A method and system for determining multi-factor multi-scale mechanical properties of a high polymer shock absorber

Abstract

The application discloses a kind of multi-factor multi-scale mechanical property determination method and system of high molecular shock absorber, the method according to the relationship of energy storage modulus of high molecular material and arbitrary strain amplitude, the difference of arbitrary strain and infinite strain amplitude, the difference of characteristic strain and infinite strain amplitude and the force-displacement relationship of single molecular chain, the force-displacement relationship of single molecular chain under energy storage modulus and loss modulus is obtained;In the relationship between the micro-molecular chain stress of high molecular material and the tensile ratio, load in the principal axis direction is introduced, shear stress and shear modulus are obtained, according to the principal stress, shear stress and shear modulus of high molecular material, the macro-scale model of high molecular rubber-based material is constructed, and temperature correlation is introduced to form a multi-scale refinement model, which can accurately describe the influence of frequency, temperature, displacement amplitude and microstructure on the multi-scale mechanical properties of high molecular rubber-based damper, and provide a theoretical basis for multi-scale design and development of high-damping damper.

Description

Technical Field

[0001] This invention relates to the field of building structure vibration reduction technology, specifically to a method and system for determining the multi-factor, multi-scale mechanical properties of a polymer vibration damper. Background Technology

[0002] In recent years, polymer rubber-based vibration damping technology has been widely used in the field of structural vibration control due to its advantages such as good energy dissipation capacity, ease of processing and installation, and low cost. In particular, it has broad application prospects in the field of seismic resistance of engineering structures.

[0003] However, traditional polymer rubber-based dampers are mostly suitable for high-frequency vibration control and are significantly affected by temperature during operation, especially exhibiting poor vibration damping and energy dissipation capabilities at medium and high temperatures. This makes them unsuitable for meeting the needs of low-frequency vibration control and wide-temperature-range (especially medium and high-temperature) service requirements of civil engineering structures under seismic loads. The mechanical models of traditional polymer rubber-based dampers are mostly phenomenological models based on macroscopic scales, lacking the ability to describe and analyze the influence of the microstructure of the polymer rubber-based damper on its macroscopic mechanics at the microscopic scale. Due to these limitations, in the actual engineering design of traditional polymer rubber-based dampers, it is difficult to use effective calculation methods to perform precise quantitative design of the dampers, thus making it impossible to design suitable polymer rubber-based damper configurations based on different working conditions. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method and system for determining the multi-factor, multi-scale mechanical properties of polymer shock absorbers, revealing the relationship between the micro-scale and macro-scale mechanical properties of viscoelastic materials from the perspective of micro-scale mechanical characteristics.

[0005] This invention is achieved through the following technical solution:

[0006] A method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber includes the following steps:

[0007] Step 1: Determine the force-displacement relationship of a single molecular chain of the polymer material in the polymer rubber-based shock absorber based on the higher-order fractional viscoelastic derivative model (FVMP).

[0008] Step 2: Under the dynamic equilibrium state inside the polymer material, determine the relationship between the storage modulus and the arbitrary strain amplitude based on the displacement amplitude correlation of the polymer material;

[0009] Step 3: Establish the relationship between the loss modulus and van der Waals bond fracture rate of polymer rubber-based materials, and determine the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, by combining the correlation of displacement amplitude of polymer materials.

[0010] Step 4: Determine the relationship between the storage modulus and the arbitrary strain amplitude, the difference between the arbitrary strain and the infinite strain amplitude, the difference between the characteristic strain and the infinite strain amplitude, and the force-displacement relationship of a single molecular chain based on the displacement amplitude correlation, so as to obtain the force-displacement relationship of a single molecular chain under the storage modulus and loss modulus.

[0011] Step 5: Determine the relationship between microscopic molecular chain stress and stretch ratio based on the total strain energy per unit volume of the polymer material. Introduce the load in the principal axis direction into the relationship between microscopic molecular chain stress and stretch ratio to obtain the principal stress of the polymer material. Determine the shear stress and shear modulus based on the principal stress. Construct a macroscopic model of the polymer rubber-based material based on the principal stress, shear stress, and shear modulus of the polymer material.

[0012] Step 6: The macroscopic model of polymer rubber-based material is modified by using the temperature correlation of polymer materials to obtain a multi-scale refined model, and the dynamic mechanical performance of polymer rubber-based shock absorber is calculated.

