Computer-implemented method for determining the elastoplastic deformation of a structure for manufacturing the structure

Abstract

The invention relates to a computer-implemented method for determining the elastoplastic deformation of a structure for manufacturing the structure, the method comprising the steps of: - receiving at least one input variable in inference comprising at least one force torsor applied at a point of application of the structure; - implementing a prediction model trained by means of a machine learning method, the machine learning method comprising the steps of: - receiving a plurality of input variables comprising at least one force torsor applied to a structure; - supplying the input variables to an encoder (ENC) so as to obtain a latent vector; - jointly supplying the latent vector: - to a first decoder (DEC_E), and - to a recurrent cell (REC), the output of the recurrent cell being connected to a second decoder (DEC_P). The parameters of the encoder (ENC), of the recurrent cell (REC), of the first decoder (DEC_E) and of the second decoder (DEC_P) are determined so as to minimize a cost function, the cost function being determined by comparing the first displacement field (Formula (I)) and the third displacement field (Formula (II)) with results of numerical simulations stored in a database.

Description

DESCRIPTION COMPUTER-IMPLEMENTED METHOD FOR DETERMINING THE ELASTOPLASTIC DEFORMATION OF A STRUCTURE FOR THE MANUFACTURE OF THE STRUCTURE technical field

[0001] The invention relates to the field of solid mechanics, and in particular to the modeling of the behavior of solids when subjected to external stress. The invention thus relates to a computer-implemented method for determining the elastoplastic deformation of a structure.

[0002] In solid mechanics, certain materials, typically metals, can be modeled by so-called elastoplastic behaviors. The elastoplastic behavior of a structure is defined by a combination of two phases (or regimes) of mechanical deformation: the elastic phase and the plastic phase.

[0003] The elastic phase is characterized by a reversible deformation: when the structure is subjected to stress, it deforms elastically, that is to say, it returns to its initial shape when the stress is released.

[0004] The plastic phase is characterized by permanent deformation: beyond a certain stress threshold (called the elastic limit), the structure enters a plastic regime where deformation is no longer reversible. Even if the stress is removed, permanent deformation remains.

[0005] This model allows us to describe everyday observations, for example, bending a metal spoon or a paperclip. In the elastic phase, the deformation is reversible. Thus, if we stop bending the spoon, it returns to its original shape. In the plastic phase, the deformation is irreversible. Even if the force is released, the spoon will not return to its original shape and will remain bent.

[0006] This elastoplastic modeling also has industrial applications, particularly whenever plastic phenomena need to be taken into consideration: simulations of accidental deformations (of cars, overhead cranes, pipe parts, etc.), material shaping (stamping, forging...), additive manufacturing, structural dimensioning, structural failure studies, simulation of interactive manipulations, etc.

[0007] Modeling these plastic deformations generally involves finite element-based numerical simulations, which are quite computationally expensive, especially when the simulations involve a large number of degrees of freedom and the displacements introduce non-linearity (large displacement hypothesis: the geometry is not updated incrementally, unlike the small displacement assumption where everything happens as if the system remained in its initial configuration).

[0008] The articles by [Gorji] and [Huang] describe the use of recurrent neural networks to model the plastic response of a material, without however distinguishing the elastic and plastic parts of a deformation and within the framework of small transformations.

[0009] There is therefore a need to determine quickly and at low cost the elastoplastic deformation of a structure, which distinguishes the elastic and plastic parts of a deformation. Summary of the invention An object of the invention is therefore a computer-implemented method for determining the elastoplastic deformation of a structure for the purpose of manufacturing the structure, comprising steps consisting of: - receive at least one inference input variable including at least one force wrench applied at a point of application of the structure;

[0010] - to implement a predictive model trained using a machine learning process, comprising steps consisting of: - receive a plurality of training input variables including at least one force wrench applied to a structure; - provide input variables to an encoder in order to obtain a latent vector; - jointly provide the latent vector: -- to a first decoder, the first decoder providing a first displacement field of the structure subjected to the force torsors, the first displacement field being determined as a function of an exclusively elastic deformation of the material constituting the structure, and -- to a recurrent cell which determines a cumulative plastic deformation of the structure over time, the output of the recurrent cell being connected to a second decoder providing a second displacement field of the structure subjected to the stress torsors, the second displacement field being determined as a function of an elastoplastic deformation of the material constituting the structure, a third displacement field being calculated by the sum of the first displacement field and the second displacement field.

