Viscoelastic material model construction method and device, electronic equipment and storage medium

Abstract

The invention relates to the technical field of chemical production, in particular to a construction method and device of a viscoelastic material model, electronic equipment and a storage medium. The construction method comprises the steps that through dynamic mechanical testing of a linear viscoelastic area, the change relation of the energy storage modulus and the loss modulus along with the angular frequency is obtained; determining the shear viscosity and the characteristic relaxation time of the material; acquiring a stress response signal under a large-amplitude oscillation shear condition, extracting a high-order harmonic coefficient representing a nonlinear behavior through harmonic analysis, preliminarily determining a nonlinear parameter of the constitutive model according to the high-order harmonic coefficient, and calculating a theoretical stress response; and finally, by taking the nonlinear parameter, the shear viscosity and the relaxation time as initial values and minimizing the deviation between a theory and actually measured stress response, iterative optimization is carried out until convergence, so that the viscoelastic material model is obtained. According to the method, the non-linear parameter identification precision and the calculation efficiency can be remarkably improved, and the constructed model has excellent prediction capability and reliability in a wide frequency and wide strain range.

Description

Technical Field

[0001] This invention relates to the field of chemical production technology, specifically to a method, apparatus, electronic device, and storage medium for constructing a viscoelastic material model. Background Technology

[0002] In the molding and processing of polymer materials, accurately predicting the stress distribution within the material is crucial for optimizing molding process parameters, controlling product deformation, reducing residual stress, and improving the mechanical properties and dimensional stability of the final product. However, polymer materials typically exhibit significant viscoelastic characteristics, meaning they simultaneously possess the behavior of viscous fluids and elastic solids. Their mechanical response depends not only on the current stress state but also on factors such as loading history, strain rate, and temperature. Traditional material constitutive models, such as linear viscoelastic models or simple non-Newtonian fluid models, often have significant limitations in describing such complex behaviors, making it difficult to accurately capture the true mechanical response of materials under multiaxial stress, large deformation, or unsteady flow conditions. Summary of the Invention

[0003] This invention provides a method, apparatus, electronic device, and storage medium for constructing a viscoelastic material model, in order to solve the problem that traditional constitutive models are difficult to accurately describe the nonlinear viscoelastic behavior of polymer materials under complex molding conditions.

[0004] In a first aspect, the present invention provides a method for constructing a viscoelastic material model, the method comprising the following steps: obtaining the actual variation relationship of the storage modulus with angular frequency and the actual variation relationship of the loss modulus with angular frequency in a linear viscoelastic region; determining the shear viscosity and characteristic relaxation time of the material based on the actual variation relationship of the storage modulus with angular frequency and the actual variation relationship of the loss modulus with angular frequency; obtaining the stress response signal measured in a large-amplitude oscillation shear test, wherein the large-amplitude oscillation shear test is carried out under the conditions of strain amplitude exceeding the upper limit of the linear viscoelastic region and under preset angular frequency and strain amplitude; performing harmonic analysis on the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material; determining the nonlinear parameters of the viscoelastic constitutive model according to the higher-order harmonic coefficients, and determining the theoretical stress response of the viscoelastic constitutive model; using the nonlinear parameters, the shear viscosity and characteristic relaxation time of the material as an initial parameter set, and iteratively optimizing the other parameters in the viscoelastic constitutive model except for the nonlinear parameters by minimizing the deviation between the theoretical stress response and the stress response signal, until a preset convergence condition is met, thereby obtaining the viscoelastic material model.

[0005] The method for constructing a viscoelastic material model provided by this invention determines linear viscoelastic parameters such as shear viscosity and characteristic relaxation time through small-amplitude oscillating shear (SAOS) experiments. Then, it combines large-amplitude oscillating shear (LAOS) experiments and harmonic analysis to obtain higher-order harmonic coefficients, which are used to initially identify nonlinear parameters such as the nonlinear factor α in the Giesekus model. Since higher-order harmonic coefficients are unique characteristics of materials under nonlinear responses and are more sensitive to nonlinear factors, they can significantly improve parameter identification accuracy. Simultaneously, this step-by-step strategy effectively reduces the optimization difficulty caused by strong coupling of multiple parameters and significantly reduces the computational load. Based on this, using the initially obtained parameters as initial values, iterative optimization is performed by minimizing the overall deviation between the theoretical stress response and the measured LAOS signal. This not only ensures that the model accurately captures nonlinear behavior but also improves its global predictive ability throughout the entire strain history. The finally constructed viscoelastic material model exhibits excellent reliability across a wide frequency and strain amplitude range, making it suitable for high-precision simulation and control of complex molding processes.

[0006] In one optional implementation, determining the shear viscosity and characteristic relaxation time of the material based on the actual variation relationship between the energy storage modulus and the loss modulus with angular frequency includes: setting the current number n of the generalized Maxwell model; fitting the actual variation relationship between the energy storage modulus and the loss modulus with angular frequency using a fitting algorithm based on the generalized Maxwell model, wherein the generalized Maxwell model contains n parallel viscoelastic modes, each mode being characterized by a relaxation time and a modulus parameter; and simultaneously determining the relaxation time of the n modes using the fitting algorithm. The modulus parameter is determined, and the viscosity parameter is determined based on the relaxation time and modulus parameter in each mode, resulting in n sets of one-to-one relaxation time-viscosity parameter pairs; it is then determined whether the current fitting result meets the preset accuracy requirements; if it does, the n sets of relaxation time-viscosity parameter pairs are used as the shear viscosity and characteristic relaxation time of the material; if it does not, 1 is added to the current mode number n to obtain the next mode number, and the next mode number is used as the new current mode number, and the process returns to the step of fitting the actual relationship between the energy storage modulus and the angular frequency and the actual relationship between the loss modulus and the angular frequency using the fitting algorithm based on the generalized Maxwell model.

