Microstructure design method for pressure sensor based on hyperelastic contact mechanics

Abstract

The present application relates to the field of pressure sensor design, and specifically discloses a pressure sensor microstructure design method based on super-elastic contact mechanics, several super-elastic constitutive models are fitted through stress-strain curves obtained by experiments, the optimal constitutive is selected by comparing the experimental and simulation results of super-elastic micro-protrusion contact; the analytical solution of super-elastic micro-protrusion contact is fitted, and its applicability to different super-elastic micro-protrusion contact problems is verified; the structure forward design meeting the requirements of target sensitivity, pressure measurement range and linearity is realized; the sensitivity curve is obtained through the electrical contact experiment, and the feasibility of the design method is verified; based on the application scene and material performance, the upper limit of the sensitivity that can be achieved by the method is given. The method has important engineering application value in the field of flexible electronics, and its outstanding advantage lies in that the microstructure parameters can be directly calculated according to the target performance requirements of the pressure sensor, realizing the accurate mapping of "performance requirements-structure parameters".

Description

Technical Field

[0001] This invention relates to a design method, specifically a microstructure design method for pressure sensors based on hyperelastic contact mechanics, belonging to the field of pressure sensor design. Background Technology

[0002] Piezoresistive flexible pressure sensors possess significant advantages such as simple structure, ease of integration, diverse materials and structures, and tunable performance, making them widely used in soft robotics, wearable devices, and biomedicine, and among the most widely applied flexible pressure sensors currently available. To achieve high sensitivity and wide linear response, multilayer microstructures are widely used as the sensitive layer in piezoresistive flexible pressure sensors. The working principle of these sensors relies on the change in contact area caused by microstructure compression, which in turn leads to a change in contact resistance, thus achieving pressure-to-electrical signal conversion. Notably, the pressure-resistance response characteristics of the sensor can be equivalently represented as the contact force-area relationship between the hyperelastic micro-protrusion and the electrode, providing a new theoretical perspective for sensor performance optimization.

[0003] However, current research faces two key challenges: first, existing contact mechanics theories are mainly based on rigid indenters, and research on the contact characteristics of hyperelastic micro-asperities remains lacking; second, sensor microstructure design heavily relies on empirical trial and error, lacking systematic theoretical guidance. This situation leads to significant blindness and randomness in the sensor development process, not only prolonging the development cycle but also hindering further performance improvements. Therefore, establishing an effective analytical solution to the hyperelastic micro-asperity contact problem, and developing a forward design method for sensor structures based on this solution, has become crucial to breaking through current technological bottlenecks. This breakthrough will overcome the dependence of sensor structure design on empirical methods, providing a theoretical foundation and reliable design tools for the development of high-performance flexible pressure sensors. Summary of the Invention

[0004] To address the problems in the prior art, this invention provides a microstructure design method for pressure sensors based on hyperelastic contact mechanics.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] The microstructure design method for pressure sensors based on hyperelastic contact mechanics includes the following steps:

[0007] Step S1: Obtain the stress-strain curve of the hyperelastic material through a uniaxial compression experiment;

[0008] Step S2: Fit several preset hyperelastic constitutive models and obtain material parameters;

[0009] Step S3: Establish a finite element contact model between the hyperelastic micro-convexity and the rigid plane, and select the optimal constitutive model suitable for the contact problem of hyperelastic materials by comparing it with the experiment.

[0010] Step S4: Based on the force-indentation depth and contact area-indentation depth curves obtained from experiments and simulations, the analytical solution for hyperelastic micro-protrusion contact is obtained by polynomial fitting.

[0011] Step S5: Verify the applicability of the analytical solution to contact problems of different hyperelastic materials and micro-protrusions of different sizes;

[0012] Step S6: Combining the equivalent sensitivity formula, a microstructure design is achieved that meets the requirements of target sensitivity, pressure measurement range, and linearity.

[0013] Step S7: Prepare the sensor microstructure and conduct an electrical contact experiment to obtain the sensitivity curve of the sensor microstructure. Compare the experimental test results with the theoretical design model to verify the feasibility of the design method.