[0013] Preferably, the method for determining the relationship between the storage modulus and any strain amplitude in step 2 is as follows:

[0014] The displacement amplitude correlation includes the fracture function relationship and reconstruction function relationship of polymer materials;

[0015] When the polymer material is in dynamic equilibrium, the number of existing reconstructed bonds is determined based on the fracture function relationship and the reconstruction function relationship, and then the relationship between the number of existing reconstructed bonds and the difference between the storage modulus of the polymer material under arbitrary strain and infinite strain amplitude is determined.

[0016] Based on the relationship between the existing number of reconstructed bonds in polymer materials and the difference between the storage modulus and the storage modulus, the relationship between the storage modulus and the arbitrary strain amplitude is determined.

[0017] Preferably, the method for determining the correlation of displacement amplitude is as follows:

[0018] The displacement amplitude correlation of polymer materials was established using the theory of microscopic physical bond breaking and reconstruction.

[0019] Preferably, the method for determining the difference between the arbitrary strain and the infinite strain amplitude, and the difference between the characteristic strain and the infinite strain amplitude, is as follows:

[0020] Based on the existing number N of reconfigurable keys v The relationship between loss modulus and van der Waals bond fracture rate was established to determine the relationship of loss modulus under arbitrary strain amplitude.

[0021] When a polymer material is subjected to an arbitrary strain equal to its characteristic strain, the difference between the characteristic strain and the infinite strain amplitude is determined based on the relationship between the loss modulus and the loss modulus under an arbitrary strain amplitude.

[0022] Based on the expression for the difference in loss modulus between characteristic strain and infinite strain amplitude, the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, are derived.

[0023] Preferably, the method for determining the relationship between the loss modulus and the van der Waals bond breakage rate is as follows:

[0024] Based on the additional frictional force generated by the breakage of bonds between carbon black particles or polymers in the rubber-based material of the shock absorber, the relationship between the loss modulus of the polymer material and the van der Waals bond breakage rate is established.

[0025] Preferably, the method for determining the total strain energy per unit volume of the polymer material in step 5 is as follows:

[0026] A six-chain spherical network model is used to describe the spatial distribution of microscopic molecular chains in polymer materials, thereby determining the strain energy of a single molecular chain.

[0027] Based on the strain energy of a single molecular chain and the spherical volume of a six-chain spherical network, determine the strain energy of a single molecular chain per unit volume.

[0028] The total strain energy per unit volume of a polymer material is determined by the strain energy of a single molecular chain per unit volume.

[0029] Preferably, in step 5, the stress-strain relationship of the polymer material is determined based on the total strain energy and the micromechanical theory of polymer rubber-based materials.

[0030] Based on the incompressible properties of polymer materials, and combined with the stress-strain relationship, the relationship between the microscopic molecular chain stress and the stretch ratio of polymer materials is determined.

[0031] By introducing a load along the principal axis into the relationship between microscopic molecular chain stress and stretch ratio, the principal stress of the polymer material is obtained. The real part of the principal stress is the storage modulus, and the imaginary part is the loss modulus.

[0032] Preferably, in step 6, the temperature-frequency equivalent method is used to construct the temperature correlation of the polymer rubber-based material.

[0033] A multi-factor, multi-scale mechanical property determination system for a polymer shock absorber includes:

[0034] The force-displacement relationship module is used to determine the force-displacement relationship of a single molecular chain of polymer material in a polymer rubber-based shock absorber based on the higher-order fractional viscoelastic derivative model FVMP.

[0035] The energy storage modulus module is used to determine the relationship between the energy storage modulus and any strain amplitude based on the displacement amplitude correlation of the polymer material when it is in a dynamic equilibrium state inside the polymer material.

[0036] The loss modulus module is used to establish the relationship between the loss modulus of polymer rubber-based materials and the van der Waals bond breakage rate, and to determine the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, by combining the displacement amplitude correlation of polymer materials.

[0037] The fusion module is used to determine the relationship between the storage modulus and the arbitrary strain amplitude, the difference between the arbitrary strain and the infinite strain amplitude, the difference between the characteristic strain and the infinite strain amplitude, and the force-displacement relationship of a single molecular chain based on the displacement amplitude correlation, so as to obtain the force-displacement relationship of a single molecular chain under the storage modulus and loss modulus.

