Method for determining the elastoplastic deformation of a structure

Abstract

The invention relates to a computer-implemented method for training a predictive model capable of determining the elastoplastic deformation of a structure, comprising steps of: - receiving a plurality of input variables including at least one force wrench applied to a structure; - providing the input variables to an encoder () so as to obtain a latent vector; - jointly providing the latent vector: -- to a first decoder (), and -- to a recurrent cell (), the output of the recurrent cell being connected to a second decoder (). The parameters of the encoder (), the recurrent cell (), the first decoder (), and the second decoder () are determined so as to minimize a cost function, the cost function being determined by comparing the first displacement field and the third displacement field ( with results of numerical simulations stored in a database. Figure for the abstract: Fig.1.

Description

Title of the invention: Method for determining the elastoplastic deformation of a 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 training a predictive model capable of determining the elastoplastic deformation of a structure, as well as 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 the 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.), shaping of materials (stamping, forging...), additive manufacturing, dimensioning of structures, study of the failure of structures, simulation of interactive manipulations, etc.

[0007] Modeling these plastic deformations generally involves finite element-based numerical simulations, which are quite computationally expensive, since the simulations involve a large number of degrees of freedom and the displacements are a source of non-linearity (large displacement hypothesis). displacements: 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 part and the plastic part of a deformation. Summary of the invention

[0010] An object of the invention is therefore a computer-implemented method for training a predictive model capable of determining the elastoplastic deformation of a structure, comprising steps consisting of: - receive a plurality of input variables including at least one force wrench applied to a structure;

[0011] - provide the input variables to an encoder so as to obtain a latent vector; - jointly provide the latent vector:

[0012] — to a first decoder, the first decoder providing a first field of displacement 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

[0013] — to a recurring cell which determines a cumulative plastic deformation of the structure over time, the output of the recurring cell being connected to a second decoder providing a second displacement field of the structure subjected to the force 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.

[0014] The parameters of the encoder, the recurrent cell, the first decoder and the second decoder are determined so as to minimize a cost function, the cost function being determined by comparing the first displacement field and the third displacement field with results of numerical simulations stored in a database.

[0015] Advantageously, the first displacement field and the third displacement field forming a first set, the results of numerical simulations are obtained by passing the plurality of input variables to a solution of numerical simulation, 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.

[0016] 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.

[0017] Advantageously, the recurrent cell is a GRU (Gated Recurrent Unit).

[0018] Advantageously the first decoder and the second decoder do not include any hidden layer.

[0019] Advantageously, the results of numerical simulations are obtained by finite element simulations.

[0020] Advantageously, the application points are determined from a random initial position on the surface, the positions of the subsequent application points being determined from a normal distribution around a previous position.

[0021] Advantageously, consecutive sequences of force torsors are applied, each sequence corresponding to a plurality of application points and with an evolution of the intensity whose form is parameterized.

[0022] Advantageously, 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.

[0023] Advantageously, the method includes a step of subsampling the database, said subsampling including the application of a reduction factor so as to remove a plurality of application points.

[0024] The invention also relates to a computer-implemented method for determining the elastoplastic deformation of a structure, comprising steps consisting of:

[0025] - receive a plurality of input variables including at least one force wrench applied to the structure;

[0026] - provide a first displacement field, and / or a second field of displacement and / or a third displacement field of the structure subjected to force wrench, by implementing the prediction model trained using the aforementioned machine learning process.

[0027] Advantageously, the process includes an additional step of manufacturing the structure.

[0028] 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.

[0029] The invention also relates to a processor-readable recording medium on which is stored a program containing instructions for executing the aforementioned process, when the program is executed by a processor. Description of the figures

[0030] Other features, details and advantages of the invention will become apparent from the description made with reference to the accompanying drawings given by way of example.

[0031] Fig. 1 illustrates an example of a prediction model which makes it possible to implement the method according to the invention.

[0032] Fig. 2 illustrates an example of a trombone mesh.

[0033] Fig. 3 illustrates an example of a mesh of a motor vehicle hood.

[0034] Figure 4 illustrates a representation of elements of the database consisting of results of finite element simulations.

[0035] Figure 5 illustrates an example of determining application points for force wrenches applied to a paperclip.

[0036] Fig. 6 illustrates three sequences of forces applied to a paperclip.

[0037] Fig. 7 illustrates a schematic example of the structure of the first decoder.

[0038] Figure 8 illustrates a work hardening curve of an elastoplastic material (stress (depending on the deformation).

[0039] Figure 9 illustrates a series of loads during the supervised learning phase.

[0040] Fig. 10 illustrates an example of subsampling of a mesh representing a motor vehicle hood.

