A method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency

Abstract

The application discloses a kind of viscoelastic material mechanics response prediction method based on thermodynamic consistency, comprising: obtaining the strain and stress path of viscoelastic material and carrying out noise reduction processing, to obtain stress strain path database;Utilize thermodynamic consistency, establish the potential function of multiple internal variables to represent the constitutive relation of viscoelastic material;Build neural network model for representing the potential function of constitutive relation, denoted as constitutive model;Long short-term memory network is constructed to generate multiple internal variable paths, to assist in training constitutive model;Constitutive model is initially trained, after completion, internal variable is classified and screened, internal variable quantity is updated, and combined with transfer learning, second training is repeatedly carried out, to obtain final constitutive model;The strain data of material are input into final constitutive model, to predict stress and internal variable.The application improves the capture ability of viscoelastic material mechanics response, and improves the prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of data-driven computational mechanics, and in particular to a method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency. Background Technology

[0002] Viscoelastic materials have wide applications in engineering structures, aerospace, transportation, and biomedicine. The mechanical response of these materials depends not only on the current strain state but is also significantly influenced by historical strain processes. Therefore, establishing constitutive models that accurately characterize the history dependence and nonlinear mechanical behavior of viscoelastic materials is of great significance for structural design and service performance prediction.

[0003] Traditional viscoelastic modeling methods, such as the generalized Maxwell model and the Prony series, can characterize the time-varying response of materials to some extent. However, their predictive ability is limited under complex loads, nonlinear behavior, and multiple time scales, and the parameter calibration process is inefficient and has limited applicability.

[0004] In recent years, the development of artificial intelligence has driven the application of data-driven methods in materials modeling. Neural networks can achieve high-precision predictions by learning strain-stress mapping relationships. Among them, recurrent neural networks and temporal convolutional networks have been used to capture the historical dependence of viscoelastic and elastoplastic materials, and convolutional neural networks have also shown potential in materials modeling driven by microscopic images and high-dimensional data. However, existing methods often treat material behavior as a black box mapping, lacking physical consistency constraints, which can easily produce results that violate physical laws in numerical simulations, affecting the interpretability and engineering generalization of the models.

[0005] To overcome the aforementioned shortcomings, existing technologies have proposed neural network constitutive models based on thermodynamic consistency. The core idea is to use neural networks to approximate the free energy and dissipated energy of materials, and to automatically differentiate and calculate stress and internal variable evolution, thereby ensuring thermodynamic consistency. While existing technologies have proposed viscoelastic constitutive models based on internal variables, they typically use a single internal variable or determine the number of internal variables through enumeration, resulting in low computational accuracy, high computational cost, low training efficiency, and difficulty in balancing model accuracy and convergence performance. Therefore, there is still an urgent need for a modeling method that can effectively improve computational accuracy and training efficiency while reasonably determining the number of internal variables, under the premise of ensuring thermodynamic consistency, to more accurately and efficiently characterize the mechanical response of viscoelastic materials. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency.

[0007] The specific technical solution is as follows:

[0008] A method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency includes the following steps:

[0009] S1: Obtain the strain and stress paths of the viscoelastic material and perform noise reduction processing to obtain a stress-strain path database;

[0010] S2: Utilizing thermodynamic consistency, a potential function with multiple internal variables is established to represent the constitutive relation of viscoelastic materials. The constitutive relation includes the strain-stress relationship equation and the internal variable evolution equation. The potential function includes: equilibrium free energy, non-equilibrium free energy, and dual dissipative potential.

[0011] S3: Construct a neural network model for the potential function to represent the constitutive relation, denoted as the constitutive model; the equilibrium free energy is represented by a fully convex neural network, and the non-equilibrium free energy and dual dissipative potential are represented by two fully convex shared neural networks respectively;

[0012] S4: Construct a long short-term memory network to generate multiple internal variable paths to assist in training the constitutive model;

[0013] S5: Perform initial training on the constitutive model. After completion, classify and filter the internal variables based on mechanical guidance, update the number of internal variables, and repeat the second training in combination with transfer learning to obtain the final constitutive model.