[0014] Step S8: Determine the applicable scope of this design method, that is, based on the application scenario of the target sensor microstructure and the properties of the conductive soft material, determine the upper limit of the sensor microstructure sensitivity that can be achieved by the forward design method.

[0015] Optionally, in step S1, a standard uniaxial compression specimen of hyperelastic material is prepared, and a uniaxial compression test is carried out to obtain the load-indentation depth curve and calculate the stress-strain curve of the hyperelastic material.

[0016] Optionally, in step S2, several preset (commonly used) hyperelastic constitutive models are selected, and the material parameters of the hyperelastic constitutive model are obtained by fitting the stress-strain curves based on uniaxial compression tests. The selected hyperelastic constitutive models include at least two of the Neo-Hookean model, Yeoh model, Mooney-Rivlin model, Ogden (N=1) model, Arrude-Boyce model, and Van der Waals model. This application uses all of the above models.

[0017] Optionally, in step S3, based on the material parameters of the hyperelastic constitutive model obtained above, a finite element contact model between the hyperelastic micro-protrusion and the rigid plane is established, a micro-protrusion compression experiment is carried out, and by comparing the finite element analysis results with the experimental data, the optimal hyperelastic constitutive model suitable for the contact problem of hyperelastic materials is determined.

[0018] Optionally, in step S4, referring to the form of the Hertz solution and combining dimensional analysis, the analytical expressions for the contact force F and contact area A of the hyperelastic micro-convex body are as follows:

[0019]

[0020] Where: h is the indentation depth, b1, b2, b3, c1, c2, c3 represent dimensionless undetermined parameters, M is the generalized hyperelastic modulus, which includes the material parameters in the hyperelastic constitutive model, and d is the geometric parameter of the micro-convexity.

[0021] Based on the contact force-indentation depth curve (Fh) and contact area-indentation depth curve (Ah) obtained from experiments and simulations, the dimensionless undetermined parameters of the analytical solution are determined by fitting polynomials (1) and (2).

[0022] Optionally, in step S5, a finite element model is established for the contact problem of different hyperelastic materials and micro-protrusions of different sizes. The finite element analysis results are compared with the analytical solution to verify the applicability of the analytical solution to the contact problem of different hyperelastic materials and micro-protrusions of different geometric sizes.

[0023] Optionally, in step S6, the design objectives are the sensitivity K and pressure measurement range P of the sensor structure, and the sensitivity curve is required to have good linearity throughout the measurement range. The sensor substrate is a square hyperelastic sheet with an area of ​​B, on which I layers of micro-protrusions of different sizes are randomly arranged, named from the first level to the second level, respectively. The size and number of micro-protrusions in each layer are represented by d. i and n i d i and n i All are target parameters for positive design;

[0024] Assume there is a rigid plane (i.e., a pressure surface) above the sensor structure. As this plane is pressed inward, more and more micro-protrusions participate in the contact. The contact stage m of the sensor structure is determined by the hierarchy of the micro-protrusions involved in the contact. For example, m = 3 indicates that the micro-protrusions from the first to the third level are involved in the contact. In the m-th contact stage (m = 1, 2, ..., I), the contact pressure P experienced by the sensor structure is... m and the total contact area S between the sensor structure and the pressure surface m The expression is as follows:

[0025]

[0026] Where m = 1, 2, ..., I; F i and A i It is the contact force and contact area of ​​a single micro-protrusion in the i-th level, which are calculated using formulas (1) and (2);

[0027] The formula for the equivalent sensitivity of the sensor structure is:

[0028]

[0029] Where U is the voltage, ΔI is the change in current, I0 is the initial current, ΔP is the change in pressure, R and R0 are the current resistance and the initial resistance, respectively, and S and S0 are the current contact area and the initial contact area, respectively.

[0030] By combining the equivalent sensitivity formula and performing staged calculations, all target parameters, namely the dimensions d of the micro-protrusions at each level, are obtained. i And quantity n i This enables the design of microstructures that meet the requirements of target sensitivity, pressure measurement range, and linearity.

[0031] Optionally, in step S7, a sensor microstructure is prepared using a conductive soft material, namely a superelastic material, and an electrical contact experiment is conducted between the sensor microstructure and the rigid conductive electrode. The sensitivity curve is obtained using pressure and resistance data and compared with the theoretically designed target sensitivity K and pressure measurement range P to evaluate the feasibility of the design method.