[0007] The above implementation method uses a generalized Maxwell model to fit the storage modulus and loss modulus data obtained from the SAOS experiment to determine the shear viscosity and characteristic relaxation time of the material. Since the Giesekus model degenerates into a Maxwell model in the linear viscoelastic region, the parameters of each viscoelastic mode can be solved step-by-step based on the generalized Maxwell model. Specifically, starting with a smaller number of modes, the number of modes is gradually increased and iterative fitting is performed until the preset accuracy requirement is met. This strategy, on the one hand, effectively alleviates the optimization difficulties caused by multi-parameter coupling by identifying linear parameters step-by-step; on the other hand, the progressive fitting method of increasing the number of modes significantly reduces computational complexity and improves fitting efficiency and stability. The relaxation time-viscosity parameter obtained in this way not only has a clear physical meaning but also lays a reliable foundation for the accurate identification of subsequent nonlinear parameters.

[0008] In one optional implementation, the fitting algorithm employs a nonlinear least squares method, which simultaneously optimizes the relaxation time and modulus parameters of the n modes by constructing and minimizing an objective function; wherein the objective function is the sum of the weighted squared deviations between the experimentally measured energy storage modulus and loss modulus and the corresponding fitted values ​​calculated based on the generalized Maxwell model.

[0009] This can improve calculation accuracy.

[0010] In one optional implementation, obtaining the stress response signal measured in the large-amplitude oscillation shear test includes: applying a shear strain in the form of a sinusoidal wave to the material, wherein the strain amplitude of the sinusoidal wave is greater than the upper limit of the strain in the linear viscoelastic region, and the angular frequency is a preset value; and obtaining the shear stress component and normal stress component generated by the material during the application of the sinusoidal shear strain as the stress response signal.

[0011] In large-amplitude oscillating shear (LAOS) tests, by applying sinusoidal shear strain in the superlinear region and simultaneously acquiring stress response signals in both the shear and normal directions, the harmonic characteristics of the two stress components can be fully utilized: shear stress mainly contributes odd harmonics, while normal stress mainly contributes even harmonics. Based on this physical mechanism, this implementation method selectively extracts harmonics from the two types of stress signals, effectively reducing the complexity of data processing and environmental noise interference, and more accurately separating the higher-order harmonic components that characterize the nonlinear viscoelastic nature of the material. This method significantly improves the calculation accuracy of higher-order harmonic coefficients, reduces the impact of invalid or redundant information on model parameter inversion, and thus enhances the stability and uniqueness of nonlinear parameter identification.

[0012] In one optional implementation, harmonic analysis of the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material includes: decomposing the shear stress component and the normal stress component into multiple harmonic components with the input strain frequency as the fundamental frequency; extracting the odd-harmonic components from the shear stress component and the even-harmonic components from the normal stress component, and calculating the amplitude or normalized intensity relative to the fundamental frequency harmonic of each harmonic component; and obtaining the higher-order harmonic coefficients based on the amplitude or normalized intensity.

[0013] The above-described implementation extracts odd and even harmonic components from the shear and normal stress components, respectively, and calculates their absolute amplitude or normalized intensity relative to the fundamental frequency. This yields a set of high-order harmonic coefficients with clear structure and explicit physical meaning. This not only achieves precise quantification of the material's nonlinearity but also effectively reduces systematic errors caused by small fluctuations in test conditions such as amplitude or frequency through normalization, significantly improving the comparability of experimental data between different batches or devices. More importantly, these high-order harmonic coefficients form the basis of a highly sensitive objective function, capable of keenly capturing subtle differences in material response, thereby greatly improving the resolution, stability, and robustness of nonlinear parameter inversion.

[0014] In one optional implementation, iterative optimization of parameters other than the nonlinear parameter in the viscoelastic constitutive model by minimizing the deviation between the theoretical stress response and the stress response signal includes: constructing an objective function using a numerical optimization algorithm to characterize the error between the stress response signal and the theoretical stress response; wherein the numerical optimization algorithm includes least squares method, genetic algorithm, or particle swarm optimization; and iteratively updating the parameters other than the nonlinear parameter in the viscoelastic constitutive model based on the objective function until the objective function reaches a preset convergence condition, thereby determining the parameters other than the nonlinear parameter in the viscoelastic constitutive model.

[0015] The above implementation transforms the amplitude or normalized intensity obtained from harmonic analysis into standardized high-order harmonic coefficients, serving as a crucial bridge connecting experimental data and theoretical models. These coefficients have clear physical meanings and can be directly used to construct objective functions, driving numerical methods such as least squares, genetic algorithms, or particle swarm optimization to efficiently iteratively optimize parameters other than nonlinearities in the viscoelastic constitutive model. Compared to traditional time-domain or full-frequency-domain global fitting methods, this method focuses on characteristic harmonics that characterize the nonlinear nature of materials, significantly reducing computational load, accelerating convergence, effectively reducing redundant information interference, improving the stability of the optimization process, and avoiding getting trapped in local optima, thereby obtaining model parameters with higher accuracy and robustness.