[0038] The macroscale model module is used to determine the relationship between microscopic molecular chain stress and stretch ratio based on the total strain energy per unit volume of polymer materials. By introducing loads along the principal axis into the relationship between microscopic molecular chain stress and stretch ratio, the principal stress of the polymer material is obtained. Based on the principal stress, the shear stress and shear modulus are determined. Based on the principal stress, shear stress, and shear modulus of the polymer material, a macroscale model of polymer rubber-based materials is constructed.

[0039] The mechanical calculation module is used to correct the macroscopic model of polymer rubber-based materials by using the temperature correlation of polymer materials, so as to obtain a multi-scale refined model and calculate the dynamic mechanical performance of polymer rubber-based shock absorbers.

[0040] An electronic device, comprising:

[0041] Memory, used to store computer programs;

[0042] A processor is used to execute the computer program to implement the steps of the method for determining the multi-factor, multi-scale mechanical properties of the polymer shock absorber.

[0043] Compared with the prior art, the present invention has the following beneficial technical effects:

[0044] This application provides a multi-factor, multi-scale mechanical performance determination method for polymer dampers. It employs a higher-order fractional derivative (FVMP) model to characterize the hyperelasticity of network and free molecular chains and the combined properties of the polymer rubber matrix. The influence of filler particles is considered using the theory of microscopic bond breaking and reconstruction, and the effect of temperature is introduced through the time-temperature equivalence principle, leading to a multi-scale refined model. This model comprehensively considers the influence of frequency, temperature, displacement amplitude, and microstructure on the mechanical performance of polymer dampers, achieving the transmission of mechanical information at different scales. The model can accurately predict the mechanical performance of high-damping acrylic rubber-based polymer rubber dampers at different frequencies, temperatures, and displacement amplitudes. This model accurately describes the influence of frequency, temperature, displacement amplitude, and microstructure on the multi-scale mechanical performance of high-damping acrylic rubber-based polymer rubber dampers, providing a theoretical basis for the multi-scale design and fabrication of high-damping dampers.

[0045] This application also proposes a multi-factor, multi-scale mechanical property determination system for polymer shock absorbers, an electronic device, and a computer storage medium, which possess all the advantages of the aforementioned multi-factor, multi-scale mechanical property determination method for polymer shock absorbers. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of a polymer shock absorber structure according to the present invention;

[0048] Figure 2 This is a schematic diagram illustrating the micro-molecular chain structure and multi-scale model establishment of a polymer shock absorber according to the present invention;

[0049] Figure 3 This is a comparison chart of the multi-factor, multi-scale mechanical performance calculation method of a polymer shock absorber of the present invention at different frequencies with experimental results;

[0050] Figure 4 This is a comparison chart of the multi-factor, multi-scale mechanical performance calculation method of a polymer shock absorber of the present invention with experimental results under different displacement amplitudes;

[0051] Figure 5 This is a comparison chart of the multi-factor, multi-scale mechanical performance calculation method of a polymer shock absorber of the present invention with experimental results at different temperatures;

[0052] Figure 6 This is a comparison chart of the force-displacement curves of the multi-factor, multi-scale mechanical performance calculation method and experimental results of a polymer shock absorber according to the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0054] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0055] See Figure 1-6 A method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber, comprising the following steps:

[0056] Step 1: Determine the force-displacement relationship of a single molecular chain of the polymer material in the polymer rubber-based shock absorber based on the constitutive equation of the higher-order fractional viscoelastic derivative model FVMP.

[0057] S1.1 The FVMP model is composed of the Maxwell model and the Kelvin model in parallel. The constitutive equation of the FVMP model is expressed as follows:

[0058]

[0059] In the formula, τ is stress and γ is strain.

[0060] S1.2. Determine the force-displacement relationship of a single molecular chain of polymer material based on the constitutive equation of the FVMP model. The expression is as follows:

[0061]

[0062] In the formula, E1 represents the stiffness of the spring element in the Maxwell model. Let η1 be the Riemann-Liouville fractional derivative operator for the spring element in the Maxwell model, η1 be the viscosity coefficient in the Maxwell model, and E2 be the stiffness of the spring element in the Kelvin model. Here, η is the Riemann-Liouville fractional derivative operator for the water bottle element in the Kelvin model, and η² is the viscosity coefficient in the Kelvin model. q0 = E2, q2 = η2, and Let α1 and α2 be parameters relating to the elasticity and viscosity of the molecular chain, and Δx be the fractional derivative. cha For the deformation at both ends of the molecular chain, F cha ω represents the force at the end of the molecular chain, ω is the angular frequency, and i is the imaginary unit.