[0011] The parameters of the encoder, the recurring cell, the first decoder, and the second decoder are determined to minimize a cost function, the cost function being determined by comparing the first displacement field and the third field displacement with numerical simulation results stored in a database. The process for determining the elastoplastic deformation of a structure also includes a step of validating or rejecting the structure based on the elastoplastic deformation obtained by implementing the prediction model, with a view to its manufacture.

[0012] Advantageously, the first displacement field and the third displacement field forming a first set, the results of numerical simulations are obtained by transmitting the plurality of input variables to a numerical simulation solution, said numerical simulation solution being configured to determine a set of first reference displacement fields, determined as a function of an exclusively elastic deformation of the material constituting the structure, said numerical simulation tool being configured to determine a set of second reference displacement fields, determined as a function of an elastoplastic deformation of the material constituting the structure, the set of first reference displacement fields and the set of second reference displacement fields forming a second set, the cost function being minimized by calculating a distance between the first set and the second set.

[0013] Advantageously, the exclusively elastic deformation of the material constituting the structure is determined by modifying the constitutive law of the material, by extending the slope corresponding to Young's modulus beyond the point of elastic limit.

[0014] Advantageously, the recurrent cell is a GRU (Gated Recurrent Unit).

[0015] Advantageously, the first decoder and the second decoder do not include any hidden layers.

[0016] Advantageously, the results of numerical simulations are obtained by finite element simulations.

[0017] Advantageously, the application points are determined from a random initial position on the surface, with the positions of subsequent application points determined from a normal distribution around a previous position.

[0018] Advantageously, consecutive sequences of force torsors are applied, each sequence corresponding to a plurality of application points and with an evolution of intensity whose shape is parameterized.

[0019] Advantageously, the intensity is zero for the first point of the sequence, then increased until it reaches a value that is randomly determined between 0 and a predefined maximum value.

[0020] Advantageously, the process includes a subsampling step of the database, said subsampling including the application of a reduction factor so as to remove a plurality of application points.

[0021] The invention also relates to a computer-implemented method for determining the elastoplastic deformation of a structure, comprising steps consisting of: - receive a plurality of input variables including at least one wrench of force applied to the structure; - provide a first displacement field, and / or a second displacement field and / or a third displacement field of the structure subjected to the force wrench, by implementing the prediction model trained using the aforementioned machine learning process.

[0022] Advantageously, the process includes an additional step of manufacturing the structure.

[0023] The invention also relates to a method for determining the loads to be applied to a structure to obtain a desired shape, said method of determination using the aforementioned method.

[0024] Advantageously, the structure is a metal plate intended to be shaped by stamping.

[0025] The invention also relates to a computer program comprising instructions for the execution of the aforementioned process, when the program is executed by a processor.

[0026] The invention also relates to a processor-readable recording medium on which is recorded a program containing instructions for the execution of the aforementioned process, when the program is executed by a processor. Description of the figures

[0027] Other features, details and advantages of the invention will become apparent from the description made with reference to the attached drawings given by way of example.

[0028] Figure 1 illustrates an example of a prediction model that allows the process according to the invention to be implemented.

[0029] Figure 2 illustrates an example of a paperclip mesh.

[0030] Figure 3 illustrates an example of a mesh for a motor vehicle hood.

[0031] Figure 4 illustrates a representation of elements from the database consisting of results from finite element simulations.

[0032] Figure 5 illustrates an example of determining application points for force torsors applied to a paperclip.

[0033] Figure 6 illustrates three sequences of forces applied to a paperclip.

[0034] Figure 7 illustrates a schematic example of the structure of the first decoder.

[0035] Figure 8 illustrates a work hardening curve of an elastoplastic material (stress as a function of strain).

[0036] Figure 9 illustrates a series of loads during the supervised learning phase.