[0016] Secondly, the present invention provides a device for constructing a viscoelastic material model, the device comprising a first acquisition module, a first processing module, a second acquisition module, a second processing module, a third processing module, and a fourth processing module; wherein, the first acquisition module is used to acquire the actual relationship between the storage modulus and the loss modulus of the material and the angular frequency in the linear viscoelastic region; the first processing module is used to determine the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the storage modulus and the loss modulus; the second acquisition module is used to acquire the stress response signal measured in a large-amplitude oscillation shear test, wherein the large-amplitude oscillation shear test is conducted when the strain amplitude exceeds the upper limit of the linear viscoelastic region of the material. The process is implemented under set angular frequency and strain amplitude conditions; the second processing module is used to perform harmonic analysis on the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material; the third processing module is used to determine the nonlinear parameters of the viscoelastic constitutive model based on the higher-order harmonic coefficients, and to determine the theoretical stress response of the viscoelastic constitutive model; the fourth processing module is used to take the nonlinear parameters, the shear viscosity of the material, and the characteristic relaxation time as the initial parameter set, and to iteratively optimize the other parameters in the viscoelastic constitutive model except for the nonlinear parameters by minimizing the deviation between the theoretical stress response and the stress response signal, until the preset convergence condition is met, and obtain the viscoelastic material model.

[0017] Thirdly, the present invention also provides an electronic device, including a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the method for constructing a viscoelastic material model according to the first aspect or any corresponding embodiment described above.

[0018] Fourthly, the present invention also provides a computer-readable storage medium storing computer instructions for causing a computer to execute the method for constructing a viscoelastic material model according to the first aspect or any corresponding embodiment described above.

[0019] Fifthly, the present invention also provides a computer program product, including computer instructions for causing a computer to execute the method for constructing a viscoelastic material model according to the first aspect or any corresponding embodiment described above. Attached Figure Description

[0020] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of an application scenario according to an embodiment of the present invention; Figure 2 This is a first flowchart of a method for constructing a viscoelastic material model according to an embodiment of the present invention; Figure 3 This is a second flowchart of the method for constructing a viscoelastic material model according to an embodiment of the present invention; Figure 4 This is a structural block diagram of a viscoelastic material model building device according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0023] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0024] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0025] As an optional application scenario of this invention, such as Figure 1 As shown, the application scenario may include at least one terminal device and at least one server. Figure 1 The system is illustrated in the example, which includes a computer 101, a mobile terminal 102, and a server 103, and the terminal devices such as the computer 101 and the mobile terminal 102 are connected to the server 103 through a network 110.

[0026] Specifically, the terminal device can be a smartphone, tablet, laptop, PDA, desktop computer, game console, smart TV, smart wearable device, in-vehicle terminal, VR (Virtual Reality) device, AR (Augmented Reality) device, etc. Server 103 can be a standalone physical server, a server cluster, a distributed system, or a cloud server providing cloud services. Network 110 can be a wired or wireless network, examples of which include, but are not limited to, the Internet, corporate intranet, local area network, wide area network, mobile communication network, and combinations thereof.

[0027] According to an embodiment of the present invention, a method for constructing a viscoelastic material model is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0028] This embodiment provides a method for constructing a viscoelastic material model, which can be used in the aforementioned mobile terminals, such as mobile phones and tablet computers. Figure 2 This is a first flowchart of a viscoelastic material model construction method according to an embodiment of the present invention, such as... Figure 2 As shown, the process includes the following steps: Step S201: Obtain the actual relationship between the storage modulus and the loss modulus of the material in the linear viscoelastic region and the actual relationship between the loss modulus and the angular frequency.

[0029] The materials are polymers, including thermoplastics, rubber and their composites.

[0030] Step S202: Determine the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the storage modulus and the angular frequency and the loss modulus.

[0031] In other words, key physical parameters are extracted from linear viscoelastic data. Shear viscosity characterizes the flow resistance of a material at extremely low shear rates, while characteristic relaxation time reflects the speed of molecular chain motion or structural relaxation. Both are core linear parameters for constructing viscoelastic constitutive models such as those by Maxwell, Giesekus, and Phan-Thien–Tanner.

[0032] Step S203: Obtain the stress response signal measured in the large-amplitude oscillation shear test, wherein the large-amplitude oscillation shear test is carried out under the conditions that the strain amplitude exceeds the upper limit of the linear viscoelastic region and the preset angular frequency and strain amplitude.

[0033] In other words, by exciting the nonlinear viscoelastic response of the material under nonlinear deformation conditions (i.e. strain amplitude exceeding the linear region), experimental data that can reflect the complex behaviors of the material such as yielding, shear thinning, and elastic hardening can be obtained, providing a basis for identifying nonlinear constitutive parameters.

[0034] Step S204: Perform harmonic analysis on the stress response signal to obtain the higher-order harmonic coefficients characterizing the nonlinear behavior of the material.

[0035] In other words, the nonsinusoidal stress response is decomposed into the fundamental frequency and its higher harmonic components, quantifying the degree of nonlinearity of the material. Higher harmonics, such as the third and fifth harmonics, are sensitive to the nonlinear mechanisms of materials, such as strain hardening and shear thinning, and can serve as characteristic indicators of nonlinear behavior.

