A discrete dislocation dynamics accelerated simulation method based on reservoir computing

Abstract

The application relates to a discrete dislocation dynamics acceleration simulation method based on reservoir computing, which effectively reduces the high computing cost caused by the global time step limit and the long-range interaction of dislocation elastic force in traditional dislocation dynamics simulation by replacing the node motion speed calculation in discrete dislocation dynamics with a trained reservoir computing model. The virtual node mechanism is innovatively proposed to solve the dimension mismatch problem caused by the dynamic change of the number of nodes in the dislocation topology evolution process, and adaptive discretization prediction is realized. The prediction error accumulation is prevented by regularly inserting the real traditional dislocation dynamics simulation calculation result in the prediction sequence, and the stability of long-term simulation is ensured. The acceleration scheme significantly reduces the computing time complexity from exponential to linear while maintaining the physical accuracy, providing a feasible technical path for efficient simulation of large-scale three-dimensional complex dislocation network evolution.

Description

Technical Field

[0001] This application relates to the field of accelerated simulation technology of discrete dislocation dynamics, and in particular to an accelerated simulation method of discrete dislocation dynamics based on reservoir calculation. Background Technology

[0002] Discrete dislocation dynamics (DDM) is a key numerical simulation tool for studying the plastic deformation of crystalline materials at the mesoscale. It simulates the motion, interaction, and multiplication of dislocation lines under external forces and internal stresses by discretizing dislocation lines into nodes and segments, thus connecting the microscopic dislocation mechanism with macroscopic plastic behavior. However, DDM simulation is computationally extremely expensive. Its core computational complexity lies in calculating the elastic force of each dislocation segment, which requires calculating the long-range elastic interaction forces of all other dislocation segments on that segment. When the dislocation density in the system is high, the computational cost increases exponentially, becoming unbearable.

[0003] Furthermore, discrete dislocation dynamics simulation systems exhibit highly nonlinear and rigid characteristics due to the close-range interactions between dislocations. Traditional explicit time integrators employ a global time step, which is limited by the "most unstable" node in the system (i.e., the node requiring the smallest time step). As dislocation networks evolve and become more refined, integrators must use increasingly smaller time steps, further exacerbating the computational burden and limiting the physical timescales that can be simulated.

[0004] In recent years, although algorithms such as the injection fast multilevel submethod, finite element method, and fast Fourier transform method have been proposed to accelerate stress field calculations and improve efficiency through parallel computing, these methods still face challenges in handling the highly nonlinear behavior of systems caused by dislocation topological evolution (such as node merging and splitting). Furthermore, some studies have attempted to use data-driven methods such as graph neural networks to accelerate the prediction of dislocation node velocities, but these methods struggle to maintain consistency in the input-output dimensions when faced with dynamically changing node numbers, limiting their robustness in practical simulations.

[0005] Therefore, there is an urgent need in this field for an accelerated method for discrete dislocation dynamics simulation that can significantly reduce computational complexity and robustly handle the topological evolution of dislocation networks. Summary of the Invention

[0006] Therefore, it is necessary to provide an accelerated simulation method for discrete dislocation dynamics based on reservoir calculations, including:

[0007] S1: Initialize a precipitate phase in a cubic simulation box and set the material parameters, loading conditions and time step Δt;

[0008] S2: Perform a traditional discrete dislocation dynamics simulation based on the precipitated phase for M time steps, and record the time step data, which includes the nodal velocity of each node in each time step;

[0009] S3: Training the reserve pool calculation model based on the node velocity of each node in each time step;

[0010] S4: Sample the node velocity of m consecutive time steps from the time step data and input it into the trained reservoir calculation model to predict the node velocity of the M+Δt time step;

[0011] S5: Update the node position of the corresponding node based on the predicted node speed, and check whether the updated node has merged or split. If so, generate a virtual node; otherwise, do nothing.

