calculation accuracy and reducing the model design error; further, the contact resistance is calculated. R c As an equivalent resistor, construct an equivalent circuit of the piezoresistive sensor, and calculate the resistance of the equivalent circuit as the total resistance of the piezoresistive sensor R TotalThis is different from the existing stacked conductive sheet sensor perception model, which only considers the intrinsic resistance of the conductive sheet during the establishment process. The contact resistance, which is much larger than the intrinsic resistance of the conductive sheet, is substituted into the model, which improves the accuracy of the strain perception model prediction. At the same time, the contact area and the number of contact points in the piezoresistive sensor are combined. n The resulting sensor sensing model is based on the area change after strain, eliminating the influence of other factors in the model and quantifying and visualizing the strain sensing process of the stacked conductive sheet sensor. Consequently, the electromechanical sensing model, based on the relationship between the resistance change rate of the piezoresistive sensor and strain, improves the measurement accuracy of the piezoresistive sensor.

[0018] (2) Compared with ignoring the influence of contact resistance on overall resistance, the present invention first quantifies the resistance of each conductive point and then calculates the resistance of each conductive point based on the contact resistance. n The contact resistance between each two stacked conductive sheets is determined by connecting the contact points in parallel, which is more in line with the actual situation of the sensor contact interface and has higher calculation accuracy.

[0019] (3) Compared with the existing model, the equivalent circuit constructed by the present invention based on the electrical contact theory includes contact resistance. Since the change of contact resistance is a factor that contributes more to the change of overall resistance than the change of intrinsic resistance of the conductive sheet, the consideration of the present invention reduces the model calculation error. At the same time, the present invention includes contact resistance R c As an equivalent resistor, an equivalent circuit is constructed, and the total resistance change rate of the piezoresistive sensor and the number of contact points are obtained. n The relationship between the resistance change rate and the number of contact points in the contact resistance is converted n The change simplifies the calculation method and improves the calculation efficiency.

[0020] (4) Before and after strain occurs, the number of contact points on each contact surface between each two stacked conductive sheets is proportional to the contact area. Therefore, the established sensor perception model is related to the area change after strain.

[0021] (5) This method is applicable to the differences in different sensor designs. It deeply understands the influence mechanism of different factors on the resistance characteristics of flexible sensors based on contact effect, can optimize material size and preparation process, and promotes customized development of flexible sensors based on contact effect under different requirements through precise analysis of contact effect and the adoption of more effective stacking distribution technology.

[0022] (6) This method provides a more sophisticated theoretical support for the design and strain monitoring of flexible sensors based on contact effect by comprehensively considering the effects of conductive sheet stacking structure, conductive sheet size, conductive sheet spacing, and conductive sheet size non-uniformity on the resistance change rate.

[0023] In summary, the present invention provides a method for establishing a strain sensing model, which improves the measurement accuracy of the flexible sensor and solves the problem of low strain measurement accuracy of the flexible sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a schematic diagram of the structural layers of a flexible piezoresistive sensor based on contact effect according to an example of the present invention.

[0025] Figure 2 This is a flowchart for establishing a perception model of a flexible piezoresistive sensor based on contact effect as an example of the present invention.

[0026] Figure 3 This is a schematic structural diagram of a uniformly stacked piezoresistive sensor in which the conductive sheet provided in an embodiment of the present invention is graphene.

[0027] Figure 4 Equivalent circuit diagram of a uniformly stacked piezoresistive sensor in which the conductive sheet provided in an embodiment of the present invention is graphene.

[0028] Figure 5 A schematic structural diagram of a piezoresistive sensor with two types of contact surfaces before and after strain provided by an embodiment of the present invention; Figure 5 (a) is a schematic diagram of the piezoresistive sensor structure before strain occurs, and (b) is a schematic diagram of the piezoresistive sensor structure after strain occurs.

[0029] Figure 6 The figure is a comparison chart of relative resistance changes of the traditional model, the model of the embodiment of the present invention and the simulation experiment under the conditions of different numbers of conductive sheets per layer.

[0030] Figure 7 3. A comparison diagram of relative resistance changes of a traditional model and a model according to an embodiment of the present invention.

[0031] Figure 8 This is a comparison diagram of relative resistance changes between the model and simulation experiment of an embodiment of the present invention under conditions of different conductive sheet spacings.

[0032] 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.

[0033] 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

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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: 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 ; S2: Ignore the intrinsic resistance of the conductive sheet in the piezoresistive sensor and use the contact resistance R c As an equivalent resistor, construct an equivalent circuit of the piezoresistive sensor, and calculate the resistance of the equivalent circuit 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 relationship; S3: The contact area between two stacked conductive sheets and the number of contact points nThe relationship between the contact area and the change after the piezoresistive sensor is strained is substituted into 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 of the piezoresistive sensor and the strain, the relationship between the total resistance change rate and the strain is constructed.