[0032] Optionally, in step S8, based on the application scenario of the target sensor microstructure and the properties of the selected conductive soft material, the upper limit of the sensitivity of the sensor microstructure that can be achieved by the forward design method is determined.

[0033] The beneficial effects of this invention are:

[0034] Compared with existing technologies, the technical solution provided by this invention has the following advantages: Firstly, by combining experiments and finite element analysis, a universal analytical solution to the contact problem of hyperelastic micro-asperities is obtained for the first time. This analytical solution is applicable to contact problems of hyperelastic micro-asperities with different geometric and material parameters. Secondly, the theoretical derivation of the analytical solution is rigorous and facilitates its widespread application in soft material contact problems. Thirdly, the sensitivity of the sensor, expressed as pressure-resistance, is equivalent to the contact force-area relationship between the hyperelastic micro-asperity and the electrode, allowing direct use of the contact area as the design basis, combining simplicity, efficiency, and high precision. Fourthly, based on the analytical solution to the contact problem, with the goals of high sensitivity, high linearity, and a large pressure range, the forward design of the microstructure of a piezoresistive flexible pressure sensor is realized, overcoming the blindness and randomness of traditional empirical structural design methods and significantly reducing R&D costs and time. This method has significant engineering application value in the field of flexible electronics. Its outstanding advantage lies in its ability to directly calculate microstructure parameters according to target performance requirements, achieving a precise mapping between "performance requirements and structural parameters." Especially in the design of flexible devices such as wearable devices and electronic skin, this method can quickly obtain optimized structures that combine high sensitivity and a wide linear measurement range. This new paradigm of "design on demand" provides a reliable theoretical model and an efficient implementation path for the development of a new generation of high-performance flexible sensors. Attached Figure Description

[0035] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0036] Figure 1 This is a flowchart of the microstructure design method for pressure sensors based on hyperelastic contact described in this invention;

[0037] Figure 2 This is a schematic diagram of the samples and experimental platform for the uniaxial compression experiment and the hemispherical compression experiment in an embodiment of the present invention;

[0038] Figure 3 This is the stress-strain fitting effect of the hyperelastic constitutive model based on uniaxial compression experimental data in the embodiments of the present invention;

[0039] Figure 4 This is a comparison chart of experimental data on micro-convexity compression in embodiments of the present invention and simulation results (Fh and Ah) under different hyperelastic constitutive models;

[0040] Figure 5 This is the polynomial fitting result of the analytical solution to the hyperelastic contact problem in the embodiments of the present invention;

[0041] Figure 6 This is a comparison of analytical solutions and numerical results for hyperelastic contact under different hyperelastic materials and different micro-protrusion sizes in the embodiments of the present invention;

[0042] Figure 7 This is a comparison between the analytical solution for contact of hyperelastic materials obtained based on PDMS material and the experimental results of contact of CB / PDMS composite conductive soft materials in the embodiments of the present invention;

[0043] Figure 8 This is an experimental sample of the sensor microstructure in an embodiment of the present invention;

[0044] Figure 9 This is a schematic diagram of the electrical contact experiment of the sensor microstructure in an embodiment of the present invention;

[0045] Figure 10 This is a comparison between the experimental results of the sensor microstructure sensitivity in this embodiment of the invention and the theoretical design target. Detailed Implementation

[0046] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Please see Figure 1-10As shown in the example, the microstructure design method for a pressure sensor based on hyperelastic contact provided in this application includes the following steps:

[0048] Step S1: Obtain the stress-strain curve of the hyperelastic material through a uniaxial compression experiment;

[0049] Step S2: Fit several of the most commonly used hyperelastic constitutive models and obtain material parameters;

[0050] Step S3: Establish a finite element contact model between the hyperelastic micro-convexity and the rigid plane, and select the optimal constitutive model suitable for the contact problem of hyperelastic materials by comparing it with the experiment.

[0051] Step S4: Based on the force-indentation depth and contact area-indentation depth curves obtained from experiments and simulations, the analytical solution for hyperelastic micro-protrusion contact is obtained by polynomial fitting.