[0036] Step S205: Determine the nonlinear parameters of the viscoelastic constitutive model based on the higher-order harmonic coefficients, and determine the theoretical stress response of the viscoelastic constitutive model.

[0037] For example, the known strain input (such as the sinusoidal strain signal set in the LAOS experiment) can be combined with the selected viscoelastic constitutive equation and nonlinear parameters to numerically solve the constitutive equation and calculate the theoretical shear stress output under the corresponding time history.

[0038] Step S206: Using the nonlinear parameter, the shear viscosity of the material, and the characteristic relaxation time as the initial parameter set, the parameters other than the nonlinear parameter in the viscoelastic constitutive model are iteratively optimized by minimizing the deviation between the theoretical stress response and the stress response signal until the preset convergence condition is met, thus obtaining the viscoelastic material model.

[0039] For example, other parameters besides the nonlinear parameters include zero shear viscosity, characteristic relaxation time modulus scaling factor, relaxation time and elastic modulus of each branch in a multimodal Maxwell element, and auxiliary constants in the constitutive model related to the molecular network structure or fluid type.

[0040] The viscoelastic material model construction method provided in this embodiment determines linear viscoelastic parameters such as shear viscosity and characteristic relaxation time through small-amplitude oscillating shear (SAOS) experiments. Then, it combines large-amplitude oscillating shear (LAOS) experiments and harmonic analysis to obtain higher-order harmonic coefficients, which are used to initially identify nonlinear parameters such as the nonlinear factor α in the Giesekus model. Since higher-order harmonic coefficients are unique characteristics of materials under nonlinear responses and are more sensitive to nonlinear factors, they can significantly improve parameter identification accuracy. Simultaneously, this step-by-step strategy effectively reduces the optimization difficulty caused by strong coupling of multiple parameters and significantly reduces the computational load. Based on this, using the initially obtained parameters as initial values, iterative optimization is performed by minimizing the overall deviation between the theoretical stress response and the measured LAOS signal. This not only ensures that the model accurately captures nonlinear behavior but also improves its global predictive ability throughout the entire strain history. The finally constructed viscoelastic material model exhibits excellent reliability across a wide frequency and strain amplitude range, making it suitable for high-precision simulation and control of complex molding processes.

[0041] This embodiment provides a method for constructing a viscoelastic material model, which can be used in the aforementioned mobile terminals, such as mobile phones and tablet computers. Figure 3 This is a second flowchart of the viscoelastic material model construction method according to an embodiment of the present invention, such as... Figure 3 As shown, the process includes the following steps: Step S301: Determine the linear viscoelastic region through small-amplitude oscillation shear test.

[0042] The small-amplitude oscillatory shear test, also known as the SAOS (Small Amplitude Oscillatory Shear) test, is conducted within the linear viscoelastic region (LVE). In this region, the material's mechanical response is linearly related to the applied strain, and the modulus remains constant regardless of the strain amplitude, ensuring the reliability and repeatability of subsequent rheological measurements. The specific operation of the small-amplitude oscillatory shear test involves first performing a strain scan at a fixed frequency, gradually increasing the strain amplitude, and monitoring the changes in the storage modulus (G') and loss modulus (G''). When G' and G'' remain essentially constant without significant decreases or deviations, the corresponding strain range is the LVE. Subsequently, within this linear region, a suitable strain amplitude is selected, and a frequency scan test is performed to obtain G' and G'' data at different frequencies.

[0043] Step S302: Obtain the actual relationship between the storage modulus and the loss modulus of the material in the linear viscoelastic region and the actual relationship between the loss modulus and the angular frequency.

[0044] Step S303: Determine the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the storage modulus and the angular frequency and the loss modulus.

[0045] In one optional implementation, determining the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the storage modulus and the loss modulus and the angular frequency includes the following steps: Step S3031: Set the current number of modes n for the generalized Maxwell model.

[0046] The value of n starts from 1 and gradually increases.

[0047] Step S3032: Based on the generalized Maxwell model, a fitting algorithm is used to fit the actual relationship between the energy storage modulus and the angular frequency and the actual relationship between the loss modulus and the angular frequency. The generalized Maxwell model contains n parallel viscoelastic modes, each of which is characterized by a relaxation time and a modulus parameter.

[0048] For example, experimental data within the linear viscoelastic region can be fitted using the following expression:

[0049] Where G'(ω) represents the storage modulus; G''(ω) represents the loss modulus; ηi represents the viscosity of the i-th mode; λi represents the relaxation time of the i-th mode; ω represents the angular frequency; and m represents the mode number.

[0050] Step S3033: Simultaneously determine the relaxation time and modulus parameters of the n modes using a fitting algorithm, and determine the viscosity parameters based on the relaxation time and modulus parameters of each mode, to obtain n sets of one-to-one corresponding relaxation time-viscosity parameter pairs.

[0051] The fitting algorithm employs a nonlinear least squares method, which simultaneously optimizes the relaxation time and modulus parameters of the n modes by constructing and minimizing an objective function. The objective function is the sum of the weighted squared deviations between the experimentally measured energy storage modulus and loss modulus and the corresponding fitted values ​​calculated based on the generalized Maxwell model.

[0052] For example, nonlinear least squares methods (such as the Levenberg-Marquardt algorithm) are used to fit experimentally measured values. G 'and G Given the data, minimize the following objective function:

[0053] in, G ′、G ′′ represents the experimental value. G fit′、 G fit′′ represents the model fit value. N This represents the number of frequency sampling points.