[0014] S6: Input the material strain data into the final constitutive model to predict stress and internal variables.

[0015] Furthermore, in S2, the strain-stress relationship equation defines stress as the partial derivative of free energy with respect to strain, where free energy depends on strain and is coupled with all internal variables;

[0016] The evolution equation of the internal variables defines the rate of change of the internal variables as the partial derivative of the dual dissipative potential with respect to the driving force, wherein the dual dissipative potential depends on the driving force, and the driving force is the negative of the partial derivative of the free energy with respect to the internal variables.

[0017] The free energy is decomposed into equilibrium free energy and non-equilibrium free energy; each internal variable corresponds to a non-equilibrium free energy, and the non-equilibrium free energy is then introduced into the strain-stress relationship equation and the internal variable evolution equation.

[0018] Furthermore, in S3, the input of the fully convex neural network is the strain in the stress-strain path database, and the output is the equilibrium free energy.

[0019] Depending on the different potential functions represented, the two fully convex shared neural networks are respectively denoted as the non-equilibrium free energy fully convex shared neural network and the dual dissipative potential fully convex shared neural network.

[0020] The fully convex shared neural network includes a shared pre-layer and a branch post-layer. The shared pre-layer is used to extract the common features of the non-equilibrium free energy and the dual dissipative potential, while the branch post-layer assigns independent response capabilities to each internal variable branch.

[0021] During the training phase, the input to the non-equilibrium free energy fully convex shared neural network is the strain in the stress-strain path database and the internal variables generated by the long short-term memory neural network. The network outputs the non-equilibrium free energy based on the difference between the strain and the internal variables. During the prediction phase, the input to the non-equilibrium free energy fully convex shared neural network is the strain of the stress response to be predicted and the internal variables obtained by the Euler method based on the rate of change of the internal variables. The network outputs the non-equilibrium free energy based on the difference between the strain and the internal variables. The rate of change of the internal variables is obtained according to the internal variable evolution equation in S2.

[0022] The input to the dual dissipative potential fully convex shared neural network is the driving force calculated based on the non-equilibrium free energy, and the output is the dual dissipative potential.

[0023] Furthermore, the inputs to the Long Short-Term Memory Network are strain paths, stress paths, and time, and the outputs are paths of multiple internal variables.

[0024] Furthermore, in step S5, the constitutive model is trained initially and then a second time, with the goal of minimizing the loss function, in conjunction with a long short-term memory network; the loss function is constructed as follows:

[0025] Substituting the equilibrium free energy and non-equilibrium free energy obtained through the constitutive model into the strain-stress relationship equation, the stress predicted by the constitutive model is obtained. The mean square error between the stress in the stress-strain path database and the stress predicted by the constitutive model is used as the first part of the loss function.

[0026] Substituting the dual dissipative potential obtained through the constitutive model into the internal variable evolution equation, we obtain the rate of change of the internal variables generated by the constitutive model; the rate of change of the internal variables generated by the long short-term memory network is obtained through the Euler method, and the mean square error of the two rates of change of the internal variables is used as the second part of the loss function.

[0027] Furthermore, in S5, both the initial training and the second training use the Adam optimizer, with a learning rate of 0.001 for the initial training and a learning rate of 0.0005 for the second training.

[0028] Furthermore, in step S5, the classification and screening of internal variables based on mechanical guidance specifically includes the following sub-steps:

[0029] (1) Using a preset constant strain sequence, predict the stress relaxation behavior of the material and calculate the relaxation time corresponding to each internal variable; the relaxation time is the ratio of stress to stress change rate corresponding to a certain internal variable;

[0030] The stress corresponding to the internal variable is predicted by the constitutive model, and the corresponding stress change rate is obtained by the Euler method.

[0031] (2) After taking the logarithm of the relaxation time corresponding to each internal variable, group them according to the order of magnitude interval, which is defined as [10 N 10 N+1 ), where N is an integer; if the relaxation time is not within any order of magnitude range, the internal variable corresponding to that relaxation time is discarded;

[0032] (3) Retain an internal variable corresponding to a relaxation time within each order of magnitude interval to obtain a definite relaxation time and its corresponding internal variable;

[0033] The updated internal variables are retained as the model parameters corresponding to the initial training, and used as the initial values ​​for the second training.