[0041] Fig. 11, Fig. 12 and Fig. 13 illustrate, comparatively, a simulation of the elastoplastic deformation of a paperclip, by finite element software and by the method according to the invention. Detailed description

[0042] The method according to the invention includes a preliminary step (not shown in [Fig. 1]) of generating a database. This database is composed of reference simulation results of two types: elastoplastic simulations and purely elastic simulations for stresses external identical to those of the elastoplastic simulations, so that each external stress gives rise to two simulations.

[0043] The database can advantageously consist of finite element simulation results. The finite element method makes it possible to simulate deformations of complex geometries represented by a mesh comprising Npts nodes.

[0044] For this purpose, the structure being simulated is transformed, by the finite element software, into finite elements, for example tetrahedral.

[0045] Fig. 2 illustrates an example of a trombone mesh, and Fig. 3 illustrates an example of a triangular mesh of a motor vehicle hood.

[0046] A file contains the list of nodes and elements of the mesh. It can be noted that the constituent elements of the mesh 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 cells are volumes, or surface, or even linear if the cells are beams) are placed on the cells.

[0047] For each simulation, a force wrench is applied. The force wrench can be expressed as a pair of vectors: the force vector F, which represents the forces acting on the object, and the moment vector, M / , which represents the moment (or couple) resulting from these forces.

[0048] Thus, at each simulation, a first reference displacement field (rPred\ t-ref) and a total reference displacement field are calculated. These two (t-ref) Reference fields define, for each node, the displacement of the node in each of the spatial dimensions of the problem under consideration: two dimensions for a planar problem, three dimensions for a problem in space.

[0049] The first reference displacement field / is determined as a function of t-ref / of an exclusively 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 constituting the structure is virtually modified to extend the elastic region beyond the point of yield strength. 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 a yield strength.

[0050] The total reference displacement field \ is determined by the t-ref / simulation of the elastoplastic deformation of the material constituting the structure, with the stress-strain relationship of the object under consideration, that is to say the elasto-plastic constitutive law chosen to describe the material of the structure.

[0051] 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.

[0052] Figure 4 illustrates an example of the representation of elements from the database consisting of 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 integrated into the database.

[0053] It may 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 force torsors. However, the database is generated once and for all (for a given structure and a range of considered forces); moreover, it can be generated using intensive computing methods and then imported by the computer system implementing the method according to the invention.

[0054] 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.

[0055] According to one embodiment, the input variables may include %load input scalars, corresponding for example to the following elements: - the coordinates of each of the application points;

[0056] - the direction and magnitude of the force Ft, expressed along the three coordinates x,y and z, at each of the points of application;

[0057] - the direction and magnitude of the moment M expressed according to the three coordinates x, y and z, at each of the points of application.

[0058] On [Fig. 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.

[0059] Fig. 5 illustrates an example of a graph which allows the coordinates of the points of application 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 points of application).

[0060] Fig. 6 illustrates three examples of force sequences applied to a paperclip (force applied at each iteration along the three coordinates x, y and z).

[0061] On the left side of [Fig. 6], a force sequence can be decomposed into three components along the x-axis (component Six), along the y-axis (component Sly), and along the z-axis (component Slz). Similarly, the central part of [Fig.6] illustrates the components S2x, S2y and S2z, and the right part of [Fig.6] illustrates the components S3x, S3y and S3z.

[0062] It can be noted that the number of force torsors (and therefore of application points) can vary from one use case to another.

[0063] In a second step, for each load, the input variables are passed to an EN C encoder configured to provide a latent vector of dimension zl. The EN C encoder is a neural network comprising at least one input layer and one output layer, and may also include one or more hidden layers. Within the scope of the present invention, an EN C encoder without a hidden layer may be sufficient to provide good results.

[0064] 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 Zload'^l weight to adjust if there are no hidden layers.

[0065] The weights and biases of the ENC encoder are parameters to be optimized, via optimization methods typically involving a learning rate.

[0066] 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.

[0067] The input variables of a load pass through the input layer, where each neuron performs calculations by applying an activation function to produce a result.

[0068] The ENC encoder thus provides, at output, a latent vector of dimension Z1 (for example Z = 64).

[0069] In a third step, the latent vector Vest is transmitted to a first CE decoder, which is a neural network capable of providing a first displacement field represented by the structure in response to the loading defined by the torsors. of effort provided as input.

[0070] The first displacement field r-pred represents the spatial distribution 9 t 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*Npts).

[0071] The first DEC E decoder determines the first displacement field repred based on an exclusively 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 ^pred is a vector of dimensions 3*Npts.

[0072] Figure 7 illustrates an example of a DEC E decoder applied to a paperclip. The latent space EL has dimension Z^ = 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, as output, a first displacement field ^Precl comprising displacement data (along the x, y, and z directions) for each point of the mesh.