[0054] Step S3034: Determine whether the current fitting result meets the preset accuracy requirements.

[0055] Step S3035: If satisfied, the n sets of relaxation time-viscosity parameter pairs are used as the shear viscosity and characteristic relaxation time of the material.

[0056] Step S3036: If not satisfied, add 1 to the current mode number n to obtain the next mode number, and use the next mode number as the new current mode number. Then return to the step of fitting the actual relationship between the energy storage modulus and the actual relationship between the loss modulus and the angular frequency using the fitting algorithm based on the generalized Maxwell model.

[0057] The above implementation method uses a generalized Maxwell model to fit the storage modulus and loss modulus data obtained from the SAOS experiment to determine the shear viscosity and characteristic relaxation time of the material. Since the Giesekus model degenerates into a Maxwell model in the linear viscoelastic region, the parameters of each viscoelastic mode can be solved step-by-step based on the generalized Maxwell model. Specifically, starting with a smaller number of modes, the number of modes is gradually increased and iterative fitting is performed until the preset accuracy requirement is met. This strategy, on the one hand, effectively alleviates the optimization difficulties caused by multi-parameter coupling by identifying linear parameters step-by-step; on the other hand, the progressive fitting method of increasing the number of modes significantly reduces computational complexity and improves fitting efficiency and stability. The relaxation time-viscosity parameter obtained in this way not only has a clear physical meaning but also lays a reliable foundation for the accurate identification of subsequent nonlinear parameters.

[0058] Step S304: Obtain the stress response signal measured in the large-amplitude oscillation shear test, wherein the large-amplitude oscillation shear test is carried out under the conditions of strain amplitude exceeding the upper limit of the linear viscoelastic region and under preset angular frequency and strain amplitude conditions.

[0059] Specifically, the large-amplitude oscillation shear test includes one of the following experimental strategies: gradually increasing the strain amplitude at multiple preset angular frequencies until the stress response deviates from linear viscoelastic behavior; or scanning the angular frequency at multiple preset strain amplitudes to cover the nonlinear response region of the material. During the test, the angular frequency ω, temperature T, measurement gap h, and corresponding stress response signal are recorded simultaneously, and the nonlinear viscoelastic behavior of the material is preliminarily identified based on stress harmonic characteristics, Lissajous curve morphology, or nonlinear modulus parameters.

[0060] In one alternative implementation, obtaining the stress response signal measured in a large-amplitude oscillation shear test includes the following steps: Step S3041: Apply a shear strain in the form of a sine wave to the material. The strain amplitude of the sine wave is greater than the upper limit of the strain in the linear viscoelastic region, and the angular frequency is a preset value.

[0061] Step S3042: Obtain the shear stress component and normal stress component generated in the material during the application of sinusoidal shear strain, as stress response signals.

[0062] In the LAOS experiment, by applying sinusoidal shear strain in the superlinear region and simultaneously acquiring stress response signals in both the shear and normal directions, the harmonic characteristics of the two stress components can be fully utilized: shear stress mainly contributes odd harmonics, while normal stress mainly contributes even harmonics. Based on this physical mechanism, this implementation method selectively extracts harmonics from the two types of stress signals, effectively reducing the complexity of data processing and environmental noise interference, and more accurately separating the higher-order harmonic components that characterize the nonlinear viscoelastic nature of the material. This method significantly improves the calculation accuracy of higher-order harmonic coefficients, reduces the impact of invalid or redundant information on model parameter inversion, and thus enhances the stability and uniqueness of nonlinear parameter identification.

[0063] Step S305: Perform harmonic analysis on the stress response signal to obtain the higher-order harmonic coefficients characterizing the nonlinear behavior of the material.

[0064] Specifically, the process of performing harmonic analysis on the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material includes the following steps: Step S3051: Decompose the shear stress component and the normal stress component into multiple harmonic components with the input strain frequency as the fundamental frequency.

[0065] Step S3052: Extract the odd-frequency harmonic components from the shear stress components and the even-frequency harmonic components from the normal stress components, and calculate the amplitude or normalized intensity of each harmonic component relative to the fundamental frequency harmonic.

[0066] Step S3053: Obtain the higher-order harmonic coefficients based on the amplitude or normalized intensity.

[0067] The above-described implementation extracts odd and even harmonic components from the shear and normal stress components, respectively, and calculates their absolute amplitude or normalized intensity relative to the fundamental frequency. This yields a set of high-order harmonic coefficients with clear structure and explicit physical meaning. This not only achieves precise quantification of the material's nonlinearity but also effectively reduces systematic errors caused by testing conditions (such as small fluctuations in amplitude or frequency) through normalization, significantly improving the comparability of experimental data between different batches or devices. More importantly, these high-order harmonic coefficients form the basis of a highly sensitive objective function, capable of keenly capturing subtle differences in material response, thereby greatly improving the resolution, stability, and robustness of nonlinear parameter inversion.

[0068] Step S306: Determine the nonlinear parameters of the viscoelastic constitutive model based on the higher-order harmonic coefficients, and determine the theoretical stress response of the viscoelastic constitutive model.