[0012] S6: For any node, in every m consecutive time steps, perform a node velocity calculation based on traditional discrete dislocation dynamics simulation to obtain the accurate node velocity for the corresponding time step; in the remaining time steps, the reservoir calculation model calculates the node velocity for the next time step based on the node velocities of the node and the virtual node.

[0013] S7: Repeat steps S5-S6 until the simulation of the interaction between dislocations and precipitation phases is completed.

[0014] Preferably, in S1, the material parameters include shear modulus, elastic modulus, and Poisson's ratio, and the loading condition includes constant strain rate.

[0015] Preferably, in S3, the calculation model for training the reserve pool based on the node velocity of each node in each time step includes:

[0016] The node velocities of each node in the M-Δt time step are used to form an input vector, and the node velocities of each node in the M-th time step are used to form an output vector.

[0017] The input vector is connected to the Reservoir via an Input or Reservoir coupler, and the input vector is connected to the Reservoir via an Output or Reservoir coupler.

[0018] Define the number of nodes in the reserve pool in the reserve pool calculation model, and connect the nodes in the reserve pool using a sparse matrix;

[0019] The state vector of the reservoir is updated based on the sparse matrix, the input vector, and the connection matrix connecting the input vector to the Reservoir. The update formula is expressed as follows:

[0020] ;

[0021] in, Indicates the first The state vector of the reservoir at each time step. Indicates the leakage rate. Represents the hyperbolic tangent function. Represents a sparse matrix. Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. Represents the input vector;

[0022] The output weight matrix is ​​calculated based on the input and output vectors using the following formula:

[0023] ;

[0024] in, This represents the output weight matrix. Indicates the output vector. Indicates transpose. Represents the regularization coefficient. Represents the identity matrix;

[0025] The trained reservoir computation model is used to map the node velocity at the next time step based on the reservoir's state vector and output weight matrix.

[0026] Preferably, in S4, predicting the node velocity at the M+Δt time step includes:

[0027] The node velocities of m consecutive time steps are sampled from the time step data to form a second input vector. The state vector of the reserve pool is updated based on the second input vector, and the update formula is:

[0028] ;

[0029] in, Indicates the first The state vector of the reservoir at each time step. Indicates the leakage rate. Represents the hyperbolic tangent function. Represents a sparse matrix. Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. This represents the second input vector;

[0030] Based on the The state vector of the reservoir at each time step and the output weight matrix are used to predict the node velocity at the (M+Δt)th time step, and the calculation formula is as follows:

[0031] ;

[0032] in, Indicates the first In the first time step The node speed of each node, This represents the output weight matrix.

[0033] Preferably, in S5, updating the node position of the corresponding node based on the predicted node speed includes:

[0034] The time step data also includes the position of each node in each time step;

[0035] The position of the corresponding node in the reserve pool at the Mth time step is updated based on the predicted node velocity at the M+Δt time step. The update formula is as follows:

[0036] ;

[0037] in, Indicates the first In the first time step The position of each node. Indicates the first In the first time step The position of each node. Indicates the first In the first time step The node speed of each node, Indicates the time step.

[0038] Preferably, in S5, the process of generating virtual nodes includes:

[0039] When nodes merge, the average of the centroid positions of the two merged nodes is used as the spatial position of the first virtual node; the average of the node velocities of the two merged nodes is used as the node velocity of the first virtual node.

[0040] When a node splits, find the two nodes adjacent to the split node, and take the average of the centroid positions of the split node and its two adjacent nodes as the spatial position of the second virtual node; take the average of the node velocities of the two adjacent nodes as the node velocity of the second virtual node.

[0041] The positions and velocities of the first and / or second virtual nodes are added to the reserve pool to align with the dimension of the node velocities of the nodes in the reserve pool of the previous time step.