[0037] Figure 10 illustrates an example of subsampling of a mesh representing a motor vehicle hood.

[0038] Figure 11, Figure 12 and Figure 13 illustrate, comparatively, a simulation of the elastoplastic deformation of a paperclip, by a finite element software and by the method according to the invention. Detailed description

[0039] The method according to the invention includes a preliminary step (not shown in Figure 1) of generating a database. This database consists of reference simulation results of two types: elastoplastic simulations, and purely elastic simulations for external stresses identical to those of the elastoplastic simulations, so that each external stress gives rise to two simulations.

[0040] The database can advantageously consist of finite element simulation results. The finite element method allows the simulation of deformations of complex geometries represented by a mesh comprising N pts knots.

[0041] To do this, the structure being simulated is transformed, by the finite element software, into finite elements, for example tetrahedral.

[0042] Figure 2 illustrates an example of a paperclip mesh, and Figure 3 illustrates an example of a triangular mesh of a motor vehicle hood.

[0043] A file contains the list of nodes and mesh elements. It should be noted that the mesh constituents can have various shapes, for example, beams (for modeling a paperclip, for example), or surface or volume elements. Finite elements (volumetric, for example, tetrahedral, if the meshes (are volumes, or surface, or linear if the meshes are beams) are placed on the meshes.

[0044] For each simulation, a force wrench is applied. The force wrench can be expressed as a pair of vectors: the force vector F t , which represents the forces acting on the object, and the moment vector, M t which represents the moment (or couple) resulting from these forces.

[0045] Thus, in each simulation, a first reference displacement field and a total reference displacement field (ref) are calculated. These two reference fields define, for each node, the displacement of the node in each of the spatial dimensions of the problem considered: two dimensions for a planar problem, three dimensions for a problem in space.

[0046] The first reference displacement field is determined based on a purely elastic deformation of the material constituting the structure. To achieve this, the constitutive law—that is, the relationship between strains and stresses—of the material is virtually modified to extend the elastic region beyond the point of elastic limit. One way to virtually extend the elastic domain is to adopt a neo-Hookean constitutive law such that it coincides with the original elastoplastic law at the original elastic limit. Thus, the stress-strain relationship does not include an elastic limit.

[0047] The total reference displacement field (-ref) is determined by the simulation of the elastoplastic deformation of the material constituting the structure, with the stress-strain relationship of the object considered, i.e. the elastoplastic constitutive law chosen to describe the material of the structure.

[0048] Thus, the database includes a set of displacements, which can be transformed so as to be exploited within the framework of the process according to the invention.

[0049] Figure 4 illustrates an example of a database representation of elements from finite element simulations. In Figure 4, three paperclip meshes (M1, M2, M3) undergo deformations (along the x, y, and z axes). The displacement fields of the nodes of the meshes (M1, M2, M3) are included in the database.

[0050] It should be noted that obtaining the results of numerical simulations used as a database can be computationally expensive due to the large number of simulations required to represent all the considered stress torsors. Nevertheless, the database is generated once and for all (for a given structure and range of considered stresses); moreover, it can be generated using various computational methods. intensive, and then be imported by the computer system implementing the process according to the invention.

[0051] The method of training a prediction model according to the invention includes a first step of receiving, at time t, a plurality of input variables comprising at least one force wrench, i.e. a force applied at a given point of the structure and a moment.

[0052] According to one embodiment, the input variables can include z ioadinput scalars, corresponding for example to the following elements: - the coordinates of each of the points of application; - the direction and magnitude of the force F t , expressed according to the three coordinates x,y and z, at each of the points of application; - the direction and magnitude of the moment M t , expressed according to the three coordinates x,y and z, at each of the points of application.

[0053] In Figure 1, the references in parentheses correspond to the dimensions of the displayed data, and the grey boxes correspond to the inputs / outputs of the different functional blocks.

[0054] Figure 5 illustrates an example of a graph that allows the coordinates of the application points of two force torsors to be identified; in this case, each point corresponds to a pair of curvilinear abscissas along the paperclip (corresponding to the two application points).