[0052] Step S5: Verify the applicability of the analytical solution to contact problems of different hyperelastic materials and micro-protrusions of different sizes;

[0053] Step S6: Combining the equivalent sensitivity formula, a microstructure design is achieved that meets the requirements of target sensitivity, pressure measurement range, and linearity.

[0054] Step S7: Prepare the sensor microstructure and conduct an electrical contact experiment to obtain the sensitivity curve of the sensor microstructure. Compare the experimental test results with the theoretical design model to verify the feasibility of the design method.

[0055] Step S8: Determine the applicable scope of this design method, that is, based on the application scenario of the target sensor microstructure and the properties of the conductive soft material, determine the upper limit of the sensor microstructure sensitivity that can be achieved by the forward design method.

[0056] In step S1, the superelastic material used in the example is polydimethylsiloxane (PDMS), a high-molecular-weight organosilicon compound with excellent flexibility, biocompatibility, and chemical stability. It is widely used in flexible electronics, microfluidic chips, biomedical devices, and soft robotics. Uniaxial compression experimental samples (such as...) were prepared using PDMS. Figure 2 As shown in figure a), a uniaxial compression test was conducted. The test sample was a cylinder with a radius of 15 mm and a thickness of 18 mm. During the experiment, the PDMS sample was placed horizontally on the stage, and the upper rigid flat indenter moved downward to compress the PDMS sample. The indenter depth was 5 mm, and the moving speed was set to 0.5 mm / min. The compression test was performed for 5 loading-unloading cycles to eliminate the influence of the Mullins effect. The Fh data of the last cycle was selected to calculate the stress-strain curve based on the uniaxial compression test.

[0057] In step S2, various hyperelastic constitutive models are fitted using the stress-strain curves described above, and the corresponding material parameters are obtained. Several commonly used hyperelastic constitutive models were selected, including: Neo-Hookean, Yeoh, Mooney Rivlin, Ogden (N=1), Arrude-Boyce, and Van der Waals models. Table 1 shows the fitted constitutive parameters. Figure 3 The fitting results of these constitutive models are presented. As can be seen from the figures, the Yeoh and Van der Waals models have the best fitting results, while the Neo-Hooke and Arrude-Boyce models have slightly larger biases. However, overall, there is no significant difference in the fitting results among the constitutive models.

[0058] Table 1 Material parameters of the hyperelastic constitutive model

[0059]

[0060] In step S3, using the above hyperelastic constitutive model and its parameters, a finite element analysis model for the hyperelastic hemispherical compression contact problem was established. Hemispherical compression specimens (such as...) were prepared using PDMS. Figure 2 (as shown in b), and a compression test was conducted. Figure 4 A comparison of experimental data on micro-convex body compression and simulation results under different hyperelastic constitutive models is presented. The simulation results obtained using the Ogden (N=1) model and the Van der Waals model are in best agreement with the experimental data. Considering computational efficiency, the Ogden (N=1) model was ultimately selected as the optimal hyperelastic constitutive model for describing the hemispherical contact problem of PDMS. Figure 4 b. The simulation results and experimental results of the contact area obtained by the Ogden (N=1) model were compared, and good consistency was found between the two. This further verifies the accuracy of the Ogden (N=1) model in describing the contact mechanical behavior of PDMS.

[0061] In step S4, based on the form of the Hertz solution and using dimensional analysis, the analytical solution to the hyperelastic hemispherical contact problem can be assumed to be:

[0062]

[0063]

[0064] Where h is the indentation depth, k, b1, b2, b3, c1, c2, and c3 represent dimensionless undetermined parameters; μ and α1 are two material parameters of the Ogden (N=1) model, μ is the initial shear modulus of the material, and α1 describes the nonlinearity of the material response; r is the radius of the micro-hemispheric.