[0034] Furthermore, S6 is specifically implemented through the following sub-steps:

[0035] S6.1: Input the initial strain and internal variables into the final constitutive model to calculate the initial stress and the rate of change of internal variables;

[0036] S6.2: Based on the Euler method, the internal variables are updated to the next time step using the current rate of change of the internal variables, and the new stress and rate of change of the internal variables are calculated based on the internal variables and strain data at the next time step.

[0037] S6.3: Repeat S6.2 until the entire time series forecast is completed.

[0038] A device for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency includes a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency.

[0039] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the aforementioned method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency.

[0040] The beneficial effects of this invention are:

[0041] (1) The present invention significantly improves the ability to capture the mechanical response of viscoelastic materials by using a multi-internal variable modeling method based on thermodynamic consistency compared with traditional data-driven methods.

[0042] (2) This invention proposes a fully convex shared neural network to represent non-equilibrium free energy and its dual dissipative potential, which accelerates the training speed and ensures model convergence.

[0043] (3) To address the high computational cost of determining the number of internal variables using traditional enumeration methods, this invention proposes a mechanically guided method for determining the number of internal variables. This method effectively reduces computational overhead by relying on the principle of uniform distribution of relaxation time on a logarithmic scale. Furthermore, this invention uses this method to select the optimal internal variables and performs secondary training through transfer learning to obtain an optimized multi-internal-variable viscoelastic constitutive model.

[0044] (4) This invention integrates mechanical knowledge with deep learning to achieve efficient establishment of constitutive relations of viscoelastic materials and accurate prediction of mechanical response, which has significant practical value and application prospects. Attached Figure Description

[0045] Figure 1 This is a flowchart of a method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, as described in an embodiment of the present invention.

[0046] Figure 2 The diagram shows the stress-strain path data of asphalt mixture under different loading frequencies and loading amplitudes in the embodiments of the present invention. (a) is a strain path diagram at 0.25 Hz, (b) is a strain path diagram at 0.33 Hz, (c) is a strain path diagram at 0.5 Hz, (d) is a stress path diagram at 0.25 Hz, (e) is a stress path diagram at 0.33 Hz, and (f) is a stress path diagram at 0.5 Hz.

[0047] Figure 3 This is a schematic diagram of a fully convex neural network in an embodiment of the present invention.

[0048] Figure 4 This is a schematic diagram of a fully convex shared neural network in an embodiment of the present invention.

[0049] Figure 5 This is a schematic diagram illustrating the generation of internal variables and the rate of change of internal variables by the LSTM neural network in an embodiment of the present invention.

[0050] Figure 6 This is a flowchart of the method for determining the number of internal variables in an embodiment of the present invention.

[0051] Figure 7 This is a schematic diagram of the 1Hz strain path data selected for prediction in an embodiment of the present invention.

[0052] Figure 8 This is a comparison chart of the predicted stress and the experimentally measured stress in an embodiment of the present invention.

[0053] Figure 9 This is a sequence of simulated strain data generated for prediction in an embodiment of the present invention.

[0054] Figure 10 For a single internal variable model based on Figure 9 A comparison chart of the stress predicted by strain data and the actual stress.

[0055] Figure 11 According to the embodiments of the present invention Figure 9 A comparison chart of the stress predicted by strain data and the actual stress.

[0056] Figure 12 This is a schematic diagram of a viscoelastic material mechanical response prediction device based on thermodynamic consistency in an embodiment of the present invention. Detailed Implementation

[0057] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0058] like Figure 1 As shown, a method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency includes the following steps:

[0059] S1: Obtain the strain and stress paths of viscoelastic materials, perform noise reduction on the data, and construct a stress-strain path database for the materials.

[0060] As an embodiment of the present invention, asphalt mixture is used as the research object to obtain its stress-strain path database. The present invention is not limited to the materials listed in this embodiment; any material with the same or similar viscoelastic properties can be used. S1 is specifically implemented through the following sub-steps:

[0061] S1.1: Continuously graded SUP-20 asphalt mixture, specifically, asphalt mixture prepared using 20% ​​SBS modified asphalt, limestone coarse and fine aggregates, and mineral powder, according to the Superpave design method.