[0055] Figure 6 illustrates three examples of force sequences applied to a paperclip (force applied at each iteration along the three coordinates x, y and z).

[0056] On the left side of Figure 6, a force sequence can be decomposed into three components along the x-axis (component S1x), along the y-axis (component S1y), and along the z-axis (component S1z). Similarly, the central part of Figure 6 illustrates the components S2x, S2y, and S2z, and the right side of Figure 6 illustrates the components S3x, S3y, and S3z.

[0057] It can be noted that the number of force torsors (and therefore points of application) can vary from one use case to another.

[0058] In a second step, for each load, the input variables are passed to an ENC encoder which is configured to provide a latent vector of dimension z. The ENC encoder is a neural network which includes at least one input layer and one output layer, and which may also include one or more hidden layers. Within the framework of the present invention, an ENC encoder not comprising a hidden layer may be sufficient to provide good results.

[0059] Each connection (or neuron) between the input and output layers has a weight that adjusts the importance of the transmitted information. The ENC encoder would therefore have z load . z1 weight to be adjusted if there are no hidden layers.

[0060] The weights and biases of the ENC encoder are parameters to be optimized, via optimization methods typically involving a learning rate.

[0061] The invention can be generalized to other types of neural networks, for example Kan neural networks, by optimizing the parameters specific to the network used.

[0062] Input variables for a load pass through the input layer, where each neuron performs calculations by applying an activation function to produce a result.

[0063] The ENC encoder thus provides, as output, a latent vector of dimension z1 (for example Z1 = 64).

[0064] In a third step, the latent vector V lat is transmitted to a first decoder DEC_E, which is a neural network capable of providing a first displacement field ^ red of the structure in response to the load defined by the input force torsors.

[0065] The first displacement field ^ redrepresents the spatial distribution of the displacements of points in the structure under the effect of the predefined load. Specifically, it indicates how each point of the structure moves relative to its initial position in response to the applied forces (dimensions 3*N). pts ).

[0066] The first decoder DEC_E determines the first displacement field ^ red based on a purely elastic deformation of the material constituting the structure, using a work hardening curve of the material constituting the structure that is virtually modified so as to extend the elastic region beyond the elastic limit point. The first displacement field ^ red is a vector of dimensions 3 * N pts .

[0067] Figure 7 illustrates an example of a DEC_E decoder applied to a paperclip. The latent space EL has dimension z1 = 64, and the first DEC_E decoder comprises two intermediate layers, respectively of size 32 (layer C1) and 16 (layer C2). The layers are fully connected. The first DEC_E decoder provides, at its output, a first displacement field ^ red including displacement data (along the x, y and z directions) of each point in the mesh.

[0068] One way to virtually extend the elastic domain is to adopt a neo-Hookean constitutive law such that it coincides with the original elastoplastic region at the original elastic limit. Thus, the stress-strain relationship does not include an elastic limit.

[0069] Figure 8 illustrates a work hardening curve for a steel, the parameters of which are as follows:

[0070] Young's modulus E = 210 GPa

[0071] Poisson's ratio v = 0.3

[0072] Density p = 7850 kg / vn?

[0073] The work hardening curve represents the stress a (force per unit area) as a function of the strain s.

[0074] In Figure 7, the elastic extension of the material's hardening curve is shown as a dashed line. This extension is virtual, as it does not reflect the actual behavior of the material.

[0075] The third step involves a transmission of the latent vector V lat to a recurrent cell REC which determines a quantity h t which is similar to the cumulative plastic deformation of the structure over time. The transmission takes place simultaneously with the transmission to the first DEC_E decoder.

[0076] Unlike other neural networks used in the context of the present invention (encoder, first decoder and second decoder), where connections propagate only from one layer to the next, the recurrent cell has a memory.

[0077] The REC recurrent cell receives two inputs (the latent vector V lat , which represents the input variables of a load, and the previous internal state h t (i), and provides, as output, the current internal state h t which serves as memory for the next load, and, the output vector V out , of dimension z2 which corresponds to an output prediction.

