Method for measuring shear modulus of soft material based on rotational deformation

Abstract

The invention relates to the technical field of material engineering, and particularly discloses a method for measuring the shear modulus of a soft material based on rotational deformation, which comprises the following steps: eliminating the initial residual stress of the soft material to finally obtain a trackable micro-mark pattern; applying centrifugal force to the micro-mark pattern through a preset rotating speed phi, and shooting micro-point grid motion of the micro-mark pattern at each angular speed omega i to obtain a time sequence image group; radial strain epsilon r (t) is extracted, and a strain sequence is obtained; performing time domain filtering and lag compensation on the strain sequence to obtain balance strain epsilon eq (omega i) and correction data; substituting sigma < r > (omega ) and epsilon < eq > (omega ) into the selected soft material constitutive model, and inverting a static shear modulus mu and a multi-mode viscoelastic parameter through a generalized Maxwell model; according to the method, through complex shear modulus fitting in the frequency domain, the energy storage and loss characteristics of the material at different frequencies can be extracted, the static shear modulus can be obtained through inversion of the constitutive model, and unified characterization of the dynamic viscoelastic behavior and the static mechanical property of the material is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of material engineering, and in particular relates to a method for measuring the shear modulus of soft materials based on rotational deformation. Background Art

[0002] In the study of the mechanical properties of soft materials (such as rubber, polymer gels, and biological soft tissues), shear modulus, as an important parameter characterizing a material's ability to resist shear deformation, is crucial for its design, application, and performance evaluation. Accurately measuring the shear modulus of soft materials contributes to a deeper understanding of their mechanical behavior, providing a reliable basis for their application in a wide range of fields, including engineering structures, biomedicine, and flexible electronics.

[0003] At present, there are many shortcomings in the existing methods for measuring the shear modulus of soft materials. Traditional shear test methods, such as the parallel plate rheometer method and the torsional shear method, often require destructive preparation of the sample. For example, in the parallel plate rheometer method, the soft material needs to be prepared into a sample of a specific shape and clamped between parallel plates for testing. This process may change the original structure of the material, introduce additional stress concentration and deformation inhomogeneity, resulting in large errors in the measurement results, and cannot truly reflect the mechanical properties of the material in its original form. In addition, these methods can usually only obtain the static or quasi-static shear modulus of the material under specific conditions, and it is difficult to fully reflect the mechanical response of the material under dynamic loading (such as different frequencies, different temperatures).

[0004] With the development of science and technology, some non-contact measurement methods have gradually emerged, such as those based on optical principles. However, these methods also have limitations when measuring the shear modulus of soft materials. Some optical methods have stringent requirements on the measurement environment and are easily affected by factors such as external light interference and sample surface roughness, resulting in low measurement accuracy. Moreover, when it comes to detecting small strains, existing non-contact methods have limited sensitivity and are difficult to capture small radial strain changes in soft materials under low stress fields or low rotation speeds, which cannot meet the demand for high-precision mechanical property characterization of soft materials.

[0005] Furthermore, existing measurement methods mostly focus on obtaining a single mechanical parameter of a material, making it difficult to simultaneously characterize both the dynamic viscoelastic behavior and the static mechanical properties of the material. Soft materials often exhibit complex viscoelastic properties, exhibiting varying mechanical responses at different frequencies and temperatures. Existing methods are unable to systematically study the temperature- and loading-rate-dependent constitutive parameters of soft materials, making it difficult to accurately assess material properties under complex engineering conditions such as high and low temperatures, and rapid and slow deformation.

[0006] Therefore, it is of great practical significance to develop a soft material shear modulus measurement method that can directly obtain the mechanical response in the original form of the sample, has high detection sensitivity and spatial resolution, and can simultaneously characterize the dynamic viscoelastic behavior and static mechanical properties of the material.