[0063] Step 2: Establish the displacement amplitude correlation of polymer materials using the theory of microscopic physical bond breaking and reconstruction. Under dynamic equilibrium conditions within the polymer material, determine the existing number N based on the displacement amplitude correlation. v Based on the relationship between the existing number and the difference between the energy storage modulus, the relationship between the energy storage modulus and the arbitrary strain amplitude is determined.

[0064] S2.1. Since the polymer rubber-based shock absorber has a strong displacement amplitude correlation, the displacement amplitude correlation of polymer materials is established by adopting the theory of microscopic physical bond breaking and reconstruction. This displacement amplitude correlation includes the breakage function relationship and reconstruction function relationship of polymer materials.

[0065] Fracture function relationship: the total number of fractured van der Waals bonds R br The existing number N v and the fracture function f br Relationship:

[0066] R br =k br N v f br (ε)

[0067] Reconstruction of functional relations: The total number of reconstructed keys R re The existing number of reconfigurable keys N v The number of reconstructed bonds without deformation, N v0 Reconstruction function f re Relationship:

[0068] R re =k re ·(N v0 -N v )·f re (ε)

[0069] In the formula, k re f is the reconstruction rate constant. br and f re The following exponential types are used respectively:

[0070]

[0071] In the formula, m is a parameter related to the fractal dimension of the carbon black network.

[0072] S2.2 When a polymer material is in dynamic equilibrium, the total number of broken van der Waals bonds is the same as the total number of reconstructed bonds, R br =R re The number N of existing reconstructed bonds is determined based on the breakage function relationship and the reconstruction function relationship. v .

[0073]

[0074] In the formula, ε c The characteristic strain can be calculated using the following formula:

[0075]

[0076] S2.3 Determine the existing number N of reconstructed bonds in the polymer material. v The relationship between the storage modulus G'(ε1)-G'(∞) and the difference between arbitrary strain and infinite strain amplitude is as follows:

[0077]

[0078] S2.3. Based on the relationship between the existing number of reconstructed bonds in polymer materials and the difference between the storage modulus and the storage modulus, the relationship between the storage modulus and any strain amplitude is determined as follows:

[0079]

[0080] Step 3: Establish the relationship between the loss modulus and van der Waals bond fracture rate of polymer rubber-based materials, and determine the relationship of loss modulus under arbitrary strain amplitude by combining the existing number of reconstructed bonds. Determine the difference between arbitrary strain and infinite strain amplitude of polymer materials, as well as the difference between characteristic strain and infinite strain amplitude.

[0081] S3.1 Considering the additional frictional force generated by bond breakage between carbon black particles or polymers, establish the relationship between the loss modulus of polymer materials and the van der Waals bond breakage rate, which are directly proportional:

[0082] G"(ε)-G"(∞)=βR br =βk br N v ε m

[0083] In the formula, β is a material-related constant.

[0084] S3.2, Based on the existing number N of reconstruction keys v By establishing the relationship between the loss modulus and the van der Waals bond fracture rate, the relationship of the loss modulus under arbitrary strain amplitude is determined:

[0085]

[0086] In the formula, It is a new constant.

[0087] S3.3 When the polymer material is at any strain equal to the characteristic strain, the difference between the characteristic strain and the loss modulus at infinite strain amplitude is determined according to the relationship of loss modulus at any strain amplitude.

[0088] That is, G"(ε) in ε=ε c When the peak value is reached, then:

[0089]

[0090] S3.4. The expression for the difference in loss modulus between characteristic strain and infinite strain amplitude is derived to obtain the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude.

[0091]

[0092] Step 4: Based on the differences between arbitrary strain and infinite strain amplitude, the differences between characteristic strain and infinite strain amplitude, and the relationship between storage modulus and arbitrary strain amplitude of polymer materials, combined with the force-displacement relationship of a single molecular chain, the force-displacement relationship of a single molecular chain under storage modulus and loss modulus is obtained as follows:

[0093]

[0094] In the formula, M1, M2, N1 and N2 are model parameters related to the elasticity and viscosity of the molecular chain.

[0095] Step 5: Use a six-chain spherical network model to determine the total strain energy per unit volume of the polymer material, and combine it with the micromechanical theory of VEM (Volume-Enhanced Mechanics) to determine the relationship between microscopic molecular chain stress and stretch ratio. Introduce loads in the principal axis direction into the relationship between microscopic molecular chain stress and stretch ratio to obtain the principal stress of the polymer material. Determine the shear stress and shear modulus based on the principal stress. Construct a macroscopic model of the polymer material based on the principal stress, shear stress, and shear modulus.