[0069] In one optional implementation, the preset viscoelastic constitutive model is the Giesekus model. Under large amplitude oscillating shear (LAOS) conditions, the applied strain is... The corresponding strain rate is The shear stress τ 12 (t) and the normal stress τ related to the first normal stress difference 11 (t) can be expressed in Fourier series form: , And substitute this expression into the differential equation of the Giesekus model:

[0070] The model is transformed into a system of nonlinear algebraic equations using numerical methods. The harmonic coefficients of each order are solved, and the stress waveform is reconstructed, thereby obtaining key parameters such as the nonlinear factor α in the Giesekus model.

[0071] Step S307: Using the nonlinear parameter, the shear viscosity of the material, and the characteristic relaxation time as the initial parameter set, the parameters other than the nonlinear parameter in the viscoelastic constitutive model are iteratively optimized by minimizing the deviation between the theoretical stress response and the stress response signal until the preset convergence condition is met, thus obtaining the viscoelastic material model.

[0072] In one optional implementation, the iterative optimization of parameters other than the nonlinear parameter in the viscoelastic constitutive model by minimizing the deviation between the theoretical stress response and the stress response signal includes: constructing an objective function using a numerical optimization algorithm to characterize the error between the stress response signal and the theoretical stress response; wherein the numerical optimization algorithm includes least squares method, genetic algorithm, or particle swarm optimization; and iteratively updating the parameters other than the nonlinear parameter in the viscoelastic constitutive model based on the objective function until the objective function reaches a preset convergence condition, thereby determining the parameters other than the nonlinear parameter in the viscoelastic constitutive model.

[0073] The above implementation transforms the amplitude or normalized intensity obtained from harmonic analysis into standardized high-order harmonic coefficients, serving as a crucial bridge connecting experimental data and theoretical models. These coefficients have clear physical meanings and can be directly used to construct objective functions, driving numerical methods such as least squares, genetic algorithms, or particle swarm optimization to efficiently iteratively optimize parameters other than nonlinearities in the viscoelastic constitutive model. Compared to traditional time-domain or full-frequency-domain global fitting methods, this method focuses on characteristic harmonics that characterize the nonlinear nature of materials, significantly reducing computational load, accelerating convergence, effectively reducing redundant information interference, improving the stability of the optimization process, and avoiding getting trapped in local optima, thereby obtaining model parameters with higher accuracy and robustness.

[0074] Furthermore, the shear viscosity obtained from steady-state shear tests can be used. and the first normal stress difference The data were used to validate the determined Giesekus model parameters, minimizing the error between the experimental data and the model predictions; cross-validation was also performed using moderate amplitude oscillating shear (MAOS) experimental data. Finally, a complete fluid viscoelastic material model was constructed based on the validated parameters for simulation analysis of polymer molding processes, in order to obtain more accurate stress prediction results.

[0075] To more clearly explain the construction method of the viscoelastic material model in this embodiment, a Giesekus fluid viscoelastic model construction method based on polycarbonate (PC) material is given to demonstrate the application process of this embodiment in actual thermoplastic polymer materials.

[0076] 1. SAOS test and linear parameter identification A polycarbonate (PC) was selected, and small-amplitude oscillating shear (SAOS) tests were conducted using a rotational rheometer at 240°C. The frequency sweep range was 0.1–500 rad / s, and the strain was controlled within 0.5% to ensure it remained within the linear viscoelastic region. After obtaining the storage modulus G′ and loss modulus G″ data, the Levenberg-Marquardt algorithm was used to fit a multimodal Maxwell model, and the relaxation times λ for the first four orders were preliminarily identified. i and the corresponding shear viscosity component η p , i As shown in the table below:

[0077] 2. LAOS test and nonlinear parameter identification Large-amplitude oscillating shear (LAOS) tests were conducted at the same temperature, with a fixed frequency of 1 rad / s, and the strain amplitude was gradually increased to 200%. The stress response was recorded, Lissajous curves were plotted, and higher-order harmonic components were extracted. The stress response was expanded into a Fourier series, substituted into the differential equations of the Giesekus model, and the nonlinear algebraic equations were solved using numerical methods (such as the Newton-Raphson iteration). The nonlinear parameters α1=0.28, α2=0.28, α3=0.24, and α4=0.18 were identified.

[0078] 3. MAOS test and steady-state shear verification Further steady-state shear tests were conducted, with shear rates ranging from 0.01 to 100 s⁻¹. -1 Measure shear viscosity and the first normal stress difference The model predictions were compared with experimental data; further MAOS experiments were conducted to measure stress response, and the model predictions were compared with experimental data. Numerical methods were used to optimize the model parameters, and the model parameters were finally confirmed.

[0079] This embodiment also provides a construction apparatus for a viscoelastic material model, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0080] This embodiment provides a device for constructing a viscoelastic material model, such as... Figure 4 As shown, it includes: The first acquisition module 401 is used to acquire the actual relationship between the storage modulus and the loss modulus of the material in the linear viscoelastic region and the actual relationship between the loss modulus and the angular frequency.

[0081] The first processing module 402 is used to determine the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the storage modulus and the angular frequency and the loss modulus and the angular frequency.

[0082] The second acquisition module 403 is used to acquire the stress response signal measured in the large-amplitude oscillation shear test, which is carried out under the conditions that the strain amplitude exceeds the upper limit of the linear viscoelastic region of the material and the set angular frequency and strain amplitude.

[0083] The second processing module 404 is used to perform harmonic analysis on the stress response signal to obtain high-order harmonic coefficients that characterize the nonlinear behavior of the material.