[0007] To this end, the inventors proposed a method for measuring the shear modulus of soft materials based on rotational deformation to solve the above problems. Summary of the Invention

[0008] The object of the present invention is to provide a method for measuring the shear modulus of soft materials based on rotational deformation, so as to solve the problems raised in the above background technology.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A method for measuring the shear modulus of a soft material based on rotational deformation comprises the following steps:

[0011] Eliminating the initial residual stress of the soft material to obtain a stress-relaxed sample; placing the stress-relaxed sample in a set temperature environment for thermal equilibrium to obtain a temperature-balanced sample; spraying a high-contrast micro-dot grid on the outer surface of the temperature-balanced sample to obtain a traceable micro-marking pattern;

[0012] Applying centrifugal force to the micro-mark pattern by rotating it step by step at a preset rotation speed Φ to obtain the centrifugal stress field σr(ωi) and the inner circumferential stretching ratio λi corresponding to each rotation speed;

[0013] The micro-point grid motion of the micro-mark pattern is photographed at each angular velocity ωi to obtain a time series image group; the time series image group is tracked at a sub-pixel level to extract the radial strain εr(t) and obtain a strain sequence;

[0014] The strain sequence is subjected to time domain filtering and hysteresis compensation to obtain the equilibrium strain εeq(ωi) and correction data; σr(ωi) and εeq(ωi) are fitted by nonlinear least squares to obtain the frequency-dependent shear modulus G*(ω);

[0015] Substitute G*(ω) into the constitutive model of the selected soft material, and invert the static shear modulus μ and multimodal viscoelastic parameters through the generalized Maxwell model.

[0016] Preferably, the shear modulus μ is calculated as:

[0017]

[0018] get:

[0019]

[0020] in The calculation formula is:

[0021]

[0022] in, is the initial radius ratio of the hose, ρ is the material density, R o is the initial outer diameter of the hose, Ri: the initial inner diameter of the hose, μ is the shear modulus, λi is the inner circumferential stretching ratio, and Φ is the rotation speed;

[0023] λz: represents the axial or longitudinal stretching ratio of a soft material during rotational loading, defined as the ratio of the current axial length to the initial axial length (λz = L / L0, where L0 is the initial length and L is the deformed length). This parameter describes the tensile deformation of the material along the axis under the action of rotating centrifugal force.

[0024] λo: represents the circumferential stretching ratio of the outer radius of the soft material, which is defined as the ratio of the circumferential circumference of the outer radius after rotation to the circumferential circumference of the initial outer radius (λo = Rcurrent / R0, where R0 is the initial outer radius and Rcurrent is the outer radius after deformation); this parameter is used to quantify the circumferential expansion deformation of the outer surface caused by centrifugal force, and Φ is the rotation speed.

[0025] Preferably, the calculation formula of the centrifugal stress field σr(ωi) is:

[0026]

[0027] Where ρ is the material density, kg·m -3 , a typical value such as natural rubber is about 1200kg·m -3 ;

[0028] ωi is the angular velocity at the i-th level of loading, rad·s -1 , which is converted from the corresponding step with a step of 100 rpm;

[0029] Ro, Ri are the outer radius, m, and inner radius, m, of the hose before rotation, which are used to determine the geometric boundary where the centrifugal force acts;

[0030] By quantifying the radial stress generated within the hose wall thickness at each rotational speed, first-hand experimental data is provided for subsequent stress-strain fitting. This formula can accurately reflect the dynamic loading field caused by rotation and is more suitable for tubular soft materials than the traditional single stress formula.

[0031] Preferably, the calculation formula of the radial strain εr(t) is:

[0032]

[0033] Δr(t) is the radial displacement of the micro-marker at time t, m is the sub-pixel displacement obtained by digital image correlation processing;

[0034] r0 is the initial reference radius, m, which is the measured radius at the micro-marking application location at zero loading;

[0035] The tiny displacements obtained by image tracking are converted into dimensionless strains, facilitating consistent comparisons across samples and rotational speeds. At sub-pixel resolution, this definition ensures high-precision strain measurements and significantly improves the sensitivity of the method.

[0036] Preferably, the frequency-dependent shear modulus G*(ω) is expressed as follows:

[0037]

[0038] Where, σr(ω) is the centrifugal stress;

[0039] εeq(ω) is the equilibrium strain at the rotation speed ω after hysteresis correction;

[0040] G′(ω) and G″(ω) represent the storage modulus and loss modulus, respectively, reflecting the elastic and dissipative properties of the material in the frequency domain.