[0042] Preferably, in S6, the nodal velocity calculation based on traditional discrete dislocation dynamics simulation includes:

[0043] The time step data also includes the node forces of each node in each time step, and the formula for calculating the node forces is:

[0044] ;

[0045] in, Indicates the first The node force of each node, Indicates the first The position of each node. Indicates the first The position of each node. Represents shape functions, Indicates the first The node and the first Any node on a dislocation segment formed by nodes This represents the total stress acting on the dislocation segment. Indicates dislocation segment The Burgers vector, Represents the L2 norm;

[0046] The nodal velocity of the corresponding node is calculated based on the nodal force, and the formula is as follows:

[0047] ;

[0048] in, Indicates the first The node velocity of each node, where t represents the time step. Represents the kinematic rule function. Represents the set of node positions.

[0049] Preferably, in S6, a nodal velocity calculation based on traditional discrete dislocation dynamics simulation is performed once every m consecutive time steps, including: performing a nodal velocity calculation based on traditional discrete dislocation dynamics simulation once in any one of the m consecutive time steps.

[0050] Preferably, in S7, in the simulation of the interaction between dislocations and precipitates, the plastic strain increment is output based on the area swept by the dislocation segments formed by the nodes, and the calculation formula is:

[0051] ;

[0052] in, Indicates the increment of plastic strain. Represents the simulated volume. Indicates dislocation segment The Burgers vector, Indicates dislocation segment time step The area swept inside, This indicates a cross product.

[0053] Preferably, the increment of applied stress is calculated based on the plastic strain increment and constant strain rate, using the following formula:

[0054] ;

[0055] in, Indicates the increment of applied stress. A fourth-order tensor representing the elastic modulus. Indicates constant strain rate. Indicates the time step. Indicates the increment of plastic strain;

[0056] The incremental stress is superimposed onto the total stress to drive the dislocation segment into the next time step. The stress and plastic strain at each time step during the simulation are recorded to obtain the stress-strain curve.

[0057] Beneficial effects: This method introduces the reservoir computation model into the simulation of discrete dislocation dynamics, achieving efficient prediction of node motion and significantly reducing computational complexity. At the same time, the introduction of the virtual node mechanism effectively solves the problem of dimensional inconsistency caused by topology evolution. This method has both high compatibility and scalability, providing a feasible technical path for the simulation of large-scale dislocation networks. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the discrete dislocation dynamics acceleration simulation method based on reservoir calculation in the embodiments of this application.

[0060] Figure 2 This is a comparison chart showing the evolution of DDD-RC prediction accuracy with the presence of obstacles in the embodiments of this application.

[0061] Figure 3 This is a graph showing the relationship between computation time and the number of nodes before and after DDD-RC acceleration in the embodiments of this application. Detailed Implementation

[0062] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0063] Furthermore, 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 at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0064] like Figure 1 As shown, this embodiment provides a method for accelerating the simulation of discrete dislocation dynamics based on reservoir calculations, including:

[0065] S1: Initialize a precipitate phase in a cubic simulation box and set the material parameters, loading conditions, and time step Δt (e.g., Δt=1).

[0066] In this embodiment, the material parameters include shear modulus, elastic modulus, and Poisson's ratio. The values ​​of each material parameter are determined according to the specific type of high-performance metal material. The loading condition includes a constant strain rate, which can be set according to actual needs.

[0067] S2: Perform a traditional discrete dislocation dynamics simulation based on the precipitated phase for M (e.g., M=10) time steps, and record the time step data, which includes the nodal velocity of each node in each time step.

[0068] S3: Training the reserve pool computation model based on the node velocity of each node in each time step.

[0069] Specifically, the training reserve pool calculation model based on the node velocity of each node in each time step includes:

[0070] The node velocities of each node in the M-Δt time step are used to form an input vector, and the node velocities of each node in the M-th time step are used to form an output vector.

[0071] The input vector is connected to the Reservoir via an Input or Reservoir coupler, and the input vector is connected to the Reservoir via an Output or Reservoir coupler.