[0065] The Fh and Ah curves obtained from the simulation were fitted using polynomials (6) and (7) to determine the undetermined parameters k, b1, b2, b3, c1, c2, and c3. The fitting results are as follows: Figure 5 As shown, the fitting result has very high accuracy. The analytical expression for PDMS hemispherical contact is:

[0066]

[0067] In step S5, considering two different material parameters and hemispherical radii, a simulation contact model of the PDMS hemisphere and the rigid plane is established to obtain the Fh and Ah curves, which are then compared with analytical solutions (8) and (9) to verify the applicability of the analytical solution to the compression problem of hyperelastic hemispheres of different materials and sizes. Figure 6 In the model, the material and geometric parameters of hemisphere one and hemisphere two are μ = 0.308 MPa, α1 = 0.324, r = 10 mm, and μ = 0.528 MPa, α1 = 3.12, r = 5 mm, respectively. A comparison between the finite element analysis results and the analytical solution is shown below. Figure 6 As shown, the finite element analysis results and analytical solutions consistently agree well for two completely different hemispheres. Therefore, it is believed that the analytical solution for the contact between a hyperelastic hemisphere and a rigid plane proposed in this application is applicable to hyperelastic hemispheres of different materials and sizes.

[0068] In step S6, the substrate selected for this example is a square sheet with a side length of 10mm and a thickness of 0.1mm. Four different radii and numbers of hemispheres are randomly arranged on this substrate, and these four hemispheres are named from largest to smallest radius as the first to fourth layers. The radii and numbers of these four layers of hemispheres are r1, r2, r3, r4 and n1, n2, n3, n4, respectively. The total number of hemispheres is N = n1 + n2 + n3 + n4. The radius of the first-layer hemisphere is defined as r1 = 0.3mm. Considering both the hemisphere size and the substrate size, the substrate's load-bearing limit is 256 hemispheres. To fully utilize the substrate area and ensure uniform deformation of the sensor structure under pressure, the total number of hemispheres N should be as large as possible within the substrate's load-bearing range, i.e., N should be as close to 256 as possible. Simultaneously, for the durability of the sensor structure, the total indentation depth H does not exceed... The goal of this example is to achieve forward design of the sensor microstructure based on the required pressure measurement range P and sensitivity K, determining the radius and number of each hemisphere, while ensuring the linearity of the sensitivity curve throughout the measurement range.

[0069] Assume there is a rigid plane above the sensor, ensuring it is in contact with the sensor structure. Assume the initial indentation depth of the plane is h0 = αr1, and the initial contact area is:

[0070]

[0071] The initial contact pressure is:

[0072]

[0073] Calculations showed that P0 was sufficiently small, and therefore could be approximated as 0. Considering the precision of the experimental instruments and to reduce systematic and random errors, the value of α was set to 0.05.

[0074] Since the sensor structure has four layers, its contact behavior with the rigid plane can also be divided into four stages. In the first stage of contact, the rigid plane only contacts the first-layer hemisphere. This stage continues until the second-layer hemisphere is introduced into the contact process, i.e., the plane begins to contact the second-layer hemisphere. In the second stage, the first and second-layer hemispheres continue to be compressed until the third-layer hemisphere is introduced into the contact process. In the third stage, the first, second, and third-layer hemispheres continue to be compressed until the fourth-layer hemisphere is introduced into contact; in the fourth stage, all layers of hemispheres participate in the contact. The contact pressure and contact area for each stage (m = 1, 2, 3, 4) can be written as:

[0075]

[0076] Among them, F i and A i The contact force and contact area of ​​the i-th level hemisphere can be calculated from the analytical solutions (8) and (9) in step S4.

[0077] Based on the required sensitivity K and pressure measurement range P, parameters r2, r3, r4, n1, n2, n3, and n4 are obtained through staged calculations using sensitivity formula (5) and formulas (8)-(13). During the design process, we found that the change in the target measurement range P1 in stage 1 has a significant impact on the total number of hemispheres N and the total indentation depth H. We determine the value of P1 using an iterative method, ensuring that N is as close as possible to 256 and... First, an initial value for P1 is set. Then, P1 is continuously adjusted through iterative calculations to ensure that N and H meet the requirements. Specifically, if N is too small or H is too large, the value of P1 is decreased; if N is too large, the value of P1 is increased, until a P1 that meets the requirements is obtained. Research has found that the proportion of P1 in P is negatively correlated with the sensitivity K. Therefore, during the design process, different P1 values ​​will be obtained for different target parameters K. To maintain the linearity of the sensitivity curve, P2 and P3 should be distributed as evenly as possible, and P4 is P.