[0096] S5.1 Using a six-chain spherical network model to describe the spatial distribution of microscopic molecular chains in polymer materials, the strain energy of a single molecular chain is:

[0097]

[0098] In the formula, r n0 Initial end-to-end distance of molecular chains.

[0099] The spherical volume of the six-chain spherical network is:

[0100]

[0101] Based on the strain energy of a single molecular chain and the spherical volume of a six-chain spherical network, determine the strain energy of a single molecular chain per unit volume:

[0102]

[0103] The total strain energy per unit volume of a polymer material is determined based on the strain energy of a single molecular chain per unit volume.

[0104] φ v =N n φ n

[0105] In the formula, N n This represents the number of microscopic molecular chains per unit volume.

[0106] S5.2. Based on the total strain energy and combined with the micromechanical theory of polymer rubber-based materials (VEM), determine the stress-strain relationship of the polymer material:

[0107]

[0108] In the formula, λ j Let be the stretch ratio in the j-direction.

[0109] Assuming the deformation of a single molecular chain is an affine deformation, a simpler deformation mode, namely the uniaxial stretching mode, is used for analysis (i.e., λ1 = λ1, ...). Based on the incompressible nature of VEM (vegetable polymer elastomer), the relationship between the chain spacings of the molecular chains can be obtained:

[0110]

[0111] S5.3. Based on the incompressible properties of polymer materials and combined with the stress-strain relationship, determine the relationship between the microscopic molecular chain stress and the stretch ratio of polymer materials:

[0112]

[0113] In the formula,

[0114] S5.4. Introducing the load ε1=ε0sin(ωt) along the principal axis into the relationship between microscopic molecular chain stress and tensile ratio, we obtain the principal stress of the polymer material. The real part of the principal stress expression is the storage modulus G', and the imaginary part is the loss modulus G". The expression for the principal stress is as follows:

[0115]

[0116] S5.5. Polymer rubber-based dampers are generally in a shear deformation state during structural vibration reduction. Therefore, the shear stress and shear modulus are determined based on the principal stresses, expressed as follows:

[0117]

[0118] In the formula, G a Let τ be the shear modulus. a For shear stress, γ a Let μ be the shear strain and μ be Poisson's ratio, taken as 0.5.

[0119] S5.6 Construct a macroscopic model of polymer rubber-based materials based on the principal stress, shear stress and shear modulus of polymer materials. The model includes the storage modulus G', loss modulus G" and energy dissipation efficiency η.

[0120]

[0121] Step 6: Modify the macroscopic model of polymer rubber-based materials by applying the temperature correlation of polymer rubber-based materials to obtain a multi-scale refined model.

[0122] Specifically, the temperature correlation of polymer rubber-based materials is constructed using the temperature-frequency equivalence method, and the expression is as follows:

[0123]

[0124] In the formula, T is the temperature, T0 is the reference temperature, and α T D1 and D2 are material constants, where D is the temperature conversion coefficient.

[0125] By incorporating the temperature-dependent properties of polymeric rubber-based materials into the macroscopic model of polymeric rubber-based materials, i.e., introducing a temperature factor into the macroscopic model of polymeric rubber-based materials, the model is modified to obtain a multi-scale refined model:

[0126]

[0127] In the formula,

[0128]

[0129] Step 7: Calculate the dynamic mechanical properties of the polymer rubber-based shock absorber based on the multi-scale refined model. Determine the installation data (size, location, quantity, etc.) of the polymer rubber-based shock absorber in actual engineering based on the dynamic mechanical properties.

[0130] The following section verifies the multi-factor, multi-scale mechanical performance determination method for the aforementioned polymer rubber-based shock absorber.

[0131] The test data of the high-damping acrylic polymer-based rubber shock absorber under various working conditions were compared and analyzed with the numerical results calculated by the above-mentioned multi-factor, multi-scale mechanical performance determination method of the polymer rubber-based shock absorber.

[0132] See Figure 1 The high-damping acrylic polymer-based rubber shock absorber comprises two pieces of high-damping acrylic polymer-based rubber material, two constraint steel plates, and one intermediate steel plate. The shock absorber is constructed by connecting the two pieces of high-damping acrylic polymer-based rubber material through high-temperature and high-pressure integral vulcanization between the constraint steel plate and the intermediate steel plate. Grooves are correspondingly arranged on the connection surfaces between the intermediate steel plate, the constraint steel plate, and the rubber material layer, significantly enhancing its force transmission and connection performance.