[0072] Set the number of nodes in the reserve pool in the reserve pool calculation model (e.g., set it to 1000 nodes), and connect the nodes in the reserve pool using a sparse matrix;

[0073] The state vector of the reservoir is updated based on the sparse matrix, the input vector, and the connection matrix connecting the input vector to the Reservoir. The update formula is expressed as follows:

[0074] ;

[0075] in, Indicates the first The state vector of the reservoir at each time step. This represents the leakage rate, which determines how much of the direct mixture from the previous state is present in the next state. Represents the hyperbolic tangent function. This represents a sparse matrix whose largest eigenvalue represents the spectral radius, which is rescaled to equal... The largest eigenvalue, Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. Represents the input vector;

[0076] In reservoir computational models, ridge regression is typically used to train output weights. An objective function is constructed based on the input and output vectors, and minimizing this objective function yields the output weight matrix. The expression for the objective function is:

[0077] ;

[0078] in, Describe the objective function. Indicates the output vector. This represents the output weight matrix, whose elements are randomly extracted from a uniform distribution [-σ, σ]. This represents the regularization coefficient, which can control the complexity of the model and prevent overfitting. Represents the L2 norm;

[0079] The analytical solution to minimize the objective function is obtained by solving for the output weight matrix based on the input and output vectors. The calculation formula is as follows:

[0080] ;

[0081] in, This represents the output weight matrix. Indicates the output vector. Indicates transpose. Represents the regularization coefficient. Represents the identity matrix;

[0082] The trained reservoir computation model is used to map the node velocity at the next time step based on the reservoir's state vector and output weight matrix.

[0083] The trained reservoir computation model is introduced into the discrete dislocation dynamics simulation to construct the Discrete Dislocation Dynamics-Reservoir Neural Network Algorithm (DDD-RC) model framework.

[0084] S4: Sample the node velocities of m (e.g., m=5) consecutive time steps from the time step data and input them into the trained reservoir calculation model to predict the node velocity at the M+Δt (e.g., M+Δt=11)th time step.

[0085] Specifically, the prediction of the node velocity at the M+Δt time step includes:

[0086] The node velocities of m consecutive time steps are sampled from the time step data to form a second input vector. The state vector of the reserve pool is updated based on the second input vector, and the update formula is:

[0087] ;

[0088] in, Indicates the first The state vector of the reservoir at each time step. Indicates the leakage rate. Represents the hyperbolic tangent function. Represents a sparse matrix. Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. This represents the second input vector;

[0089] Based on the The state vector of the reservoir at each time step and the output weight matrix are used to predict the node velocity at the (M+Δt)th time step, and the calculation formula is as follows:

[0090] ;

[0091] in, Indicates the first In the first time step The node speed of each node. This represents the output weight matrix.

[0092] S5: Update the node position of the corresponding node based on the predicted node speed, and check whether the updated node has merged or split. If so, generate a virtual node; otherwise, do nothing.

[0093] Specifically, updating the node position based on the predicted node speed includes:

[0094] The time step data also includes the position of each node in each time step;

[0095] The position of the corresponding node in the reserve pool at the Mth time step is updated based on the predicted node velocity at the M+Δt time step. The update formula is as follows:

[0096] ;

[0097] in, Indicates the first In the first time step The position of each node. Indicates the first In the first time step The position of each node. Indicates the first In the first time step The node speed of each node. Indicates the time step.

[0098] In discrete dislocation dynamics simulations, the topological evolution of dislocations is often accompanied by changes in the number of nodes, enabling them to adapt to local curvature. Node evolution mainly includes node merging and splitting. Therefore, unifying the data from m time steps to the same dimension to accommodate the reservoir neural network algorithm remains a significant challenge. When using the reservoir neural network algorithm to predict node velocities, the dimension of the output matrix is ​​determined by the number of nodes at the current time step. However, the dislocation configurations built into discrete dislocation dynamics follow topological evolution laws, meaning there are differences in the number of nodes between time steps, resulting in different dimensions of the output matrix at each time step. This prevents the output matrix of the previous time step from being coupled into the reservoir neural network algorithm of the next time step.