[0078] Taking the calculation of stage 1 as an example, this stage requires simultaneously achieving the design sensitivity K and the measurement range P1. The sensitivity formula and formulas (12) and (13) can be written as:

[0079]

[0080] S1=n1·A1 (16)

[0081] F1 and A1 can be represented as:

[0082]

[0083]

[0084] By solving equations (14)-(18) simultaneously, the target parameters n1 and r2 for stage 1 can be obtained. All target parameters can be obtained by solving them in stages, and the calculation process for other stages is similar to that for stage 1. The target parameters for stage 2 are n2 and r3, the target parameters for stage 3 are n3 and r4, and the target parameter for stage 4 is n4.

[0085] Based on the above design method and calculation process, a forward design of a sensor structure with a given sensitivity and pressure measurement range can be achieved, ensuring the linearity of the sensor.

[0086] In this embodiment, the target performance is K = 10 kPa. -1 Given P = 4 kPa, r1 = 0.3 mm, and α = 0.05, P1 = 0.22 kPa was obtained through iterative calculation. P2 and P3 were set to P2 = 1.5 kPa and P3 = 3 kPa, respectively. The target parameters obtained through the above design process are shown in Table 2.

[0087] Table 2. K = 10 kPa -1 Structural parameters of the sensor structure when P = 4 kPa

[0088]

[0089] In step S7, the sensor structure is prepared, an electrical contact experiment is conducted, and the sensor structure is verified to achieve the expected design goals.

[0090] In this embodiment, carbon black (CB) is used as a conductive filler to prepare a conductive PDMS composite material. First, a CB / PDMS composite conductive material is prepared using a mechanical mixing method. Since the analytical solution for the hyperelastic contact in step S4 is based on pure PDMS material, it is necessary to first verify whether this analytical solution is applicable to the hyperelastic contact problem of the CB / PDMS composite material.

[0091] Based on the stress-strain curves obtained from compression experiments of CB / PDMS composite conductive materials, an Ogden (N=1) model was fitted, and the initial shear modulus μ=0.25MPa and strain hardening exponent α1=0.511 of the CB / PDMS composite conductive materials were obtained. The analytical solutions (8) and (9) were compared with the compression experimental data of the CB / PDMS hemisphere, as shown in... Figure 7 As shown, the analytical solution for the hyperelastic hemispherical contact based on PDMS provided in this application is still applicable to the hemispherical compression problem of CB / PDMS composite conductive materials.

[0092] Sensor microstructures were fabricated using a casting-demolding method. The mold model used to fabricate the sensor structure and the final experimental sample are shown below. Figure 8 As shown, the sensor microstructure sample was connected to the circuit, and an electrical contact experiment was performed to obtain the sensitivity curve. Figure 9 This is a schematic diagram of an electrical contact experiment of a sensor structure.

[0093] The sensitivity curve obtained from the electrical contact experiment is compared with the designed target sensitivity curve, such as... Figure 10 As shown, firstly, the sensor structure exhibits excellent linearity across the entire measurement range. Secondly, the sensor structure's measurement range is 0-3.8 kPa, achieving 95% of the expected performance. The sensitivity is 10.19 kPa. -1 The error was 1.9%. In conclusion, experiments have confirmed that the sensor structure has basically met the design expectations.

[0094] In step S8, the flexible pressure sensors can be divided into three categories according to different working scenarios: low-pressure, medium-pressure, and high-pressure sensors. Among them, low-pressure sensors with an operating range of less than 1 kPa are mainly used to measure vibration signals caused by breathing, sound, etc.; medium-pressure sensors with an operating range of 1-10 kPa are usually used to detect physiological signals such as heartbeat, pulse, and muscle stretching; and high-pressure sensors with an operating range of more than 10 kPa are suitable for monitoring activities such as finger bending.