[0133] Test results from randomly selected operating conditions were used to fit the undetermined parameters in the model. A genetic algorithm was employed, and a corresponding MATLAB program was developed to determine the undetermined parameters (as shown in Table 1). Based on this, the proposed multi-scale refined model was used to predict the dynamic mechanical properties of the high-damping acrylic polymer-based rubber shock absorber, and the results were compared with those from a subset of tests that were not used in determining the undetermined parameters to verify the accuracy and effectiveness of the model.

[0134] Table 1. Fitting results of refined model parameters

[0135]

[0136]

[0137] like Figure 3-5 The figures show comparison curves of the storage modulus, loss modulus, and loss factor between the numerical calculations and experimental results of the model at different frequencies, displacement amplitudes, and temperatures. Table 2 lists the error statistics of the numerical calculations and experimental results of the proposed multi-scale refined model. As can be seen from the tables and figures, the numerical calculations and experimental results of the storage modulus, loss modulus, and loss factor of the high-damping acrylic polymer-based rubber damper show good agreement at different frequencies, displacement amplitudes, and temperatures. In particular, the errors in the storage modulus, loss modulus, and loss factor under each operating condition are all below 10%, with errors exceeding 5% under only a few operating conditions.

[0138] Table 2 Error Statistics of Multi-Scale Refinement Model

[0139]

[0140] To verify the accuracy and effectiveness of the multi-scale refinement model proposed in this invention, the force-displacement hysteresis curves under the corresponding working conditions can be calculated based on the energy storage modulus G' (Figure a), loss modulus G" (Figure b), and loss factor η (Figure c) calculated by the model. The relationship between shear strain and shear stress over time is as follows:

[0141]

[0142]

[0143] In the formula, This is the phase difference between the nominal stress and the equivalent strain, and is related to the loss factor.

[0144] like Figure 6 As shown in the figure, the hysteresis curves of numerical calculations and experimental results are compared under different frequencies, temperatures, and displacement amplitudes. It can be seen from the figure that the hysteresis curves calculated by the model under different frequencies, temperatures, and displacement amplitudes agree well with the experimental results, indicating that the multi-scale refinement model proposed in this invention can accurately predict the force-displacement relationship of high-damping acrylic polymer-based rubber shock absorbers. In summary, the multi-scale refinement model proposed in this invention has good predictive ability and can accurately predict the influence of frequency, temperature, and displacement amplitude on the dynamic mechanical properties of high-damping acrylic polymer-based rubber shock absorbers.

[0145] The method in this application reveals the relationship between the micro-scale and macro-scale mechanical properties of polymer rubber-based materials from the perspective of micro-scale mechanical characteristics. By introducing the time-temperature equivalence principle, the influence of temperature on polymer rubber-based materials is fully considered, and a multi-scale refined model is proposed. The effectiveness and accuracy of the model are verified by corresponding experimental data.

[0146] Correspondingly, this application also provides a multi-factor, multi-scale mechanical property determination system for polymer shock absorbers, including:

[0147] The force-displacement relationship module is used to determine the force-displacement relationship of a single molecular chain of polymer material in a polymer rubber-based shock absorber based on the higher-order fractional viscoelastic derivative model FVMP.

[0148] The energy storage modulus module is used to determine the relationship between the energy storage modulus and any strain amplitude based on the displacement amplitude correlation of the polymer material when it is in a dynamic equilibrium state inside the polymer material.

[0149] The loss modulus module is used to establish the relationship between the loss modulus of polymer rubber-based materials and the van der Waals bond breakage rate, and to determine the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, by combining the displacement amplitude correlation of polymer materials.

[0150] The fusion module is used to determine the relationship between the storage modulus and the arbitrary strain amplitude, the difference between the arbitrary strain and the infinite strain amplitude, the difference between the characteristic strain and the infinite strain amplitude, and the force-displacement relationship of a single molecular chain based on the displacement amplitude correlation, so as to obtain the force-displacement relationship of a single molecular chain under the storage modulus and loss modulus.