[0062] S1.2: Prepare asphalt mixture specimens. Specifically, use a Superpave rotary compactor to compact the asphalt mixture and core samples to obtain asphalt mixture specimens with a diameter of 100 mm and a height of 150 mm.

[0063] S1.3: In this embodiment, the strain and stress path of the material are obtained through tensile and compression tests. Specifically, high-strength structural adhesive is used to bond the upper and lower end faces of the asphalt mixture specimen to metal clamps, and high-precision LVDT sensors with a range of 2mm and a maximum accuracy of 0.0001mm are installed around the asphalt mixture specimen. The displacement and stress of the asphalt mixture specimen are collected in real time, and the strain of the material is calculated based on the displacement to obtain the strain and stress path of the asphalt mixture.

[0064] S1.4: In this embodiment, a Savitzky-Golay filter is used to denoise the data. Specifically, the filter window length is set to 21 and the order of the fitted polynomial is 3. The total variation of the filtered data is reduced by no less than 50% compared to the original data. After denoising, a stress-strain path database of asphalt mixture is obtained. The stress-strain path data under different loading frequencies and loading amplitudes are as follows: Figure 2 As shown.

[0065] S2: Utilizing thermodynamic consistency, a potential function with multiple internal variables is established to represent the constitutive relation of viscoelastic materials. This potential function includes free energy and dual dissipative potential. Internal variables (such as plastic strain, damage variable, phase transition fraction, back stress, viscous strain, etc.) are used to characterize the evolution of the material's internal state, such as irreversible deformation, microstructural changes, or dissipative processes. They are key parameters describing the behavior of inelastic, nonlinear, and time-dependent materials. In this invention, the internal variable represents viscous strain.

[0066] In one embodiment of the present invention, S2 is specifically implemented through the following sub-steps:

[0067] S2.1: The constitutive relation for multiple internal variables consists of the strain-stress relationship equation and the internal variable evolution equation, and the specific expression is as follows:

[0068]

[0069]

[0070] In the formula, σ represents stress, Ψ represents free energy, ε represents strain, and α represents... k Represents the k-th internal variable. K represents the rate of change of the internal variables; K represents the total number of internal variables. Let F represent the k-th dual dissipative potential. k This represents the k-th internal driving force.

[0071] S2.2: Decompose free energy into equilibrium free energy and non-equilibrium free energy, the specific expression is as follows:

[0072]

[0073] In the formula, Represents equilibrium free energy. This represents non-equilibrium free energy.

[0074] S2.3: k internal variables correspond to k non-equilibrium free energies, and the input of the non-equilibrium free energies can be expressed as... The specific expression for stress is:

[0075]

[0076] In the formula, Let represent the k-th non-equilibrium free energy.

[0077] The specific expression for internal driving force is:

[0078]

[0079] S3: Construct a neural network model for the potential function representing the constitutive relation in S2, denoted as the constitutive model.

[0080] In one embodiment of the present invention, S3 is specifically implemented through the following sub-steps:

[0081] S3.1: Based on deep learning technology, construct a fully convex neural network (FC-NN) model to represent equilibrium free energy (e.g., ...). Figure 3 As shown), the specific expression is:

[0082]

[0083]

[0084] In the formula, x is the input of the neural network; These are the weights of the input layer of the FC-NN. It is the FC-NN number The output of the hidden layer, It is the FC-NN number Hidden layer and the first The weights between hidden layers, where the weight values ​​are non-negative. It is the input layer of the FC-NN and the first The weights of the hidden layers, It is the bias of the neural network, L FC-NN This represents the total number of hidden layers. It is an activation function. .