[0084] The third processing module 405 is used to determine the nonlinear parameters of the viscoelastic constitutive model based on the higher-order harmonic coefficients, and to determine the theoretical stress response of the viscoelastic constitutive model.

[0085] The fourth processing module 406 is used to take the nonlinear parameter, the shear viscosity of the material and the characteristic relaxation time as the initial parameter set, and to iteratively optimize the other parameters in the viscoelastic constitutive model except for the nonlinear parameter by minimizing the deviation between the theoretical stress response and the stress response signal until the preset convergence condition is met, so as to obtain the viscoelastic material model.

[0086] In some optional implementations, the first processing module 402 is specifically used for: setting the current number of modes n of the generalized Maxwell model; fitting the actual relationship between the energy storage modulus and the loss modulus with angular frequency using a fitting algorithm based on the generalized Maxwell model, wherein the generalized Maxwell model contains n parallel viscoelastic modes, each mode being characterized by a relaxation time and a modulus parameter; synchronously determining the relaxation time and modulus parameters of the n modes using the fitting algorithm, and determining the viscosity parameter according to the relaxation time and modulus parameters of each mode, obtaining n sets of one-to-one corresponding relaxation time-viscosity parameter pairs; determining whether the current fitting result meets the preset accuracy requirements; if it does, then using the n sets of relaxation time-viscosity parameter pairs as the shear viscosity and characteristic relaxation time of the material; if it does not, adding 1 to the current number of modes n to obtain the next number of modes, and using the next number of modes as the new current number of modes, and returning to the step of fitting the actual relationship between the energy storage modulus and the loss modulus with angular frequency using a fitting algorithm based on the generalized Maxwell model.

[0087] In some optional implementations, the fitting algorithm employs a nonlinear least squares method to simultaneously optimize the relaxation time and modulus parameters of the n modes by constructing and minimizing an objective function; wherein the objective function is the sum of the weighted squared deviations between the experimentally measured energy storage modulus and loss modulus and the corresponding fitted values ​​calculated based on the generalized Maxwell model.

[0088] In some optional embodiments, the second acquisition module 403 is specifically used to: apply a shear strain in the form of a sine wave to the material, wherein the strain amplitude of the sine wave is greater than the upper limit of the strain in the linear viscoelastic region and the angular frequency is a preset value; and acquire the shear stress component and normal stress component generated by the material during the application of the sine shear strain as stress response signals.

[0089] In some optional embodiments, the second processing module 404 is specifically used to: decompose the shear stress component and the normal stress component into multiple harmonic components with the input strain frequency as the fundamental frequency; extract the odd-frequency harmonic components from the shear stress component and the even-frequency harmonic components from the normal stress component, and calculate the amplitude or normalized intensity relative to the fundamental frequency harmonic of each harmonic component; and obtain the higher-order harmonic coefficients based on the amplitude or normalized intensity.

[0090] In some optional implementations, the fourth processing module 406 is specifically used to: construct an objective function using a numerical optimization algorithm to characterize the error between the stress response signal and the theoretical stress response; wherein the numerical optimization algorithm includes least squares method, genetic algorithm or particle swarm optimization; and iteratively update other parameters in the viscoelastic constitutive model other than the nonlinear parameter based on the objective function until the objective function reaches a preset convergence condition, thereby determining other parameters in the viscoelastic constitutive model other than the nonlinear parameter.

[0091] The viscoelastic material model construction apparatus provided in this embodiment of the invention can execute the viscoelastic material model construction method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method. Further functional descriptions of the above modules and units are the same as in the corresponding embodiments described above, and will not be repeated here.

[0092] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0093] The following is a detailed reference. Figure 5The diagram illustrates a structural schematic suitable for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 501, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 502 or a program loaded from memory 508 into random access memory (RAM) 503. The RAM 503 also stores various programs and data required for the operation of the electronic device. The processor 501, ROM 502, and RAM 503 are interconnected via a bus 504. An input / output (I / O) interface 505 is also connected to the bus 504.

[0094] Typically, the following devices can be connected to I / O interface 505: input devices 506 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 507 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 508 including, for example, magnetic tapes, hard disks, etc.; and communication devices 509. Communication device 509 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 5 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0095] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 509, or installed from a memory 508, or installed from a ROM 502. When the computer program is executed by the processor 501, it performs the functions defined in the method for constructing a viscoelastic material model according to embodiments of the present invention.

[0096] Figure 5 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0097] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the method for constructing the viscoelastic material model shown in the above embodiments is implemented.

[0098] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0099] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for constructing a viscoelastic material model, characterized in that, The method includes: Obtain the actual relationship between the storage modulus and the loss modulus of the material as a function of angular frequency in the linear viscoelastic region; The shear viscosity and characteristic relaxation time of the material are determined based on the actual relationship between the energy storage modulus and the angular frequency and the actual relationship between the loss modulus and the angular frequency. Acquire the stress response signal measured in a large-amplitude oscillation shear test, wherein the large-amplitude oscillation shear test is carried out under conditions where the strain amplitude exceeds the upper limit of the linear viscoelastic region and at a preset angular frequency and strain amplitude. Harmonic analysis was performed on the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material; The nonlinear parameters of the viscoelastic constitutive model are determined based on the higher-order harmonic coefficients, and the theoretical stress response of the viscoelastic constitutive model is determined. Using the nonlinear parameter, the shear viscosity of the material, and the characteristic relaxation time as the initial parameter set, the parameters other than the nonlinear parameter in the viscoelastic constitutive model are iteratively optimized by minimizing the deviation between the theoretical stress response and the stress response signal until the preset convergence condition is met, thus obtaining the viscoelastic material model.