[0151] The macroscale model module is used to determine the relationship between microscopic molecular chain stress and stretch ratio based on the total strain energy per unit volume of polymer materials. By introducing loads along the principal axis into the relationship between microscopic molecular chain stress and stretch ratio, the principal stress of the polymer material is obtained. Based on the principal stress, the shear stress and shear modulus are determined. Based on the principal stress, shear stress, and shear modulus of the polymer material, a macroscale model of polymer rubber-based materials is constructed.

[0152] The mechanical calculation module is used to correct the macroscopic model of polymer rubber-based materials by using the temperature correlation of polymer materials, so as to obtain a multi-scale refined model and calculate the dynamic mechanical performance of polymer rubber-based shock absorbers.

[0153] It should be noted that, in the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another device, or some features may be ignored or not executed. The modules described as separate components may or may not be physically separated. The components shown as modules may be one or more physical units, that is, they may be located in one place or distributed in multiple different places. Some or all of the modules can be selected to achieve the purpose of the solution in this embodiment according to actual needs.

[0154] Furthermore, in the various embodiments of the present invention, the modules can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit described above can be implemented in hardware or as a software functional unit.

[0155] An electronic device provided in this application includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber as described in any of the above embodiments.

[0156] Another electronic device provided in this application embodiment may further include: an input port connected to a processor for transmitting multimodal data collected by an external acquisition device to the processor; a display unit connected to the processor for displaying the processor's processing results to the outside world; and a communication module connected to the processor for enabling communication between the electronic device and the outside world. The display unit may be a display panel, a laser scanning display, etc.; the communication method adopted by the communication module includes, but is not limited to, Mobile High Definition Link (HML), Universal Serial Bus (USB), High Definition Multimedia Interface (HDMI), and wireless connection (including Wi-Fi, Bluetooth, Bluetooth Low Energy, and IEEE 802.11s-based communication technology).

[0157] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber as described in any of the above embodiments.

[0158] For descriptions of relevant parts in the multi-factor, multi-scale mechanical property determination system, electronic device, and computer-readable storage medium for polymer shock absorbers provided in this application, please refer to the detailed descriptions of the corresponding parts in the multi-factor, multi-scale mechanical property determination method for polymer shock absorbers provided in this application, which will not be repeated here. Furthermore, parts of the technical solutions provided in this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0159] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber, characterized in that, Includes the following steps: Step 1: Determine the force-displacement relationship of a single molecular chain of the polymer material in the polymer rubber-based shock absorber based on the higher-order fractional viscoelastic derivative model (FVMP). Step 2: Under the dynamic equilibrium state inside the polymer material, determine the relationship between the storage modulus and any strain amplitude based on the correlation of the displacement amplitude of the polymer material; Step 3: Establish the relationship between the loss modulus and van der Waals bond fracture rate of polymer rubber-based materials, and determine the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, by combining the correlation of displacement amplitude of polymer materials. Step 4: Determine the relationship between storage modulus and arbitrary strain amplitude, the difference between arbitrary strain and infinite strain amplitude, the difference between characteristic strain and infinite strain amplitude, and the force-displacement relationship of a single molecular chain based on the displacement amplitude correlation, so as to obtain the force-displacement relationship of a single molecular chain under storage modulus and loss modulus. Step 5: Determine the relationship between microscopic molecular chain stress and stretch ratio based on the total strain energy per unit volume of the polymer material. Introduce the load in the principal axis direction into the relationship between microscopic molecular chain stress and stretch ratio to obtain the principal stress of the polymer material. Determine the shear stress and shear modulus based on the principal stress. Construct a macroscopic model of the polymer rubber-based material based on the principal stress, shear stress, and shear modulus of the polymer material. Step 6: The macroscopic model of polymer rubber-based material is modified by using the temperature correlation of polymer materials to obtain a multi-scale refined model, and the dynamic mechanical performance of polymer rubber-based shock absorber is calculated.

2. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 1, characterized in that, The method for determining the relationship between the storage modulus and arbitrary strain amplitude in step 2 is as follows: The displacement amplitude correlation includes the fracture function relationship and reconstruction function relationship of polymer materials; When the polymer material is in dynamic equilibrium, the number of existing reconstructed bonds is determined based on the fracture function relationship and the reconstruction function relationship, and then the relationship between the number of existing reconstructed bonds and the difference between the storage modulus of the polymer material under arbitrary strain and infinite strain amplitude is determined. Based on the relationship between the existing number of reconstructed bonds in polymer materials and the difference between the storage modulus and the storage modulus, the relationship between the storage modulus and the arbitrary strain amplitude is determined.

3. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 2, characterized in that, The method for determining the correlation of displacement amplitude is as follows: The displacement amplitude correlation of polymer materials was established using the theory of microscopic physical bond breaking and reconstruction.

4. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 1, characterized in that, The methods for determining the difference between the arbitrary strain and the infinite strain amplitude, and the difference between the characteristic strain and the infinite strain amplitude, are as follows: Based on the existing number N of reconfigurable keys v The relationship between loss modulus and van der Waals bond fracture rate was established to determine the relationship of loss modulus under arbitrary strain amplitude. When a polymer material is subjected to an arbitrary strain equal to its characteristic strain, the difference between the characteristic strain and the infinite strain amplitude is determined based on the relationship between the loss modulus and the loss modulus under an arbitrary strain amplitude. Based on the expression for the difference in loss modulus between characteristic strain and infinite strain amplitude, the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, are derived.

5. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 4, characterized in that, The method for determining the relationship between the loss modulus and the van der Waals bond breakage rate is as follows: Based on the additional frictional force generated by the breakage of bonds between carbon black particles or polymers in the rubber-based material of the shock absorber, the relationship between the loss modulus of the polymer material and the van der Waals bond breakage rate is established.

6. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 1, characterized in that, The method for determining the total strain energy per unit volume of the polymer material in step 5 is as follows: A six-chain spherical network model is used to describe the spatial distribution of microscopic molecular chains in polymer materials, thereby determining the strain energy of a single molecular chain. Based on the strain energy of a single molecular chain and the spherical volume of a six-chain spherical network, determine the strain energy of a single molecular chain per unit volume. The total strain energy per unit volume of a polymer material is determined by the strain energy of a single molecular chain per unit volume.

7. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 6, characterized in that, In step 5, the stress-strain relationship of the polymer material is determined based on the total strain energy and the micromechanical theory of polymer rubber-based materials. Based on the incompressible properties of polymer materials, and combined with the stress-strain relationship, the relationship between the microscopic molecular chain stress and the stretch ratio of polymer materials is determined. By introducing a load along the principal axis into the relationship between microscopic molecular chain stress and stretch ratio, the principal stress of the polymer material is obtained. The real part of the principal stress is the storage modulus, and the imaginary part is the loss modulus.

8. The method for determining the multi-factor, multi-scale mechanical properties of a polymer shock absorber according to claim 1, characterized in that, In step 6, the temperature-frequency equivalence method is used to construct the temperature correlation of polymer rubber-based materials.

9. A multi-factor, multi-scale mechanical property determination system for a polymer shock absorber, characterized in that, include: The force-displacement relationship module is used to determine the force-displacement relationship of a single molecular chain of polymer material in a polymer rubber-based shock absorber based on the higher-order fractional viscoelastic derivative model FVMP. The energy storage modulus module is used to determine the relationship between the energy storage modulus and any strain amplitude based on the displacement amplitude correlation of the polymer material when it is in a dynamic equilibrium state inside the polymer material. The loss modulus module is used to establish the relationship between the loss modulus of polymer rubber-based materials and the van der Waals bond breakage rate, and to determine the difference between arbitrary strain and infinite strain amplitude, as well as the difference between characteristic strain and infinite strain amplitude, by combining the displacement amplitude correlation of polymer materials. The fusion module is used to determine the relationship between the storage modulus and the arbitrary strain amplitude, the difference between the arbitrary strain and the infinite strain amplitude, the difference between the characteristic strain and the infinite strain amplitude, and the force-displacement relationship of a single molecular chain based on the displacement amplitude correlation, so as to obtain the force-displacement relationship of a single molecular chain under the storage modulus and loss modulus. The macroscale model module is used to determine the relationship between microscopic molecular chain stress and stretch ratio based on the total strain energy per unit volume of polymer materials. By introducing loads along the principal axis into the relationship between microscopic molecular chain stress and stretch ratio, the principal stress of the polymer material is obtained. Based on the principal stress, the shear stress and shear modulus are determined. Based on the principal stress, shear stress, and shear modulus of the polymer material, a macroscale model of polymer rubber-based materials is constructed. The mechanical calculation module is used to correct the macroscopic model of polymer rubber-based materials by using the temperature correlation of polymer materials, so as to obtain a multi-scale refined model and calculate the dynamic mechanical performance of polymer rubber-based shock absorbers.

10. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the method for determining the multi-factor, multi-scale mechanical properties of the polymer shock absorber as described in any one of claims 1-8.

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