[0095] Taking a medium-pressure sensor as an example, the target measurement range of the sensor is P = 10 kPa. Based on the material parameters of the selected CB / PDMS composite conductive soft material, the upper limit of the sensitivity of the sensor microstructure achievable by the forward design method is determined. Research has found that the upper limit of sensitivity K... max The sensitivity is negatively correlated with n1 (i.e., negatively correlated with P1), but to ensure the uniformity of microstructure deformation, we limit the minimum value of n1 to 4. We obtain the upper limit K of the sensitivity through an iterative method. max The specific process is as follows: Given an initial sensitivity value K, calculate the sensor microstructure parameters according to the method described in step S6. If n1 = 4, then the limit K is considered to have been found. maxOtherwise, increase K until n1 = 4 is satisfied. Ultimately, the upper limit of sensitivity K... max The corresponding sensor structure satisfies the conditions: n1 = 4, N ≈ 256 or Based on the above conditions, the upper limit of sensitivity that can be achieved under the current application scenario and selected materials is calculated to be K. max =7.2kPa -1 For any value less than K max The sensitivity of each parameter can be obtained using the aforementioned forward design method to obtain the microstructure parameters. Table 3 shows the parameters at the maximum sensitivity and when the sensitivity is 6 kPa. -1 4kPa -1 2kPa -1 The pressure measurement range of the sensor structure in four stages is shown in Table 4. Table 4 provides the structural parameters of the corresponding sensor structure.

[0096] Table 3. Pressure measurement range in four stages at different sensitivity Ks when P = 10 kPa.

[0097]

[0098] Table 4. Structural parameters of the sensor structure at different sensitivities K when P = 10 kPa.

[0099]

[0100] Studies have shown that the upper limit of sensitivity achievable through forward design of sensor microstructures is inversely proportional to the target measurement range P. As the target measurement range P increases, the achievable upper limit of sensitivity decreases accordingly; conversely, as P decreases, the upper limit of sensitivity increases. Table 5 shows the pressure measurement ranges of the sensor structure at four stages when the target pressure measurement range is 3 kPa, 6 kPa, and 9 kPa. Table 6 shows the upper limit of sensitivity achievable through forward design of the sensor microstructure, as well as the structural parameters of the sensor structure, when the target pressure measurement range is 3 kPa, 6 kPa, and 9 kPa.

[0101] Table 5. Pressure measurement range in four stages under different target measurement ranges P

[0102]

[0103]

[0104] Table 6. Upper limit of sensitivity K under different target pressure measurement ranges P max and sensor structural parameters

[0105]

[0106] Assuming the selected materials remain constant, the measurement range P has boundaries. Studies show that the initial shear modulus of the material is positively correlated with the pressure measurement range P, and materials with lower initial shear modulus are more suitable for the design of low-range pressure sensors. Table 7 shows the pressure measurement range of the sensor structure in four stages under low pressure (1 kPa) and high pressure (50 kPa). By selecting materials with different initial shear moduli, Table 8 shows the maximum achievable sensitivity and corresponding structural parameters under low and high pressure measurement ranges.

[0107] Table 7. Pressure measurement range of the sensor structure in four stages under high and low pressure conditions.

[0108]

[0109] Table 8. Structural parameters of the sensor structure under low and high pressure.

[0110]

[0111] The results show that the smaller the pressure measurement range, the greater the achievable sensitivity coefficient.