[0041] Mapping the experimentally measured stress-strain data into a complex modulus can simultaneously characterize the elastic and viscous behavior of the material, providing a unified parameterized result for the structural design and dynamic analysis of soft materials at multiple frequencies and temperatures.

[0042] Preferably, the inversion formula of the generalized Maxwell model is:

[0043]

[0044] G∞: high-frequency limiting modulus (Pa), corresponding to the rigid response of the material under ultra-fast loading;

[0045] Gk, τk: relaxation modulus and relaxation time constant of the kth mode, reflecting the energy dissipation at different time scales;

[0046] N: The number of model modes, which is selected as 2–5 to balance fitting accuracy and parameter simplicity.

[0047] Through least squares optimization, multiple relaxation processes are separated, and the static shear modulus μ=G∞+∑Gk and various relaxation parameters are obtained; a quantitative connection can be established between macro applications (such as shock absorber design) and micro mechanisms (such as molecular chain relaxation).

[0048] Preferably, the sample pretreatment includes placing the hose sample at room temperature (25° C.) for not less than 24 hours to eliminate the initial residual stress generated during the manufacturing and handling process, thereby obtaining a stress-relaxed sample;

[0049] The thermal balance is carried out by isothermal regulation of the stress-relaxed sample in a constant temperature box for at least 1 hour to obtain the temperature-balanced sample under different temperature conditions such as 25°C or 50°C, so as to study the effect of temperature on the shear modulus;

[0050] The grid marking pattern is obtained by spraying black micro dots with a diameter of 0.2 mm on the outer surface of the hose in a matrix form with a spacing of 1 mm for subsequent sub-pixel tracking using a digital image correlation method.

[0051] Preferably, the step-by-step rotation loading includes: starting from 100 rpm and gradually increasing to 1000 rpm in steps of 100 rpm, applying a centrifugal force field to the sample C to obtain the centrifugal stress σr(ωi) and the inner circumferential stretching ratio λi at each rotation speed.

[0052] Preferably, a high-speed camera with a frame rate of ≥1000 fps is coaxially aligned with the sample, and a shooting time of at least 1 s is maintained at each ωi to obtain an image group of the time-varying micro-point grid motion.

[0053] Preferably, a cross-correlation operation is performed on adjacent frames in the image group to extract the radial displacement distribution and calculate the time domain strain εr(t) to obtain a strain sequence;

[0054] An exponential decay filter is performed on the initial transient part of the strain sequence, and the principal strain hysteresis is compensated to obtain the equilibrium strain εeq(ωi) and correction data at each ωi.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) This invention uses centrifugal rotation loading and synchronous high-speed imaging to directly obtain the mechanical response of the sample in its original form without cutting or disturbing the sample structure, thus avoiding the errors and waste of resources caused by destructive sample preparation in traditional shear tests. The use of micro-point grid marking combined with sub-pixel digital image correlation analysis can detect extremely small radial strain changes, allowing reliable data to be obtained even at low rotation speeds or in small stress fields, significantly improving the detection sensitivity and spatial resolution of the method.

[0057] (2) The present invention not only extracts the energy storage and loss characteristics of the material at different frequencies (i.e., different rotational speeds) through complex shear modulus fitting in the frequency domain, but also obtains the static shear modulus through constitutive model inversion, achieving a unified characterization of the material's dynamic viscoelastic behavior and static mechanical properties. The device can operate in a controllable temperature environment. Combined with temperature balance and multi-frequency loading, it can systematically study the constitutive parameters of soft materials that vary with temperature and loading rate, providing a theoretical basis for structural design and life prediction under high and low temperature, fast and slow deformation conditions.