[0078] The recurrent cell thus makes it possible to take into account the "cumulative plastic deformation," which reflects the internal state of the solid at each node of the structure's mesh. Indeed, in plasticity / elastoplasticity, the state of the system depends not only on current plastic and elastic deformations, but also on the deformation history.

[0079] Initially, if the structure has not undergone plastic deformation, the cumulative plastic deformation is zero, and the previous internal state can be initialized to 0 at any node of the mesh.

[0080] The current internal state h t is calculated via an update function, often a nonlinear function such as the hyperbolic tangent or the sigmoid function, applied to a linear combination of the latent vector V lat and the previous internal state h t-1 , as expressed for example by the following formula:

[0081] ht = tanh (

[0082] W h and U h are weight matrices learned by the network.

[0083] b h is a bias learned through the network.

[0084] tanh is the activation function that introduces non-linearity.

[0085] In this case, the parameters are the weight matrices and the bias.

[0086] It may be advantageous to use a GRU (for "Gated recurrent unit") type recurrent cell to minimize gradient evanescence effects.

[0087] The output of the recurring cell REC is connected to a second decoder DEC_P which provides a second displacement field ( t corr , determined as a function of an elastoplastic deformation of the material constituting the structure. In order to determine the second displacement field ( t corr, the actual work hardening curve of the material is used (solid line figure 7).

[0088] A third field of movement ^ ot is then obtained by summing the first displacement field (^ red ) and the second displacement field ( t orr ) ■_ corr St

[0089] The third displacement field ^ ot represents the spatial distribution of the displacements of the points of the structure under the effect of the predefined loading (for N pts nodes of the structure). Specifically, it is a vector of dimensions 3 * N pts , which indicates how each point of the structure moves relative to its initial position in response to the application of one or more force wrench(s).

[0090] Weights, bias and learning rate are parameters to be optimized for the first DEC_E decoder and for the second DEC_P decoder.

[0091] During the training phase of the model illustrated in Figure 1, for each new load (defined by a force wrench), the first displacement field ^ red and the third displacement field ^ ot are compared to the first reference displacement field ^l^ d f and to the reference total displacement field stored in the database, and corresponding to an identical load.

[0092] A distance dist, representing the difference between the prediction and the reference, is calculated between a first set Ens consisting of the first displacement field ^ red and the third displacement field ^ ot on the one hand, and a second set Ens ref consisting of the first reference displacement field ^l r ed f and the second reference total displacement field part.

[0093] Thus, the goal of the training phase is to minimize the distance between the first set Ens and the second set Ens ref The distance can be calculated by concatenating the first displacement field ^ red and the third displacement field ^ ot , and by concatenating on the other hand the first reference displacement field ^l^ d f and the second reference displacement field A Euclidean distance can be calculated to determine the dist distance, this distance being well suited to measure the similarity or difference between data points.

[0094] Network training involves adjusting the parameters of the encoder, recurrent cell, first decoder and second decoder to minimize the distance dist (also called cost function).

[0095] The distance can thus be minimized by a minimization algorithm using backpropagation.

[0096] It is important to note that parameter minimization must take place for all neural networks, simultaneously and jointly, for each new inference data input.

[0097] In inference, the computer-implemented process for determining the elastoplastic deformation of a structure includes a step of receiving a plurality of input variables including at least one wrench of force applied to the structure.

[0098] Thus, in inference, input variables are provided to the model, such as: - the coordinates of one or more points of application; - the direction and magnitude of the force F t , expressed according to the three coordinates x,y and z, at each of the points of application; - the direction and magnitude of the moment M t , expressed according to the three coordinates x,y and z, at each of the points of application.

[0099] The model provides a first displacement field ^ red , and / or a second displacement field ^ orr and / or a third displacement field ^ ot of the submitted structure to the effort wrench, by implementing the prediction model trained using the aforementioned machine learning process.

[0100] The method for determining the elastoplastic deformation of a structure according to the invention further includes a step of validating or not the structure based on the elastoplastic deformation obtained by implementing the prediction model, with a view to its manufacture.

[0101] This helps determine if the structure is suitable for the stresses defined in the objective of manufacturing the structure.