[0085] S3.2: Based on deep learning technology, construct a fully convex share neural network (FC-SNN) for representing non-equilibrium free energy, and a dual dissipative potential FC-SNN for representing dual dissipative potential; such as Figure 4 As shown, both fully convex shared neural networks include a shared pre-layer and a branch post-layer. The shared pre-layer is used to extract the common features among k non-equilibrium free energies and the common features among k dual dissipative potentials. The branch post-layer assigns independent response capabilities to each internal variable branch. The specific expression of FC-SNN is:

[0086]

[0087]

[0088]

[0089] In the formula, x n It is the nth input to the neural network, and each input corresponds to a branch; These are the weights of the input layer of the FC-SNN. It is the FC-SNN number The output of the hidden layer; It is the FC-SNN number Hidden layer and the first The weights between hidden layers, where the weight values ​​are non-negative. It is the input layer of FC-SNN and the first The weights of the hidden layers; These are the weights from the hidden layer to the output layer of an FC-SNN. These are the weights from the input layer to the output layer of the FC-SNN. Furthermore, both of these weights are specific to the nth branch. It is not negative; It is the exclusive bias for the nth branch, L FC-NN This represents the total number of hidden layers.

[0090] S3.3: A fully convex neural network used to represent the equilibrium free energy. During the training phase, the input is the strain from the stress-strain path database, and the output is the equilibrium free energy. The specific expression is as follows:

[0091]

[0092] In the formula, Ψ FC-NN Represents a fully convex neural network. This represents the parameters of a fully convex neural network.

[0093] In this embodiment, the network parameters of FC-NN are: 1 input layer, 4 hidden layers, 64 neurons in each hidden layer, and 1 output layer.

[0094] S3.4: The input to the non-equilibrium free energy FC-SNN during the training phase is the strain ε in the stress-strain path database and the predicted internal variables (i.e., the internal variables generated by the LSTM prediction in S4.1). The non-equilibrium free energy FC-SNN is based on the difference between the two. The output is the non-equilibrium free energy; the input in the prediction stage is the strain ε of the stress response to be predicted and the rate of change of the internal variable α of S2.1 obtained by the Euler method. k The non-equilibrium free energy FC-SNN is based on the difference between the two. This outputs the non-equilibrium free energy. The specific expression for the non-equilibrium free energy is:

[0095]

[0096] In the formula, This represents the non-equilibrium free energy FC-SNN. The parameters represent the non-equilibrium free energy of the FC-SNN.

[0097] In this embodiment, the network parameters of the non-equilibrium free energy FC-SNN are as follows: 1 input layer, 4 hidden layers, 64 neurons in each hidden layer, the weights and biases of the first three layers of the neural network are shared among the non-equilibrium free energies corresponding to each internal variable, and 8 output layers (i.e., the maximum number of internal variables is 8).

[0098] S3.5: The input to the dual dissipative potential FC-SNN is the driving force (calculated using the expression in S2.3 based on the results in S3.4), and the output is the dual dissipative potential, specifically expressed as follows:

[0099]

[0100] In the formula, This represents the dual dissipative potential FC-SNN. The parameter represents the dual dissipative potential of the FC-SNN.

[0101] In this embodiment, the network parameters of the dual dissipative potential FC-SNN are as follows: 3 input layers, 4 hidden layers, 64 neurons in each hidden layer, the weights and biases of the first three layers of the neural network are shared among the dual dissipative potentials corresponding to each internal variable, and 8 output layers (maximum number of internal variables).

[0102] S4: Construct a Long Short-Term Memory (LSTM) network to generate multiple internal variable paths to assist in training the two neural networks in S3. It should be noted that the LSTM is only used for the two training sessions and is not integrated into the constitutive model.

[0103] like Figure 5 As shown, the input to the LSTM network is the strain path, stress path, and time, and the output is the paths of multiple internal variables. The specific expression is as follows:

[0104]

[0105] In the formula, N represents the intrinsic variables generated by the LSTM network. lstm This indicates an LSTM network.

[0106] Figure 5 middle, This represents the strain at time i. This represents the stress at time i. This represents the time at time i. Denotes the internal variable at time i. This represents the rate of change of the internal variable at time i.

[0107] In this embodiment, the parameters of the LSTM network are: 3 input layers, 4 hidden layers, 64 neurons in each hidden layer, and 8 output layers (number of internal variables).