[0099] To address this issue, the concept of virtual nodes was proposed. Virtual nodes possess two main attributes: position and velocity. Specifically, the generation process of a virtual node includes:

[0100] When nodes merge, the average of the centroid positions of the two merged nodes i and j is taken as the spatial position of the first virtual node p. The formula for calculating the spatial position of the first virtual node is:

[0101] ;

[0102] in, This represents the spatial location of the first virtual node p at the (n-1)th time step. This represents the centroid position of the i-th merged node at the (n-1)-th time step. This represents the centroid position of the j-th merged node at the (n-1)-th time step;

[0103] The average of the node velocities of the two merged nodes i and j is taken as the node velocity of the first virtual node p. The formula for calculating the node velocity of the first virtual node is:

[0104] ;

[0105] in, This represents the node velocity of the first virtual node p at the (n-1)th time step. This represents the node velocity of the i-th merged node at the (n-1)-th time step. This represents the node velocity of the j-th merged node at the (n-1)-th time step.

[0106] When a node splits, find the two nodes adjacent to the split node, and take the average of the centroid positions of the split node a and its two adjacent nodes b and c as the spatial positions of the second virtual nodes g and h. The formula for calculating the spatial position of the second virtual node is:

[0107] ;

[0108] ;

[0109] in, This represents the spatial position of the second virtual node g at the (n-1)th time step. This represents the spatial location of the second virtual node h at the (n-1)th time step. This represents the centroid position of the a-th split node at the (n-1)th time step. This represents the centroid position of node b, the neighboring node of split node a, at time step n-1. This indicates the position of the centroid of the neighboring node c of the split node a at the (n-1)th time step;

[0110] The average of the node velocities of two adjacent nodes b and c is taken as the node velocity of the second virtual nodes g and h. The formula for calculating the node velocity of the second virtual node is:

[0111] ;

[0112] ;

[0113] in, This represents the node velocity of the second virtual node g at the (n-1)th time step. This represents the node velocity of the second virtual node h at the (n-1)th time step. This represents the node velocity of the a-th split node at the (n-1)-th time step. This represents the node velocity of node b, the neighboring node of split node a, at time step n-1. This represents the node velocity of the neighboring node c of the split node a at the (n-1)th time step;

[0114] The positions and velocities of the first and / or second virtual nodes are added to the reserve pool to align with the dimension of the node velocities of the nodes in the reserve pool of the previous time step.

[0115] It is important to note that the dimension of the final input matrix is ​​determined by the last time step. This allows us to determine the historical information of the additional virtual nodes in the current time step compared to the previous frame, thus obtaining an output matrix with the same dimension as the current time step.

[0116] S6: For any node, in every m consecutive time steps, perform a node velocity calculation based on traditional discrete dislocation dynamics simulation to obtain the accurate node velocity for the corresponding time step; in the remaining time steps, the reservoir calculation model calculates the node velocity for the next time step based on the node velocities of the node and the virtual node.

[0117] Specifically, the calculation of nodal velocities based on traditional discrete dislocation dynamics simulation includes:

[0118] The time step data also includes the node forces of each node in each time step, and the formula for calculating the node forces is:

[0119] ;

[0120] in, Indicates the first The node force of each node, Indicates the first The position of each node. Indicates the first The position of each node. Represents shape functions, Indicates the first The node and the first Any node on a dislocation segment formed by nodes This represents the total stress acting on the dislocation segment. Indicates dislocation segment The Burgers vector, This represents the L2 norm.

[0121] The total stress can be divided into two parts: external stress (caused by external loads and internal stresses) and elastic interaction forces between dislocation segments; therefore, the nodal forces can also be expressed as:

[0122] ;

[0123] in, Indicates the first The node force of each node, Indicates the first External loads applied to each node, Indicates the relationship with the first The elastic interaction force between dislocation segments associated with each node.

[0124] The nodal velocity of the corresponding node is calculated based on the nodal force, and the formula is as follows:

[0125] ;

[0126] in, Indicates the first The node velocity of each node, where t represents the time step. Represents the kinematic rule function. Represents the set of node positions.