[0102] The advantage of the method according to the invention is that it allows for the creation of a neural network with a shorter distance (dist) than the state of the art (i.e., it learns better). Indeed, joint training makes it possible to constrain the latent space to be more representative of the mechanics.

[0103] Advantageously, the validation of the structure is carried out when a difference between the elastoplastic deformation obtained by the implementation of the prediction model and a reference elastoplastic deformation is less than a predefined threshold.

[0104] The deviation can be measured according to a criterion chosen by the user, for example in relation to a reference elastoplastic deformation, or in relation to a criterion defined by a maximum stress / stiffness of the material.

[0105] Advantageously, the process also includes a structural optimization step designed to compensate for the elastoplastic deformation obtained by implementing the prediction model, when the structure is not validated, the optimization step involving a modification of the elastoplastic properties and / or the geometry of the structure.

[0106] Furthermore, inference (i.e., the evaluation of neural networks) is fast (approximately 10,000 to 100,000 times faster than the finite element method for certain applications). In other words, the process is more accurate than state-of-the-art methods, at the same training cost. The performance and accuracy of the second decoder DEC_P are improved due to the joint training of the first decoder DEC_E and the second decoder DEC_P, compared to a model using only the second decoder DEC_P.

[0107] Another advantage of the process is that it allows joint access to the elastic part and the elastoplastic part, which makes it possible to analyze and model the behavior of the structure in detail, in particular by providing the locations of the areas that have plasticized.

[0108] Figure 9 illustrates an example of a series of 350 loads during the inference phase of neural networks. In Figure 9, the loads model moves hammer blows on the hood of a motor vehicle. A sequence of hammer blows is represented by a triangular signal composed of n hits points. Each sequence of hammer blows has an intensity that starts at p = 0, reaching a maximum value p m which can be randomly determined between 0 and a maximum value defined by the user.

[0109] If n hits hammer blows are applied in a sequence; the series of loads includes n t= N pts . n hits loading values. Thus, in the inference phase, the input variables of each load (amplitude and direction of the force wrench) can be defined from the series of sequences as illustrated by Figure 9. Force torsors can be grouped into consecutive sequences of force torsors, each sequence corresponding to a plurality of points whose intensity has a parameterized shape. In particular, the intensity can be zero for the first point of the sequence, then increase until it reaches a value that is randomly determined between 0 and a predefined maximum value (triangular shape). The shape of the sequences illustrated by Figure 9 helps the finite element software to calculate a solution that converges.

[0110] In the inference phase, it is best to vary the points of application. The location can be defined by a position (coordinates (%, y)) in the plane of the hammer, and by the radius R of the hammer. Working along a single x-coordinate (i.e., with the other y-coordinate constant), the series of x-positions t application points t can be generated by randomly selecting the initial position x0, then calculating each subsequent position x t+1 from a normal distribution with the position x t as average, and a standard deviation equal to 2R.

[0111] The normal distribution is implemented so that two successive hammer blows are more likely to be close together than far apart, which is more representative of a scenario in which the user strikes in places close to each other.

[0112] According to an advantageous embodiment, the database does not include the first reference displacement field and the second reference displacement field for all nodes of the structure, but only for a portion of the nodes, by applying a reduction factor.

[0113] Subsampling thus reduces the size of the data stored in the database and accelerates learning. The reduction factor is between 0 and 1, and can be adjusted to satisfy a compromise between good accuracy in representing the displacement fields of the structure and a reasonable database size. so that the data can be processed quickly. Figure 9 illustrates an example of node subsampling with a reduction factor of 0.25. The undersampled mesh shown in Figure 10 can be used to reduce the size of the database and speed up training.

[0114] In one embodiment, the reduction factor varies depending on the area of ​​the structure to be modeled. In particular, the reduction factor is higher in areas where greater accuracy is required.

[0115] If the subsampling is included in the original mesh, the reference displacement fields are obtained directly from their values ​​on the original mesh. Otherwise, the reference displacements on the reduced mesh must be obtained by interpolating the reference displacements on the original mesh.