[0108] S5: Establish a method for determining the number of internal variables. After the initial training, select and determine the number of internal variables, and combine transfer learning for secondary training to obtain the final constitutive model.

[0109] like Figure 6 As shown, in one embodiment of the present invention, S5 is specifically implemented through the following sub-steps:

[0110] S5.1: Using an LSTM network, the constitutive model is initially trained with the goal of minimizing the loss function. The loss function is constructed as follows:

[0111] Substituting the equilibrium free energy (S3.3) and non-equilibrium free energy (S3.4) obtained through the constitutive model into the strain-stress relationship equation (S2.3), the stress predicted by the constitutive model is obtained. The mean square error between the stress in the stress-strain path database and the stress predicted by the constitutive model is used as the first part of the loss function.

[0112] Substituting the dual dissipative potential (S3.5) obtained through the constitutive model into the internal variable evolution equation (S2.1), we obtain the rate of change of the internal variables generated by the constitutive model; the rate of change of the internal variables generated by the LSTM network (S4.1) is obtained by the Euler method, and the mean square error of the rate of change of the internal variables generated by the two different networks is used as the second part of the loss function.

[0113] The expression for the loss function is obtained as follows:

[0114]

[0115] In the formula, This represents the p-th predicted stress path. This represents the p-th actual stress path, where P is the total number of stress paths, and J... p This represents the number of sampling points on the P-th path.

[0116] In this embodiment, the Adam optimizer is used for the initial training with a learning rate of 0.001.

[0117] S5.2: Establish a method for determining the number of internal variables. Screening existing internal variables helps reduce computational overhead and improve model response speed. This method specifically includes the following sub-steps:

[0118] (5.2.1) After model training, a preset constant strain sequence is used to predict the stress relaxation behavior of the material, and the relaxation time corresponding to each internal variable is calculated. For the stress corresponding to each internal variable predicted by the constitutive model, the stress change rate corresponding to each internal variable is obtained by the Euler method. The expression for calculating the relaxation time is as follows:

[0119]

[0120]

[0121] In the formula, τ k σ represents the relaxation time corresponding to the k-th internal variable. k This represents the stress corresponding to the k-th internal variable. This represents the rate of change of stress corresponding to the k-th internal variable.

[0122] In this embodiment, the relaxation time for each internal variable is shown in Table 1.

[0123] Table 1

[0124]

[0125] (5.2.2) After taking the logarithm of the relaxation time corresponding to each internal variable, group the data by order of magnitude interval, which is defined as

[10] . N 10N+1 ), where N is an integer; if the relaxation time is not within any order of magnitude range, the internal variable corresponding to that relaxation time is discarded.

[0126] In this embodiment, τ1 and τ3 belong to the order of magnitude [1, 10), τ2 and τ4 belong to the order of magnitude [10, 100), τ7 belongs to the order of magnitude [0.1, 1), and τ5, τ6 and τ8 do not belong to any interval, and their corresponding internal variables are directly discarded.

[0127] (5.2.3) Within each order-of-magnitude interval, a representative relaxation time corresponding to the intrinsic variable is retained to obtain a determined relaxation time and its corresponding intrinsic variable; further, the representative relaxation time is randomly selected. The updated intrinsic variables are retained as the model parameters corresponding to the initial training, and used as the initial values ​​for the second training. In this embodiment, the intrinsic variables determined after filtering each order-of-magnitude interval are (α1, α2, α7).

[0128] S5.3: Combining transfer learning, the constitutive model is trained a second time (i.e., repeating S5.1) using the internal variables determined in S5.2 corresponding to the model parameters in the initial training as initial values, and finally the trained constitutive model is obtained. In this embodiment, the Adam optimizer is used for the second training with a learning rate of 0.0005.

[0129] S6: Input the material strain data into the trained constitutive model to predict stress and internal variables. S6 is implemented through the following sub-steps:

[0130] S6.1: Input the initial strain and internal variables into the trained constitutive model to calculate the initial stress and the rate of change of internal variables.

[0131] S6.2: Based on the Euler method, the internal variables are updated to the next time step using the rate of change of the internal variables, and the new stress and rate of change of the internal variables are calculated based on the strain data of the internal variables and the next time step.