[0127] In this embodiment, a node velocity calculation based on traditional discrete dislocation dynamics simulation is performed once every m consecutive time steps. This includes: in any time step (e.g., step 16, 21, 26...) of every m consecutive time steps, a node velocity calculation based on traditional discrete dislocation dynamics simulation is performed once. The accurate node velocity calculated by traditional discrete dislocation dynamics is used to update the historical node velocity state of the reserve pool, and the input history of the reserve pool neural network algorithm model is refreshed accordingly.

[0128] When the number of time steps is a multiple of m, the nodal velocity calculation is performed using traditional discrete dislocation dynamics simulation, ensuring accurate nodal velocities for the current time step. Subsequent time steps are replaced by a reserve pool neural network algorithm. Inserting an accurate dislocation nodal velocity calculation in the m-th time step allows for real-time dynamic correction of nodal velocity errors, preventing the infinite accumulation and expansion of errors that could lead to extremely exaggerated results. This parameter m allows for flexible control over both computational accuracy and acceleration efficiency.

[0129] It is important to note the calculation of nodal forces. In calculating nodal velocities based on traditional discrete dislocation dynamics simulations, the interactions between all dislocation segments must be considered. Therefore, the calculation of nodal velocities... The time complexity is When the number of nodes is huge, this usually requires a lot of computation. Due to the dynamic nature of discrete dislocation simulation, the recurrently connected reservoir neural network algorithm is particularly suitable for this task, as it can predict the future velocity of nodes in the system in real time, thereby greatly reducing the computational load of discrete dislocation dynamics simulation.

[0130] S7: Repeat steps S5-S6 until the simulation of the interaction between dislocations and precipitation phases is completed.

[0131] In the simulation of the interaction between dislocations and precipitates, the plastic strain increment is output based on the area swept by the dislocation segments formed by the nodes, and the calculation formula is as follows:

[0132] ;

[0133] in, Indicates the increment of plastic strain. Represents the simulated volume. Indicates dislocation segment The Burgers vector, Indicates dislocation segment time step The area swept inside, its direction is perpendicular to the dislocation segment. The plane of motion, This indicates a cross product.

[0134] Based on the plastic strain increment and constant strain rate, the increment of applied stress is calculated using the following formula:

[0135] ;

[0136] in, Indicates the increment of applied stress. A fourth-order tensor representing the elastic modulus. Indicates constant strain rate. Indicates the time step. Indicates the increment of plastic strain;

[0137] The incremental stress is superimposed onto the total stress to drive the dislocation segment into the next time step. The stress and plastic strain at each time step during the simulation are recorded to obtain the stress-strain curve.

[0138] Prediction accuracy and dynamic error correction of the DDD-RC algorithm:

[0139] In this embodiment, the Discrete Dislocation Dynamics (DDD-RC) algorithm is used in the first 10 time steps to obtain the real information of each node, including node force, node velocity, and dislocation configuration. This information is then used to obtain the input matrix of the reservoir in the reservoir neural network algorithm. Acceleration is initiated in the 11th time step. It should be noted that the DDD-RC algorithm only calculates the node velocity component. Figure 2The diagram shows a comparison of dislocation evolution before and after acceleration. It can be seen that the accuracy of the DDD-RC algorithm is quite reliable before encountering similar precipitated microstructures, but the prediction accuracy drops sharply once the dislocation passes through an obstacle.

[0140] Therefore, in this embodiment, it is decided to insert a piece of real information obtained from discrete dislocation dynamics after every 5 time steps of prediction. This keeps the prediction error of the probability event of a dislocation encountering an obstacle at each time step within a small range, thereby ensuring the accuracy of DDD-RC. This achieves real-time dynamic error correction, preventing the error from accumulating and expanding indefinitely, which could lead to extremely exaggerated results.

[0141] Results Analysis: Comparison of dislocation configuration evolution obtained by the traditional discrete dislocation dynamics simulation and the DDD-RC method of this invention (see reference) Figure 2 ) and total calculation time (reference) Figure 3 It can be observed that the DDD-RC method maintains a high degree of consistency in dislocation evolution trajectories while significantly reducing computation time and decreasing time complexity from the traditional quadratic time complexity to an approximate linear complexity, thus greatly improving computational efficiency.