[0058] (3) The present invention utilizes a generalized Maxwell or other constitutive model and, through least squares fitting of multiple sets of experimental data, is able to separate different relaxation modes and their corresponding time constants, revealing the correspondence between the internal molecular chain relaxation mechanism and the macroscopic viscoelastic properties of the material, thereby enhancing the method's physical explanatory power and engineering prediction capabilities. The method has a clear flow, interconnected steps, and a self-calibrated micro-point grid and high-speed imaging that can be highly automated with digital image correlation algorithms, facilitating its application in laboratories and industrial fields, and laying the foundation for future intelligent online monitoring and quality control. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of a method for measuring the shear modulus of soft materials based on rotational deformation according to the present invention;

[0060] Figure 2 Schematic diagram of the principle of the method of the present invention. DETAILED DESCRIPTION

[0061] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0062] Example 1:

[0063] See also Figure 1 As shown, the shear modulus of natural rubber hose at 25°C is measured:

[0064] 1. Samples and experimental parameters:

[0065] Material: natural rubber tube;

[0066] Initial inner radius Ri = 5.0 mm; initial outer radius Ro = 7.0 mm;

[0067] Material density ρ = 1200 kg·m -3

[0068] Temperature: 25°C (equilibrated in a thermostat for 1 h);

[0069] Angular velocity step: 100rpm, 300rpm, 500rpm;

[0070] High-speed camera frame rate: 1200fps;

[0071] 2. Data acquisition:

[0072] Spray black micro dots with a diameter of 0.2 mm and a spacing of 1.0 mm on the outer surface of the hose.

[0073] After the stepper load reaches the specified rotation speed, the micro-point is continuously photographed for 1 s using a 1200 fps camera to obtain 1200 frames of images.

[0074] Digital image correlation (DIC) software was used for sub-pixel tracking to extract the equilibrium radial strain εeq at each rotation speed.

[0075] 3. Detailed calculation process:

[0076] Angular velocity conversion:

[0077] ω=rpm×2π / 60

[0078]

[0079] Centrifugal stress calculation:

[0080]

[0081] Where Ro and Ri are converted to meters.

[0082] Equilibrium strain (obtained by DIC):

[0083]

[0084] Complex shear modulus calculation

[0085]

[0086] The storage modulus G′ is obtained (the loss modulus can be approximately ignored under pure centrifugal loading).

[0087] Take N = 2 modes and fit the G*(ω) curve by least squares to solve: G∞,G1,τ1,G2,τ2

[0088] And calculate the static shear modulus μ=G∞+G1+G2.

[0089] 4. The results are summarized in Table 1 below:

[0090] Table 1

[0091]

[0092] Maxwell model fitting results:

[0093] G∞=0.80MPa

[0094] G1=1.20MPa,τ1=0.10s

[0095] G2=0.50MPa,τ2=1.00s

[0096] Static shear modulus μ=0.80+1.20+0.50=2.50MPa

[0097] From the above, it can be seen that through centrifugal stress-DIC strain coupling, the introduction of viscoelastic hysteresis correction and Maxwell model inversion, high-precision (<5% error) and wide-frequency (10–50 rad / s) static and dynamic shear modulus characterization is achieved.

[0098] Example 2:

[0099] Shear modulus measurement of silicone elastic tube at 50°C:

[0100] 1. Samples and experimental parameters:

[0101] Material: medical grade silicone tube;

[0102] Initial inner radius Ri = 4.0 mm; initial outer radius Ro = 6.0 mm;

[0103] Material density ρ = 970 kg·m -3

[0104] Temperature: 50°C (equilibrated in a thermostat for 1 h);

[0105] Angular velocity step: 200rpm, 400rpm, 600rpm;

[0106] High-speed camera frame rate: 1500fps;

[0107] 2. Data acquisition is the same as in Example 1, but the temperature is increased to 50°C;

[0108] DIC tracking obtained the equilibrium strain εeq: 0.0080, 0.0200, and 0.0330.

[0109] 3. Detailed calculation process:

[0110] Angular velocity conversion:

[0111]

[0112] Centrifugal stress calculation:

[0113] Complex shear modulus calculation:

[0114] Maxwell model inversion (take N = 3);

[0115] 4. The results are summarized in Table 2 below:

[0116] Table 2

[0117] Speed (rpm) <![CDATA[ω(rad·s -1 )]]> σr(kPa) εeq G′(MPa) 200 20.94 0.178 0.0080 22.3 400 41.89 0.712 0.0200 35.6 600 62.83 1.600 0.0330 48.5

[0118] Maxwell model fitting results:

[0119] G∞=0.60MPa

[0120] G1=0.90MPa,τ1=0.05s

[0121] G2=0.50MPa,τ2=0.50s

[0122] G3=0.30MPa,τ3=2.00s

[0123] Static shear modulus μ=0.60+0.90+0.50+0.30=2.30MPa

[0124] As can be seen from the above, at higher temperatures, this scheme can still accurately obtain the dynamic and static shear moduli, and reveals the significant influence of temperature on the viscoelastic properties of the material (both the storage modulus and relaxation time are reduced at high temperatures), providing reliable data support for the design of rubber parts under high-temperature conditions.