[0132] S6.3: Repeat S6.2 until the entire time series forecast is completed.

[0133] Using the method of the present invention, for example Figure 7 The prediction results obtained by using the 1Hz strain path data shown are as follows (i.e. Figure 8 The “prediction” in the text and the actual experimental results (i.e. Figure 8 The “experiment” in the text refers to, for example, Figure 8 As shown.

[0134] To verify the advantages of the method of this invention over traditional single internal variable methods for stress prediction, the following was generated: Figure 9The simulated strain data sequence shown illustrates the comparison between the stress prediction results obtained using the traditional single internal variable method and the actual stress data. Figure 10 As shown in the figure, the deviation between the predicted stress and the actual stress is relatively large; a comparison between the stress prediction results using the method of this invention and the actual stress data is shown in the figure. Figure 11 As shown in the figure, the stress prediction accuracy of the method of the present invention is significantly improved compared with the single internal variable method.

[0135] Compared with traditional model building methods, this invention significantly reduces the need for experimental data. Comparison with single-internal-variable models shows that this invention is more accurate in characterizing the viscoelastic behavior of materials, with significantly improved prediction precision, fully demonstrating its advanced nature in viscoelastic mechanical response modeling. The trained constitutive model can be incorporated into finite element software for high-precision structural mechanical response analysis.

[0136] Based on the above-mentioned method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, the present invention also provides a device for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency.

[0137] like Figure 12 As shown in the figure, an embodiment of the present invention provides a device for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency in the above embodiment.

[0138] This invention provides a thermodynamically consistent viscoelastic material mechanical response prediction device that can be applied to any device with data processing capabilities, such as a computer. The thermodynamically consistent viscoelastic material mechanical response prediction device can be implemented through software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 12 The diagram shown is a hardware structure diagram of any data processing-capable device, including the thermodynamically consistent viscoelastic material mechanical response prediction device of the present invention. (Except for...) Figure 12 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in which the device of the present invention is located in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0139] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0140] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0141] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements the method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency as described in the above embodiments.

[0142] The computer-readable storage medium can be an internal storage unit of any data-processing device in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data-processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., mounted on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data-processing device and external storage devices. The computer-readable storage medium is used to store computer programs and other programs and data required by any data-processing device, and can also be used to temporarily store data that has been output or will be output.

[0143] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, characterized in that, Includes the following steps: S1: Obtain the strain and stress paths of the viscoelastic material and perform noise reduction processing to obtain a stress-strain path database; S2: Utilizing thermodynamic consistency, a potential function with multiple internal variables is established to represent the constitutive relation of viscoelastic materials. The constitutive relation includes the strain-stress relationship equation and the internal variable evolution equation. The potential function includes: equilibrium free energy, non-equilibrium free energy, and dual dissipative potential. S3: Construct a neural network model for the potential function to represent the constitutive relation, denoted as the constitutive model; the equilibrium free energy is represented by a fully convex neural network, and the non-equilibrium free energy and dual dissipative potential are represented by two fully convex shared neural networks respectively; S4: Construct a long short-term memory network to generate multiple internal variable paths to assist in training the constitutive model; S5: Perform initial training on the constitutive model. After completion, classify and filter the internal variables based on mechanical guidance, update the number of internal variables, and repeat the second training in combination with transfer learning to obtain the final constitutive model. S6: Input the strain data of the material into the final constitutive model to predict stress and internal variables; In S2, the strain-stress relationship equation defines stress as the partial derivative of free energy with respect to strain. This free energy depends on strain and is coupled with all internal variables. The evolution equation of the internal variables defines the rate of change of the internal variables as the partial derivative of the dual dissipative potential with respect to the driving force, wherein the dual dissipative potential depends on the driving force, and the driving force is the negative of the partial derivative of the free energy with respect to the internal variables. The free energy is decomposed into equilibrium free energy and non-equilibrium free energy; each internal variable corresponds to a non-equilibrium free energy, and the non-equilibrium free energy is then introduced into the strain-stress relationship equation and the internal variable evolution equation. In S3, the input of the fully convex neural network is the strain in the stress-strain path database, and the output is the equilibrium free energy. Depending on the different potential functions represented, the two fully convex shared neural networks are respectively denoted as the non-equilibrium free energy fully convex shared neural network and the dual dissipative potential fully convex shared neural network. The fully convex shared neural network includes a shared pre-layer and a branch post-layer. The shared pre-layer is used to extract the common features of the non-equilibrium free energy and the dual dissipative potential, while the branch post-layer assigns independent response capabilities to each internal variable branch. During the training phase, the input to the non-equilibrium free energy fully convex shared neural network is the strain in the stress-strain path database and the internal variables generated by the long short-term memory neural network. The network outputs the non-equilibrium free energy based on the difference between the strain and the internal variables. During the prediction phase, the input to the non-equilibrium free energy fully convex shared neural network is the strain of the stress response to be predicted and the internal variables obtained by the Euler method based on the rate of change of the internal variables. The network outputs the non-equilibrium free energy based on the difference between the strain and the internal variables. The rate of change of the internal variables is obtained according to the internal variable evolution equation in S2. The input to the dual dissipative potential fully convex shared neural network is the driving force calculated based on the non-equilibrium free energy, and the output is the dual dissipative potential.