[0073] One way to virtually extend the elastic domain is to adopt a neo-Hookean constitutive law such that it coincides with the original elastoplastic part at the original elastic limit. Thus, the stress-strain relationship does not include an elastic limit.

[0074] Figure 8 illustrates a work hardening curve of a steel and whose parameters are as follows:

[0075] Young’s modulus E = 210 GPa

[0076] Poisson's ratio P = 0.3

[0077] Density p = 7850 kg / m3

[0078] The work hardening curve represents the stress a (force per unit area) as a function of the strain Σ.

[0079] In [Fig. 7], the elastic extension of the material's hardening curve is shown as a dashed line. The extension of the hardening curve is virtual, as it does not reflect the actual behavior of the material.

[0080] The third step comprises a transmission of the latent vector V to a recurrent cell REC which determines a quantity ht that is similar to the cumulative plastic deformation of the structure over time. The transmission takes place concurrently with the transmission to the first decoder DEC E.

[0081] 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.

[0082] The recurrent cell REC receives two inputs (the latent vector V|at, which represents the input variables of a load, and the previous internal state ht.p), and provides, as output, the current internal state ht which serves as memory for the next load, and, the output vector Vout, of dimension z2 which corresponds to an output prediction.

[0083] The recurring 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 mesh of the structure. Indeed, in plasticity / elastoplasticity, the state of the system does not depend only on current plastic and elastic deformations, but also on the history of deformations.

[0084] Initially, if the structure has not undergone plastic deformation, the cumulative plastic deformation is zero, and the previous internal state ht4 can be initialized to 0 at any node of the mesh.

[0085] The current internal state ht is calculated via an update function, often a non-linear function such as the hyperbolic tangent or the sigmoid function, applied to a linear combination of the latent vector Vjat and the previous internal state h^, as expressed for example by the following formula:

[0086] ht = ïaiû^W11Vlat+Uhht.1+b^

[0087] Wjj and Uh are weight matrices learned by the network.

[0088] bh is a bias learned by the network.

[0089] tanh is the activation function which introduces non-linearity.

[0090] In this case, the parameters are the weight matrices as well as the bias.

[0091] It may be advantageous to use a GRU (for "Gated recurrent unit") type recurrent cell to minimize gradient evanescence effects.

[0092] The output of the recurrent cell RE C is connected to a second decoder DE CP which provides a second displacement field ^CO11, determined as a function of an elastoplastic deformation of the material constituting the structure. In order to determine the second displacement field ^coir^, the actual hardening curve of the material is used (solid line [Fig.7]).

[0093] A third displacement field is then obtained by summing the first displacement field and the second displacement field (rcorr\ • rtot _ rpred ^corr H* +½ '

[0094] The third displacement field ?tot represents the spatial distribution of the st Displacements of points in the structure under the effect of the predefined load (for Npts nodes of the structure). Concretely, this is a vector of dimensions 3*Npts, 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(es).

[0095] The weights, bias, and learning rate are parameters to be optimized for the first DEC E decoder and for the second DEC P- decoder

[0096] During the training phase of the model illustrated in Figure 1, for each new load (defined by a force wrench), the first displacement field rpred and the third displacement field ftot are compared to the first field of reference displacement prred and to the total reference displacement field t-ref rtot, stored in the database, and corresponding to an identical load. t-ref

[0097] 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 rPred 9 t and the third displacement field on the one hand, and a second set EnSref consists of the first reference displacement field rpred and the t-ref second total reference displacement field rtot on the other hand. t-ref

[0098] Thus, the goal of the training phase is to minimize the distance between the first set Eus and the second set EllSref. The distance can be calculated by concatenating the first displacement field rPred and the third field t of displacement ftot, and by concatenating on the other hand the first displacement field st of reference rPred and the second reference displacement field. A S t_ref S t-ref Euclidean distance can be calculated to determine the dist distance, this distance being well suited to measure the similarity or difference between data points.

[0099] Network training consists of adjusting the parameters of the encoder, the recurrent cell, the first decoder and the second decoder in order to minimize the distance dist (also called the cost function).

[0100] The distance can thus be minimized by a minimization algorithm using backpropagation.

[0101] It is important to note that parameter minimization must take place for all neural networks, simultaneously and jointly, for each new inference data input.

[0102] In inference, the computer-implemented method 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.

[0103] Thus, in inference, input variables are provided to the model, such as: - the coordinates of one or more application points;

[0104] - the direction and magnitude of the force Ft, expressed along the three coordinates x,y and z, at each of the points of application;

[0105] - the direction and magnitude of the moment MExpressed according to the three coordinates x, y and z, at each of the points of application.