[0125] As can be seen above, centrifugal rotation loading and simultaneous high-speed imaging allow the mechanical response of the sample to be directly captured in its original form without cutting or disturbing the sample structure, avoiding the errors and resource waste associated with destructive sample preparation in traditional shear tests. The use of micro-point grid marking combined with sub-pixel digital image correlation analysis enables the detection of extremely small radial strain changes, enabling reliable data to be obtained even at low rotation speeds or in minimal stress fields, significantly improving the method's detection sensitivity and spatial resolution.

[0126] This method, through frequency-domain complex shear modulus fitting, not only extracts the material's energy storage and loss characteristics at different frequencies (i.e., different rotational speeds), but also derives the static shear modulus through constitutive model inversion, achieving a unified characterization of the material's dynamic viscoelastic behavior and static mechanical properties. The device can operate in a temperature-controlled environment. Combined with temperature balancing and multi-frequency loading, it can systematically study the constitutive parameters of soft materials as they vary with temperature and loading rate, providing a theoretical basis for structural design and life prediction under high- and low-temperature, fast- and slow-deformation conditions.

[0127] By utilizing generalized Maxwell or other constitutive models and fitting multiple sets of experimental data through least-squares fitting, different relaxation modes and their corresponding time constants can be separated, revealing the corresponding relationship between the internal molecular chain relaxation mechanism and the macroscopic viscoelastic properties of the material, thereby enhancing the method's physical explanatory power and engineering predictive capabilities. The method has a clear workflow and interconnected steps. The self-calibrated micro-point grid and high-speed imaging enable highly automated integration with digital image correlation algorithms, facilitating its application in laboratories and industrial fields, and laying the foundation for future intelligent online monitoring and quality control.

[0128] Example 3:

[0129] Given the initial radius ratio and material density of hose 1, it is rotated around the central axis 4 at a certain rotation speed 4. After rotation, its shape is transformed into the rotated hose 2. The ratio of the inner and outer diameters of the rotated hose 2 is measured. The speed 4 and the radius ratio after rotation are known and substituted into the theoretical formula to derive the shear modulus.

[0130] like Figure 2 As shown, the inner diameter of the tubular structure 1 is R i , outer diameter is R o , the deformation of the tubular structure 1 rotating at high speed around the rotation center line 3 at an angular velocity Φ can be regarded as a uniform expansion deformation. Select the soft material energy density function:

[0131]

[0132] The stress components are obtained:

[0133]

[0134] This gives the equation for adding rotation to the stress equilibrium equation:

[0135]

[0136] The relationship between the final speed 4 and the deformation is obtained:

[0137]

[0138] In the description of this specification, the reference terms "one embodiment", "some embodiments", "examples", "specific examples" or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0139] In the drawings of the embodiments disclosed in the present invention, only the structures related to the embodiments disclosed in the present invention are involved. Other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other.

[0140] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for measuring the shear modulus of soft materials based on rotational deformation, characterized in that: The following steps are involved: Eliminating the initial residual stress of the soft material to obtain a stress-relaxed sample; placing the stress-relaxed sample in a set temperature environment for thermal equilibrium to obtain a temperature-balanced sample; and spraying a high-contrast micro-dot grid on the outer surface of the temperature-balanced sample to obtain a micro-marking pattern; Applying centrifugal force to the micro-mark pattern by rotating it step by step at a preset rotation speed Φ to obtain the centrifugal stress field σr(ωi) and the inner circumferential stretching ratio λi corresponding to each rotation speed; Shooting the micro-point grid motion of the micro-mark pattern at each angular velocity ωi to obtain a time series image group; Performing sub-pixel tracking on the time series image group, extracting radial strain εr(t) and obtaining a strain sequence; The strain sequence is subjected to time domain filtering and hysteresis compensation to obtain the equilibrium strain εeq(ωi) and correction data; σr(ωi) and εeq(ωi) are fitted by nonlinear least squares to obtain the frequency-dependent shear modulus G*(ω); Substitute G*(ω) into the constitutive model of the selected soft material, and invert the static shear modulus μ and multimodal viscoelastic parameters through the generalized Maxwell model.

2. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The shear modulus μ is calculated as: get: in The calculation formula is: in, is the initial radius ratio of the hose, ρ is the material density, R o is the initial outer diameter of the hose, Ri: the initial inner diameter of the hose, μ is the shear modulus, and λi is the inner circumferential stretching ratio; λz: represents the stretching ratio of the soft material along the axial or longitudinal direction during rotational loading, which is defined as the ratio of the current axial length to the initial axial length; λo: represents the circumferential stretching ratio of the outer radius of the soft material, which is defined as the ratio of the circumferential circumference of the outer radius after rotation to the circumferential circumference of the initial outer radius, and Φ is the rotation speed.

3. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The calculation formula of the centrifugal stress field σr(ωi) is: Where ρ is the material density, kg·m -3 ; ωi is the angular velocity at the i-th level of loading, rad·s -1 , which is converted from the corresponding step with a step of 100 rpm; Ro, Ri are the outer radius, m, and inner radius, m, of the hose before rotation, which are used to determine the geometric boundary where the centrifugal force acts.

4. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The calculation formula of the radial strain εr(t) is: Δr(t) is the radial displacement of the micro-marker at time t, m is the sub-pixel displacement obtained by digital image correlation processing; r0 is the initial reference radius, m, which is the measured radius of the micro-marking application position at zero load.

5. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The formula for the frequency-dependent shear modulus G*(ω) is: Where, σr(ω) is the centrifugal stress; εeq(ω) is the equilibrium strain at the rotation speed ω after hysteresis correction; G′(ω) and G″(ω) represent the storage modulus and loss modulus, respectively, reflecting the elastic and dissipative properties of the material in the frequency domain.

6. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The inversion formula of the generalized Maxwell model is: G∞: high-frequency limiting modulus (Pa), corresponding to the rigid response of the material under ultra-fast loading; Gk, τk: relaxation modulus and relaxation time constant of the kth mode, reflecting the energy dissipation at different time scales; N: number of model modes.

7. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The sample pretreatment includes placing the hose sample at room temperature (25° C.) for no less than 24 hours to eliminate the initial residual stress generated during the manufacturing and handling process, thereby obtaining a stress-relaxed sample; The thermal balance is carried out by isothermal regulation in a constant temperature box for at least 1 hour to keep the stress-relaxed sample in equilibrium, thereby obtaining the temperature-balanced sample at different temperature conditions of 25° C. or 50° C., for studying the effect of temperature on the shear modulus; The grid marking pattern is obtained by spraying black micro dots with a diameter of 0.2 mm on the outer surface of the hose in a matrix form with a spacing of 1 mm for subsequent sub-pixel tracking using a digital image correlation method.

8. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The step-by-step rotation loading includes: starting from 100 rpm and gradually increasing to 1000 rpm in steps of 100 rpm, applying a centrifugal force field to the micro-mark pattern to obtain the centrifugal stress σr(ωi) and the inner circumferential stretching ratio λi at each rotation speed.

9. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: The image set is coaxially aligned with the sample using a high-speed camera with a frame rate ≥ 1000 fps, and a shooting time of at least 1 s is maintained at each ωi to obtain an image set of time-varying micro-point grid motion.

10. The method for measuring the shear modulus of soft materials based on rotational deformation according to claim 1, characterized in that: Performing cross-correlation operation on adjacent frames in the image group, extracting radial displacement distribution and calculating time domain strain εr(t) to obtain a strain sequence; An exponential decay filter is performed on the initial transient part of the strain sequence, and the principal strain hysteresis is compensated to obtain the equilibrium strain εeq(ωi) and correction data at each ωi.

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