2. The method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency according to claim 1, characterized in that, The inputs to the Long Short-Term Memory Network are strain path, stress path, and time, and the outputs are paths of multiple internal variables.

3. The method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency according to claim 1, characterized in that, In step S5, the constitutive model is trained initially and then a second time, with the goal of minimizing the loss function, in conjunction with a long short-term memory network. The loss function is constructed as follows: Substituting the equilibrium free energy and non-equilibrium free energy obtained through the constitutive model into the strain-stress relationship equation, the stress predicted by the constitutive model is obtained. The mean square error between the stress in the stress-strain path database and the stress predicted by the constitutive model is used as the first part of the loss function. Substituting the dual dissipative potential obtained through the constitutive model into the internal variable evolution equation, we obtain the rate of change of the internal variables generated by the constitutive model; the rate of change of the internal variables generated by the long short-term memory network is obtained through the Euler method, and the mean square error of the two rates of change of the internal variables is used as the second part of the loss function.

4. The method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency according to claim 1, characterized in that, In S5, the Adam optimizer is used for both the initial training and the second training. The learning rate for the initial training is 0.001, and the learning rate for the second training is 0.0005.

5. The method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency according to claim 1, characterized in that, In step S5, the classification and screening of internal variables based on mechanical guidance specifically includes the following sub-steps: (1) Using a preset constant strain sequence, predict the stress relaxation behavior of the material and calculate the relaxation time corresponding to each internal variable; the relaxation time is the ratio of stress to stress change rate corresponding to a certain internal variable; The stress corresponding to the internal variable is predicted by the constitutive model, and the corresponding stress change rate is obtained by the Euler method. (2) After taking the logarithm of the relaxation time corresponding to each internal variable, group them according to the order of magnitude interval, which is defined as [10]. N 10 N+1 ), where N is an integer; If the relaxation time is not within any order of magnitude range, then the internal variable corresponding to that relaxation time is discarded. (3) Retain an internal variable corresponding to a relaxation time within each order of magnitude interval to obtain a definite relaxation time and its corresponding internal variable; The updated internal variables are retained as the model parameters corresponding to the initial training, and used as the initial values ​​for the second training.

6. The method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency according to claim 1, characterized in that, S6 is specifically implemented through the following sub-steps: S6.1: Input the initial strain and internal variables into the final constitutive model to calculate the initial stress and the rate of change of internal variables; S6.2: Based on the Euler method, the internal variables are updated to the next time step using the current rate of change of the internal variables, and the new stress and rate of change of the internal variables are calculated based on the internal variables and strain data at the next time step. S6.3: Repeat S6.2 until the entire time series forecast is completed.

7. A device for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, characterized in that, The device includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, It stores a program that, when executed by a processor, implements the method for predicting the mechanical response of viscoelastic materials based on thermodynamic consistency, as described in any one of claims 1-6.

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