[0106] The model provides a first displacement field ^pred^ and / or a second displacement field ^corr and / or a third displacement field ^tot of the structure subjected to the force wrench, by implementing the prediction model trained by means of the aforementioned machine learning process.

[0107] The advantage of the method according to the invention is that it allows for the creation of a neural network that corresponds to a smaller 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

[0108] Moreover, 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 those of the prior art, 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-

[0109] 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.

[0110] Figure 9 illustrates an example of a series of 350 loads during the inference phase of neural networks. In Figure 9, the loads model hammer blows on the hood of a motor vehicle. A sequence of hammer blows is represented by a triangular signal composed of H-hit points. Each sequence of hammer blows has an intensity that starts at p = 0, reaching a maximum value Pm that can be randomly determined between 0 and a user-defined maximum value.

[0111] If H-hits hammer blows are applied in a sequence, the series of loads comprises nt = Npts-Hhits load values.

[0112] 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 [Fig.9].

[0113] 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).

[0114] The shape of the sequences illustrated by [Fig.9] helps the finite element software to calculate a solution that converges.

[0115] In the inference phase, it is preferable to vary the points of application. The location can be defined by a position (coordinates (x, 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 positions xt of the points of application st can be generated by randomly selecting the initial position -¾, and then calculating each subsequent position ^t+1 from a normal distribution with the position xt as the mean, and a standard deviation equal to ^R.

[0116] The normal distribution is implemented so that two successive hammer blows are more likely to be close than far apart, which is more representative of a scenario in which the user strikes at places close to each other.

[0117] 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 part of the nodes, by applying a reduction factor.

[0118] Subsampling thus makes it possible to reduce the size of the data stored in the database and accelerate 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 database size that allows the data to be processed quickly. Figure 9 illustrates an example of node subsampling with a reduction factor of 0.25. The subsampled mesh shown in Figure 10 can be used to reduce the size of the database and accelerate learning.

[0119] According to 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.

[0120] If the subsampling is included in the original mesh, the reference displacement fields are obtained directly from their value on the original mesh. Otherwise, the reference displacements on the reduced mesh must be obtained by interpolating the reference displacements on the original mesh.

[0121] 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").

[0122] In [Fig. 11], no stress is applied to the paperclip. [Fig. 12] illustrates the ability of the invention to predict the deformation (B) in accordance 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 implemented by the finite element simulation (A) was calculated in approximately ten minutes, whereas that implemented with the method according to the invention was calculated in a few tenths of a second.

[0123] The invention advantageously makes it possible to manufacture the structure which has been modeled according to the invention, by having a detailed knowledge of the behavior when the structure is subjected to elastoplastic deformations.

[0124] Documents cited

[0125] [Gorji] « On the potential of récurrent neural networks for modeling path dépendent 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

[0126] [Huang] « A machine leaming based plasticity model using proper orthogonal décomposition » (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 training a predictive model capable of determining the elastoplastic deformation of a structure, comprising steps of: - receiving a plurality of input variables including at least one applied force wrench at a point of application of the structure; - providing the input variables to an encoder (ENC) so as to obtain a latent vector; - jointly providing 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 wrenches, the first displacement field being determined as a function of an exclusively elastic deformation of the constitutive material of 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 ^COrrj of the structure subjected to the force torsors, the second displacement field being determined as a function of an elastoplastic deformation of the constitutive material of the structure, a third displacement field ( being calculated by the sum / of the first displacement field and the second displacement field ^corrj, 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 displacement field (r-tot\ with results of ) numerical simulations stored in a database.

2. A method according to claim 1, wherein, the first displacement field zrPred\ and the third displacement field ( rtot\ t ) ) forming a first set (Ens), 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 1 determined as a function of an elastoplastic deformation of the material constituting the structure,the set of first reference displacement fields (r-Pi ed\ t-ref) and the set of second reference displacement fields forming a second set (Ensref), the cost function 'Ç t-ref) being minimized by calculating a distance between the first set (Ens) and the second set (EllSref).,

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 (st).

10. A computer-implemented method for determining the elastoplastic deformation of a structure, comprising steps of: - receiving a plurality of input variables including at least one force wrench applied at a point of application of the structure; - providing a first displacement field ^P1 and / or a second displacement field ^COrrj and / or a third displacement field of the structure subjected to the force wrench, by implementing the prediction model trained by means of the machine learning method according to any one of the preceding claims.

11. A method according to claim 10, wherein the application points (st) 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.

12. A method according to any one of claims 10 or 11, comprising an additional step of manufacturing the structure.

13. A computer program comprising instructions for carrying out a process according to any one of the preceding claims, when the program is executed by a processor.

14. 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 12, when the program is executed by a processor.

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