2. The method according to claim 1, characterized in that, The determination of the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the energy storage modulus and the loss modulus and the actual relationship between the energy storage modulus and the angular frequency includes: Define the current number of modes n in the generalized Maxwell model; Based on the generalized Maxwell model, a fitting algorithm is used to fit the actual relationship between the energy storage modulus and the angular frequency and the actual relationship between the loss modulus and the angular frequency. The generalized Maxwell model contains n parallel viscoelastic modes, each of which is characterized by a relaxation time and a modulus parameter. The relaxation time and modulus parameters of the n modes are determined synchronously by fitting algorithm, and the viscosity parameters are determined according to the relaxation time and modulus parameters of each mode, resulting in n sets of one-to-one corresponding relaxation time-viscosity parameter pairs. Determine whether the current fitting result meets the preset accuracy requirements; If satisfied, the n sets of relaxation time-viscosity parameter pairs are taken as the shear viscosity and characteristic relaxation time of the material; If the condition is not met, add 1 to the current mode number n to obtain the next mode number, and use the next mode number as the new current mode number. Then return to the step of fitting the actual relationship between the energy storage modulus and the loss modulus with the angular frequency using the fitting algorithm based on the generalized Maxwell model.

3. The method according to claim 2, characterized in that, The fitting algorithm employs a nonlinear least squares method, which simultaneously optimizes the relaxation time and modulus parameters of the n modes by constructing and minimizing an objective function; wherein, the objective function is the sum of the weighted squared deviations between the experimentally measured energy storage modulus and loss modulus and the corresponding fitted values ​​calculated based on the generalized Maxwell model.

4. The method according to claim 1, characterized in that, The acquisition of the stress response signal measured in the large-amplitude oscillation shear test includes: A shear strain in the form of a sine wave is applied to the material, wherein the strain amplitude of the sine wave is greater than the upper limit of the strain in the linear viscoelastic region, and the angular frequency is a preset value. The shear stress component and normal stress component generated in the material during the application of the sinusoidal shear strain are obtained as the stress response signal.

5. The method according to claim 4, characterized in that, The harmonic analysis of the stress response signal to obtain higher-order harmonic coefficients characterizing the nonlinear behavior of the material includes: The shear stress component and the normal stress component are respectively decomposed into multiple harmonic components with the input strain frequency as the fundamental frequency; The odd-frequency harmonic components are extracted from the shear stress components, and the even-frequency harmonic components are extracted from the normal stress components. The amplitude of each harmonic component or the normalized intensity relative to the fundamental harmonic is calculated respectively. The higher-order harmonic coefficients are obtained based on the amplitude or normalized intensity.

6. The method according to claim 1, characterized in that, The iterative optimization of parameters other than the nonlinear parameters in the viscoelastic constitutive model by minimizing the deviation between the theoretical stress response and the stress response signal includes: A numerical optimization algorithm is used to construct an objective function to characterize the error between the stress response signal and the theoretical stress response; wherein the numerical optimization algorithm includes least squares method, genetic algorithm or particle swarm optimization. Based on the objective function, the parameters other than the nonlinear parameter in the viscoelastic constitutive model are iteratively updated until the objective function reaches the preset convergence condition, thereby determining the parameters other than the nonlinear parameter in the viscoelastic constitutive model.

7. A device for constructing a viscoelastic material model, characterized in that, The device includes: The first acquisition module is used to acquire the actual relationship between the storage modulus and the loss modulus of the material in the linear viscoelastic region and the actual relationship between the loss modulus and the angular frequency. The first processing module is used to determine the shear viscosity and characteristic relaxation time of the material based on the actual relationship between the energy storage modulus and the angular frequency and the actual relationship between the loss modulus and the angular frequency; The second acquisition module is used to acquire the stress response signal measured in the large-amplitude oscillation shear test, which is carried out under the conditions that the strain amplitude exceeds the upper limit of the linear viscoelastic region of the material and the set angular frequency and strain amplitude. The second processing module is used to perform harmonic analysis on the stress response signal to obtain high-order harmonic coefficients characterizing the nonlinear behavior of the material. The third processing module is used to determine the nonlinear parameters of the viscoelastic constitutive model based on the higher-order harmonic coefficients, and to determine the theoretical stress response of the viscoelastic constitutive model. The fourth processing module is used to take the nonlinear parameter, the shear viscosity of the material, and the characteristic relaxation time as the initial parameter set, and to iteratively optimize the other parameters in the viscoelastic constitutive model except for the nonlinear parameter by minimizing the deviation between the theoretical stress response and the stress response signal, until the preset convergence condition is met, so as to obtain the viscoelastic material model.

8. An electronic device, characterized in that, include: A memory and a processor are interconnected, the memory storing computer instructions, and the processor executing the computer instructions to perform the method for constructing a viscoelastic material model according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a computer to execute the method for constructing a viscoelastic material model according to any one of claims 1 to 6.

10. A computer program product, characterized in that, Includes computer instructions for causing a computer to execute the method for constructing a viscoelastic material model according to any one of claims 1 to 6.

Images