[0142] This embodiment demonstrates that the method can effectively accelerate the simulation of three-dimensional dislocation dynamics and accurately capture the physical properties of dislocation density increasing with plastic deformation, providing a powerful tool for efficient and high-precision simulation of material plastic behavior.

[0143] The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation provided in this embodiment has the following advantages:

[0144] This method effectively reduces the high computational cost of traditional dislocation dynamics simulations caused by global time step limitations and long-range interactions of dislocation elastic forces by replacing the calculation of node motion velocity in discrete dislocation dynamics with a trained reservoir computational model. It innovatively proposes a virtual node mechanism to solve the dimensionality mismatch problem caused by the dynamic change in the number of nodes during dislocation topology evolution, achieving adaptive discretization prediction. This method also introduces a periodic error correction mechanism, which periodically inserts real traditional dislocation dynamics simulation results into the prediction sequence to prevent the accumulation of prediction errors and ensure the stability of long-term simulations. This acceleration scheme significantly reduces computation from exponential time complexity to linear time complexity while maintaining physical accuracy, providing a feasible technical path for efficient simulation of the evolution of large-scale three-dimensional complex dislocation networks. The relevant theoretical models analyzed in this invention can effectively solve key problems in traditional discrete dislocation dynamics simulations, such as high computational cost, time step limitation by the most unstable node, and difficulty in simulating the long-term evolution of large-scale dislocation networks. It provides an efficient simulation method for studying dislocation evolution behavior during the plastic deformation of materials, and has important theoretical guiding significance for the development of high-performance metallic materials and the optimization of material processing technology.

[0145] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0146] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for accelerating the simulation of discrete dislocation dynamics based on reservoir calculations, characterized in that, include: S1: Initialize a precipitate phase in a cubic simulation box and set the material parameters, loading conditions and time step Δt; S2: Perform a traditional discrete dislocation dynamics simulation based on the precipitated phase for M time steps, and record the time step data, which includes the nodal velocity of each node in each time step; S3: Training the reserve pool calculation model based on the node velocity of each node in each time step; S4: Sample the node velocities of m consecutive time steps from the time step data and input them into the trained reservoir calculation model to predict the node velocity at the M+Δt time step, including: The node velocities of m consecutive time steps are sampled from the time step data to form a second input vector. The state vector of the reserve pool is updated based on the second input vector, and the update formula is: ； in, Indicates the first The state vector of the reservoir at each time step. Indicates the leakage rate. Represents the hyperbolic tangent function. Represents a sparse matrix. Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. This represents the second input vector; Based on the The state vector and output weight matrix of the reservoir at each time step are used to predict the node velocity at the (M+Δt)th time step. The calculation formula is as follows: ； in, Indicates the first In the first time step The node speed of each node, This represents the output weight matrix; S5: Update the node position of the corresponding node based on the predicted node speed, and check whether the updated node has merged or split. If so, generate a virtual node; otherwise, do nothing. The process of generating virtual nodes includes: When nodes merge, the average of the centroid positions of the two merged nodes is used as the spatial position of the first virtual node; the average of the node velocities of the two merged nodes is used as the node velocity of the first virtual node. When a node splits, find the two nodes adjacent to the split node, and take the average of the centroid positions of the split node and its two adjacent nodes as the spatial position of the second virtual node; take the average of the node velocities of the two adjacent nodes as the node velocity of the second virtual node. Add the position and node velocity of the first virtual node and / or the second virtual node to the reserve pool to align with the dimension of the node velocity of the nodes in the reserve pool of the previous time step; S6: For any node, in every m consecutive time steps, perform a node velocity calculation based on traditional discrete dislocation dynamics simulation to obtain the accurate node velocity for the corresponding time step; in the remaining time steps, the reservoir calculation model calculates the node velocity for the next time step based on the node velocities of the node and the virtual node. S7: Repeat steps S5-S6 until the simulation of the interaction between dislocations and precipitation phases is completed.

2. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 1, characterized in that, In S1, the material parameters include shear modulus, elastic modulus, and Poisson's ratio, and the loading condition includes constant strain rate.

3. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 2, characterized in that, In S3, the calculation model for training the reserve pool based on the node velocity of each node in each time step includes: The node velocities of each node in the M-Δt time step are used to form an input vector, and the node velocities of each node in the M-th time step are used to form an output vector. The input vector is connected to the Reservoir via an Input or Reservoir coupler, and the input vector is connected to the Reservoir via an Output or Reservoir coupler. Define the number of nodes in the reserve pool in the reserve pool calculation model, and connect the nodes in the reserve pool using a sparse matrix; The state vector of the reservoir is updated based on the sparse matrix, the input vector, and the connection matrix connecting the input vector to the Reservoir. The update formula is expressed as follows: ； in, Indicates the first The state vector of the reservoir at each time step. Indicates the leakage rate. Represents the hyperbolic tangent function. Represents a sparse matrix. Indicates the first The state vector of the reservoir at each time step. This represents the connection matrix connecting the input vector to the Reservoir. Represents the input vector; The output weight matrix is ​​calculated based on the input and output vectors using the following formula: ； in, This represents the output weight matrix. Indicates the output vector. Indicates transpose. Represents the regularization coefficient. Represents the identity matrix; The trained reservoir computation model is used to map the node velocity at the next time step based on the reservoir's state vector and output weight matrix.

4. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 1, characterized in that, In S5, updating the node position of the corresponding node based on the predicted node speed includes: The time step data also includes the position of each node in each time step; The position of the corresponding node in the reserve pool at the Mth time step is updated based on the predicted node velocity at the M+Δt time step. The update formula is as follows: ； in, Indicates the first In the first time step The position of each node. Indicates the first In the first time step The position of each node. Indicates the first In the first time step The node speed of each node, Indicates the time step.

5. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 4, characterized in that, In S6, the calculation of nodal velocities based on traditional discrete dislocation dynamics simulation includes: The time step data also includes the node forces of each node in each time step, and the formula for calculating the node forces is: ； in, Indicates the first The node force of each node, Indicates the first The position of each node. Indicates the first The position of each node. Represents shape functions, Indicates the first The node and the first Any node on a dislocation segment formed by nodes This represents the total stress acting on the dislocation segment. Indicates dislocation segment The Burgers vector, Represents the L2 norm; The nodal velocity of the corresponding node is calculated based on the nodal force, and the formula is as follows: ； in, Indicates the first The node velocity of each node, where t represents the time step. Represents the kinematic rule function. Represents the set of node positions.

6. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 1, characterized in that, In S6, a nodal velocity calculation based on traditional discrete dislocation dynamics simulation is performed once every m consecutive time steps, including: performing a nodal velocity calculation based on traditional discrete dislocation dynamics simulation once in any one of the m consecutive time steps.

7. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 5, characterized in that, In S7, during the simulation of the interaction between dislocations and precipitates, the plastic strain increment is output based on the area swept by the dislocation segments formed by the nodes. The calculation formula is as follows: ； in, Indicates the increment of plastic strain. Represents the simulated volume. Indicates dislocation segment The Burgers vector, Indicates dislocation segment time step The area swept inside, This indicates a cross product.

8. The accelerated simulation method for discrete dislocation dynamics based on reservoir calculation according to claim 6, characterized in that, Based on the plastic strain increment and constant strain rate, the increment of applied stress is calculated using the following formula: ； in, Indicates the increment of applied stress. A fourth-order tensor representing the elastic modulus. Indicates constant strain rate. Indicates the time step. Indicates the increment of plastic strain; The incremental stress is superimposed onto the total stress to drive the dislocation segment into the next time step. The stress and plastic strain at each time step during the simulation are recorded to obtain the stress-strain curve.

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