[0116] Figures 11, 12 and 13 illustrate, comparatively, a simulation of the elastoplastic deformation of a paperclip, by a finite element software (reference "A") and by the method according to the invention (reference "B").

[0117] In Figure 11, no stress is applied to the paperclip. Figure 12 illustrates the invention's ability to predict the deformation (B) consistent with that calculated by the finite element simulation (A), the advantage being that the deformation according to the invention is calculated much faster (approximately 10,000 times faster). It has been tested that the deformation performed by the finite element simulation (A) was calculated in about ten minutes, whereas that performed using the method according to the invention was calculated in a few tenths of a second.

[0118] The invention advantageously allows the structure that has been modeled according to the invention to be manufactured, with a detailed knowledge of the behavior when the structure is subjected to elastoplastic deformations.

[0119] The invention may be particularly useful for calculating how a structure made of a plastic material (typically, metals) deforms or would deform under such loads.

[0120] Thus, the invention also relates to a method of determining the loads to be applied to a structure to obtain a desired shape, said method of determination using the aforementioned method of determining elastoplastic deformation.

[0121] The prediction model is implemented for a load to be applied to the structure in the form of an input variable comprising at least one force wrench, and the load to be applied is selected (or validated) when the elastoplastic deformation obtained corresponds to a desired predefined elastoplastic deformation.

[0122] The prediction model can alternatively be implemented for several applied loads (multiple input variables, each including at least one force wrench), so as to determine an elastoplastic deformation for each load. The selected load is the one that produces an elastoplastic deformation closest to the desired predefined elastoplastic deformation.

[0123] In particular, the invention finds its application for the dimensioning of a structure, in civil engineering (metal framework, pylon) or for aerospace, or automotive.

[0124] Indeed, during the design phase, the engineer is often faced with a structure (given geometry and given material), and must predict whether it will withstand the stresses it will be subjected to.

[0125] If there were only one point of application (a single load) to simulate, a finite element analysis might suffice. But in practice, there are usually many load cases to consider. For example, in civil engineering, load cases can include very strong winds, weak winds coupled with a moderate earthquake, or the presence of snow on the structure, combined with wind and the weight of a person working on the roof.

[0126] In practice, hundreds, or even thousands, of "load cases" can be considered. The invention allows only some of these to be calculated "traditionally" (for example, using finite elements), and the prediction model allows the others to be calculated.

[0127] Other applications can be considered, for example, for shaping materials, particularly stamping, such as for manufacturing an automotive door (stamping transforms a flat metal plate into a door). The predictive model allows for faster calculation of load response, which can be useful for determining where to apply pressure to a plate. The structure can thus be a metal plate in a stamping operation. Documents cited

[0128] [Gorji] “On the potential of recurrent neural networks for modeling path dependent plasticity” (Maysam B. Gorji, Mojtaba Mozaffar, Julian N. Heidenreich, Jian Cao, Dirk Mohr), Journal of the Mechanics and Physics of Solids, Volume 143, October 2020, 103972

[0129] [Huang] « A machine learning based plasticity model using proper orthogonal decomposition » (Dengpeng Huang, Jan Niklas Fuhg, Christian WeiBenfels, Peter Wriggers), Computer Methods in Applied Mechanics and Engineering, Volume 365, 15 June 2020, 113008

Claims

DEMANDS 1. A computer-implemented method for determining the elastoplastic deformation of a structure for the purpose of manufacturing the structure, comprising steps consisting of: - receive at least one inference input variable including at least one force wrench applied at a point of application of the structure; - implement a predictive model trained using a machine learning process comprising steps consisting of: - receive a plurality of drive input variables including at least one force wrench applied at a point of application of the structure; - provide input variables to an encoder (ENC) in order to obtain a latent vector; - jointly provide the latent vector: -- to a first decoder (DEC_E), the first decoder (DEC_E) providing a first displacement field of the structure subjected to the force torsors, the first displacement field ( t pred ) being determined as a function of an exclusively elastic deformation of the material constituting the structure, and - to a recurrent cell (REC) which determines a cumulative plastic deformation of the structure over time, the output of the recurrent cell being connected to a second decoder (DEC_P) providing a second displacement field (^ orr ) of the structure subjected to the force torsors, the second displacement field (f t corr ) being determined as a function of an elastoplastic deformation of the material constituting the structure, a third displacement field being calculated by the sum of the first displacement field and the second displacement field (f t corr), characterized in that the parameters of the encoder (ENC), the recurrent cell (REC), the first decoder (DEC_E) and the second decoder (DEC_P) are determined so as to minimize a cost function, the cost function being determined by comparing the first displacement field and the third field of displacement with results of numerical simulations stored in a database, the process of determining the elastoplastic deformation of a structure further includes a step of validating or not the structure according to the elastoplastic deformation obtained by the implementation of the prediction model, with a view to its manufacture.