[0038] In the design concept of the present invention, since the contact resistance between the two stacked conductive sheets is much larger than the intrinsic resistance of the conductive sheets, the resistance change of the piezoresistive sensor is mainly caused by the change of the contact resistance. R c It can reflect the electrical contact performance of the sensitive layer of the conductive sheet stack.

[0039] In step S1 of the present invention, the contact resistance is expressed by R.Holm electrical contact theory. R c , the conductivity of the conductive sheet in the piezoresistive sensor is ρ , the contact point is considered as a circle with a diameter of a , the number of contact points per unit area is b The total number of contact points on the contact surface is n .

[0040] Based on R.Holm's electrical contact theory, the essence of contact resistance is conductor resistance, which is proportional to the resistivity of the contact conductive material and inversely proportional to the diameter of the conductive contact point. Therefore, the contact resistance of each contact point in the sensitive layer of the conductive sheet stack is The calculation formula is expressed as: ; The contact resistance between two stacked conductive sheets is calculated using the Cooper-Mikic-Yovanovich correlation. The contact resistance of each contact point is in parallel on the contact surface, that is, n The resistance of the contact point is connected in parallel to form the contact surface resistance: .

[0041] 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 nSimilarly, 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.

[0042] 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.

[0043] 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: ; in, S is the contact area between the two conductive sheets, b is the number of contact points per unit area.

[0044] Specifically, the changes in the contact area and the strain of the piezoresistive sensor include the following: Initial contact area between two stacked conductive sheets at zero strain S 0 Expressed as: ; 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: ; 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.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] The method for establishing a strain sensing model for a flexible piezoresistive sensor based on contact effect specifically includes the following steps: 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.

[0050] The contact resistance is more than 2 orders of magnitude of the intrinsic resistance of the conductive sheet. Ignoring the intrinsic resistance to construct an equivalent circuit, and not considering the contact resistance between the electrode and the stacked conductive sheet, the total resistance of the sensor is R Total Expressed as: .

[0051] The contact resistance between the two stacked conductive sheets is calculated based on the R.Holm theory. R c ; Furthermore, before and after 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: ; in, S is the contact area between the two conductive sheets, b is the number of contact points per unit area.

[0052] For the zero strain state, that is, the initial number of conductive points of the model is expressed as: ; in L is the length of each conductive sheet, d is the spacing between the conductive sheets, b A constant that expresses the relationship between contact length and the number of contact points; for ɛ Strain state, the total deformation is , since the elastic model of the conductive sheet is more than two orders of magnitude larger than that of the flexible substrate, the overall deformation during stretching can be considered to be caused by ( k -1) The larger the spacing, the number of contact points in each contact area n' It can be defined by the following formula: ; and for: .

[0053] Then, the relative resistance change ΔR / R is defined as: .

[0054] That is, the relative resistance change rate-strain curve is established.

[0055] 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 ,in, ,and , odd-numbered conductive sheets L 1 、L 2 The two lengths are distributed alternately, and the length of the conductive sheets distributed in the even layers is L 3 , and form contact surfaces with two types of sizes.

[0056] At this time, there are two types of contact surface sizes in the piezoresistive sensor. The contact resistance and number of contact points on these two types of contact surfaces are expressed as: , ; , ; 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, is the contact resistance of the first type of contact surface, is the contact resistance of 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.

[0057] Furthermore, there are two types of contact surface sizes in the piezoresistive sensor. Considering the unevenness of the conductive sheet, the total resistance of the stacked conductive sheet sensor is R By 2 ( k -1) series resistors parallel to the direction of the sensitive layer, each of which consists of a ( m -1) / 2 first contact resistance and ( m -1) / 2 second contact form contact resistors are connected in parallel, and the total resistance of the piezoresistive sensor is expressed as: .

[0058] The number of contact points on the two types of contact surfaces after strain occurs is: .

[0059] The contact resistance after the change is: ; refer to Figure 5 , the relationship between the resistance change rate and strain after strain occurs is: .

[0060] That is, during the stretching process, when the sensor is strained, When , the short conductive sheet will be disconnected first, changing the relationship between the resistance change rate and strain, which corresponds to the piecewise linear characteristics of the actual sensor.

[0061] In other embodiments of the present invention, a strain prediction method for a flexible piezoresistive sensor based on contact effect uses a strain sensing model of a flexible piezoresistive sensor based on contact effect obtained as described in any one of the first aspects of the present invention to perform strain prediction, including: determining the strain of the piezoresistive sensor based on the total resistance of the piezoresistive sensor measured before and after the strain.

[0062] Sensitivity is an important factor in evaluating the sensing performance of flexible piezoresistive sensors based on contact effect. It represents the relative resistance per unit strain ΔR / R and is defined by the following formula: .

[0063] The following verification effect is achieved by combining the traditional model with the flexible piezoresistive sensor strain electrical sensing model based on the contact effect described in the above embodiment.

[0064] In existing models, the contact resistance between graphene layers is ignored, leading to calculation errors. Existing models assume that under strain conditions, the overall resistance is mainly affected by the change in the length of the electron migration path caused by the relative sliding of overlapping graphene layers, and calculate the overall resistance as follows: ; in, s is 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 ; Existing models assume m 1 and m 2 are roughly equal, the relative change in resistance can be simplified to .