[0112] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A microstructure design method for pressure sensors based on hyperelastic contact mechanics, characterized in that, Includes the following steps: Step S1: Obtain the stress-strain curve of the hyperelastic material through a uniaxial compression experiment; Step S2: Fit several preset hyperelastic constitutive models and obtain material parameters; Step S3: Establish a finite element contact model between the hyperelastic micro-convexity and the rigid plane, and select the optimal constitutive model suitable for the contact problem of hyperelastic materials by comparing it with the experiment. Step S4: Based on the force-indentation depth and contact area-indentation depth curves obtained from experiments and simulations, the analytical solution for hyperelastic micro-protrusion contact is obtained by polynomial fitting. Step S5: Verify the applicability of the analytical solution to contact problems of different hyperelastic materials and micro-protrusions of different sizes; Step S6: Combining the equivalent sensitivity formula, a microstructure design is achieved that meets the requirements of target sensitivity, pressure measurement range, and linearity. Step S7: Prepare the sensor microstructure and conduct an electrical contact experiment to obtain the sensitivity curve of the sensor microstructure. Compare the experimental test results with the theoretical design model to verify the feasibility of the design method. Step S8: Based on the application scenario of the target sensor microstructure and the properties of the conductive soft material, determine the upper limit of the sensor microstructure sensitivity that can be achieved by the forward design method; In step S6, the design objective is to improve the sensitivity of the sensor structure. K and pressure measurement range P The sensor substrate has an area of B A square, superelastic sheet has I layers of micro-protrusions of different sizes randomly arranged on it, named from level 1 to level 2. I The hierarchy, and the size and number of micro-protrusions in each layer are respectively expressed as follows: d i and n i , d i and n i All are target parameters for positive design; The sensor structure is classified into contact stages based on the hierarchical division of the micro-protrusions involved in the contact. m The contact pressure that the sensor structure withstands Pm and the total contact area between the sensor structure and the pressure surface Sm The expression is as follows: ,(3) ,(4) in, m =1, 2, ..., I ; Fi and Ai It is the first i The contact force and contact area of ​​a single micro-protrusion at each level are calculated using formulas (1) and (2); The formula for the equivalent sensitivity of the sensor structure is: in, U For voltage, Δ I The change in current I 0 represents the initial current, Δ P This is the change in pressure. R and R 0 represents the current resistance and the initial resistance, respectively. S and S 0 represents the current contact area and the initial contact area, respectively; By combining the equivalent sensitivity formula and performing staged calculations, all target parameters, namely the dimensions of the micro-protrusions at each level, are obtained. di and quantity ni This enables the design of microstructures that meet the requirements of target sensitivity, pressure measurement range, and linearity.

2. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 1, characterized in that, In step S1, a standard uniaxial compression specimen of hyperelastic material is prepared, and a uniaxial compression test is carried out to obtain the load-indentation depth curve and calculate the stress-strain curve of the hyperelastic material.

3. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 2, characterized in that, In step S2, several preset hyperelastic constitutive models are selected, and the material parameters of the hyperelastic constitutive models are obtained by fitting the stress-strain curves obtained based on uniaxial compression tests. The selected hyperelastic constitutive models include at least two of the Neo-Hookean model, Yeoh model, Mooney-Rivlin model, Ogden model, Arrude-Boyce model, and Van der Waals model.

4. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 3, characterized in that, In step S3, based on the material parameters of the hyperelastic constitutive model obtained above, a finite element contact model between the hyperelastic micro-protrusion and the rigid plane is established, and a micro-protrusion compression experiment is carried out. By comparing the finite element analysis results with the experimental data, the optimal hyperelastic constitutive model suitable for hyperelastic material contact problems is determined.

5. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 4, characterized in that, In step S4, referring to the form of the Hertz solution and combining dimensional analysis, the contact force of the hyperelastic micro-convex body is... F and contact area A The parsing expression is: , (1) , (2) in: h For the depth of indentation, b 1. b 2. b 3. c 1. c 2. c 3 indicates a dimensionless undetermined parameter. M The generalized hyperelastic modulus includes the material parameters in the hyperelastic constitutive model. d These are the geometric parameters of the micro-convexity; Based on the contact force-indentation depth curves and contact area-indentation depth curves obtained from experiments and simulations, the dimensionless undetermined parameters of the analytical solution are determined by fitting polynomials (1) and (2).

6. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 5, characterized in that, In step S5, a finite element model is established for the contact problem of different hyperelastic materials and micro-protrusions of different sizes. The finite element analysis results are compared with the analytical solution to verify the applicability of the analytical solution to the contact problem of different hyperelastic materials and micro-protrusions of different geometric sizes.

7. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 6, characterized in that, In step S7, a sensor microstructure is fabricated using conductive soft materials, and an electrical contact experiment is conducted between the sensor microstructure and the rigid conductive electrode. Sensitivity curves are obtained using pressure and resistance data and compared with the theoretically designed target sensitivity. K and pressure measurement range P Compare and evaluate the feasibility of the design methods.

8. The microstructure design method for pressure sensors based on hyperelastic contact mechanics according to claim 7, characterized in that, In step S8, based on the application scenario of the target sensor microstructure and the properties of the selected conductive soft material, the upper limit of the sensitivity of the sensor microstructure that can be achieved by the forward design method is determined.

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