2. A method according to claim 1, wherein, the first displacement field and the third displacement field forming a first set (Set), the Numerical simulation results are obtained by passing the plurality of input variables to a numerical simulation solution, said numerical simulation solution being configured to determine a set of first reference displacement fields determined as a function of an exclusively elastic deformation of the material constituting the structure, said numerical simulation tool being configured to determine a set of second reference displacement fields (t-ref), determined as a function of an elastoplastic deformation of the material constituting the structure, the set of first reference displacement fields and the set of second reference displacement fields (-ref) forming a second set (Ens ref ), the cost function being minimized by calculating a distance between the first set (Ens) and the second set (Ens) re f).

3. A method according to any one of the preceding claims, wherein the exclusively elastic deformation of the material constituting the structure is determined by modifying the constitutive law of the material, by extending the slope corresponding to Young's modulus beyond the point of elastic limit.

4. A method according to any one of the preceding claims, wherein the recurrent cell is a GRU (Gated Recurrent Unit).

5. A method according to any one of the preceding claims, wherein the first decoder and the second decoder do not include any hidden layer.

6. A method according to any one of the preceding claims, wherein the results of numerical simulations are obtained by finite element simulations.

7. A method according to any one of the preceding claims, wherein consecutive sequences of force torsors are applied, each sequence corresponding to a plurality of application points and with an evolution of intensity whose shape is parameterized.

8. A method according to claim 7, wherein the intensity is zero for the first point of the sequence, then increased until it reaches a value which is determined randomly between 0 and a predefined maximum value.

9. A method according to any one of the preceding claims, comprising a step of subsampling the database, said subsampling comprising the application of a reduction factor so as to remove a plurality of application points (s t ).

10. A method according to any one of the preceding claims, wherein the validation of the structure is carried out when a difference between the elastoplastic deformation obtained by implementing the prediction model and a reference elastoplastic deformation is less than a predefined threshold.

11. A method according to any one of the preceding claims, further comprising a step of optimization of the structure intended to compensate for the elastoplastic deformation obtained by the implementation of the prediction model, when the structure is not validated, the optimization step comprising a modification of the elastoplastic properties and / or the geometry of the structure.

12. A computer-implemented method for determining the elastoplastic deformation of a structure, comprising steps consisting of: - receive a plurality of input variables including at least one force wrench applied at a point of application of the structure; - provide an initial field of movement and / or a second displacement field (^rcorr) et ou ur| third field of movement of the structure subjected to the force wrench, by implementing the prediction model trained by means of the machine learning process according to any one of the preceding claims.

13. A method according to claim 12, wherein the application points (s t ) are determined from a random initial position on the surface of the structure, the positions of the subsequent application points being determined from a normal distribution around a previous position.

14. A method according to any one of claims 12 or 13, comprising an additional step of manufacturing the structure.

15. Method for determining the loads to be applied to a structure to obtain a desired shape, said method of determination using the computer-implemented method for determining the elastoplastic deformation of a structure for the manufacture of the structure according to any one of claims 1 to 14.

16. Method according to claim 15, wherein the structure is a metal plate intended to be shaped by stamping.

17. Computer program comprising instructions for the execution of a process according to any one of the preceding claims, when the program is executed by a processor.

18. Processor-readable recording medium on which is recorded a program containing instructions for the execution of a process according to any one of claims 1 to 16, when the program is executed by a processor.

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