[0065] 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: .

[0066] 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.

[0067] 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.

[0068] 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: ; ; J 1, J 2 are the currents of the upper contact point and the lower contact point respectively, V 1, V 2 are the voltages of the upper contact point and the lower contact point respectively, n is the number of contact points, is the conductivity at the interface of two bodies due to incomplete contact caused by surface roughness: ; here, H c is the microhardness of the softer material, p is the contact pressure, σ contact is the harmonic mean of the contact surface conductivity, σ asp is the rough mean height, m asp is the rough mean slope: ; σ u , σ u is the conductivity of the two contact surfaces, is the harmonic mean of the conductivity of the contact surfaces relative pressure p / H c You can specify it directly H c Or use c 1 and c 2 (Vickers correlation coefficient and size index) are evaluated using the following relative pressure relationship: ; Brinell hardness H B express, H 0 is equal to 3.178 GPa.

[0069] The roughness was set to an average roughness height of 1 μm, an average roughness slope of 0.4, a contact pressure of 100 kPa, and a microhardness of 3 GPa. A 1 A current was applied to one end of the graphene sheet, while the other end was grounded, and the overall resistance was calculated.

[0070] In order to verify that the present invention is more suitable for flexible piezoresistive sensors based on contact effect, traditional model calculations are used for comparison. Figure 6 The length of the graphene sheet is 10 μm, the spacing is 5 μm, and the number of conductive sheets on the odd layer is given. k The comparison of the relative resistance change values calculated by the traditional model, the model of the embodiment of the present invention and the simulation experiment under the conditions of 5, 10 and 20 respectively. Figure 7 The relative change values of resistance calculation of the traditional model and the model of the embodiment of the present invention are given. k A comparison chart of the changes. Figure 6 and Figure 7 It can be seen that the relative resistance change value calculated by the model of the embodiment of the present invention is greater than that of the traditional model, and the error is significantly smaller than the calculation result of the traditional model, which illustrates the effectiveness of the present invention in improving the accuracy of the electromechanical sensing model.

[0071] Furthermore, in order to verify the wide applicability of the model building method of the embodiment of the present invention, graphene sheets of different sizes were used to compare the results. Figure 8 The length of the conductive sheet is 10μm, the spacing is 1μm, 5μm, and 7μm respectively, and the number of conductive sheets in each layer is 10. Figure 9 The lengths of the conductive sheets are 6 μm, 8 μm, and 10 μm, respectively, with a spacing of 1 μm. The number of conductive sheets per layer is 10. As can be seen from the figure, under various conditions, the results of the optimization model fit well with the finite element model, which also demonstrates the applicability of the present invention to various layered sensors.

[0072] Furthermore, in order to improve the degree of fit between the present invention and the actual sensor performance, the non-uniformity of the graphene sheet is taken into consideration, such as Figure 2 As shown. The length of the conductive sheet is L 1 =8μm, L 2 =12μm, L 3 =10μm, conductive sheet spacing d =7μm, the calculated results are compared with the experimental results, as shown in the following figure Figure 10 ,The calculation method fits the experimental results well and has high accuracy.

[0073] Through the above Figures 1 to 10 An improved flexible piezoresistive sensor electromechanical sensing model based on contact effect in the illustrated embodiment combines the contact characteristics of the conductive sheet and the strain distribution relationship of the conductive sheet to obtain an improved strain sensing model, thereby improving the accuracy of the strain sensing model, quantifying and visualizing the strain transfer process of the flexible sensor, improving the measurement accuracy of the flexible sensor, and solving the problem of low strain measurement accuracy of the flexible sensor. The calculation is simple and accurate, and the model has strong engineering applicability.

[0074] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, to the extent such modifications and variations fall within the scope of the present invention and its equivalents, the present invention is intended to encompass such modifications and variations. The above-described embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention and are not intended to limit the scope of protection. Any equivalent substitutions or modifications made by those skilled in the art based on the present invention are also within the scope of protection of the present invention.

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 An equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistor, 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 relationship; 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 contact resistance R c An equivalent circuit of the piezoresistive sensor is constructed as an equivalent resistor, comprising: The contact resistance R c As an equivalent resistor, the equivalent circuit of the piezoresistive sensor is constructed in combination with the distribution of the conductive sheets in the piezoresistive sensor, including the following: 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.

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 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.

5. 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.

6. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 5, 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 Expressed as: ； 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.

7. 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.

8. The method for establishing a strain sensing model of a flexible piezoresistive sensor based on contact effect according to claim 5, 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 ,in, ,and , odd-numbered conductive sheets L 1 、L 2 The two lengths are distributed alternately, and the length of the conductive sheets distributed in the even layers is L 3 , and forming contact surfaces with two types of 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.

9. 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 8.

10. 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 according to claim 9 to perform strain prediction, 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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