Computer-implemented method for outputting parameter values describing at least one elastoplastic mechanical response of one or more materials

Abstract

The application disclosed herein relates to a computer-implemented method for outputting a parameter value describing at least one elastoplastic mechanical response of one or more materials, most preferably one or more polymers. The application also relates to a non-transitory computer-readable storage medium for tangibly storing computer program instructions executable by a processor, the computer program instructions defining one or more steps of a computer-implemented method for outputting parameter values as described herein.

Description

Technical Field

[0001] The application disclosed herein relates to a computer-implemented method for outputting parameter values that describe at least one elastoplastic mechanical response of one or more materials, the one or more materials being most preferably one or more polymers. The present application also relates to a non-transitory computer-readable storage medium that tangibly stores computer program instructions executable by a processor, the computer program instructions defining steps in one or more of the steps of the computer-implemented method for outputting parameter values as described herein.

[0002] More specifically, a method for extracting material properties from complex information sources, such as one or more force-displacement signals obtained from impact tests, such as instrumented Charpy tests, instrumented Izod tests, instrumented puncture tests, and / or instrumented drop weight tests or any other mechanical impact test involving dynamic loading of any test sample, is presented herein. Background Art

[0003] In modern supply chains, such as those used in the automotive industry, original equipment manufacturers (OEMs) and their suppliers require and utilize intrinsic material property data to design and manufacture components of their products. In this context, there is a growing need to generate material property data that can describe the behavior of materials under one or more impact loading conditions, especially for higher-end applications.

[0004] WO 2021 / 110690 A1 discloses a method for determining material properties based on images of foam samples to reduce the test effort. Here, structural features, especially at the microscale level (i.e., microstructure), such as pores, walls, struts, nodes, unit cells, are measured from the images, and the measured structural features are provided to a material model. The material model is a data-driven model, such as a trained machine learning model, that correlates the structural features and material properties without the need for knowledge of physical laws. Here, the structural features can be measured directly from the images. Such measurement requires additional (expensive) equipment, which increases the complexity of the method. In addition, the results and their errors of the measurement process need to be transformed to make them suitable as input parameters. This transformation reduces the accuracy and further increases the complexity of the method. No intrinsic material property information can be obtained from the test results.

[0005] US10,955,362B2 discloses methods for determining polymer quality in real time. Herein, a Raman spectrum of a polymer sample is obtained, and the performance / characteristics of the polymer are calculated by comparing chemical and / or structural fingerprints with pre-stored performance data using machine learning tools. The algorithms of the machine learning tools are trained using historical Raman data and the polymer performance / characteristics of known samples measured by traditional methods in the laboratory. For desired polymer performance, a data set (including measured polymer performance / characteristics and corresponding Raman spectral data) is entered into a database accessible through an application programming interface (API). Herein, direct measurement of structural features and recording of Raman spectra are required. Such measurements and data provision require additional (expensive) equipment and increase the complexity of the method. No information on the inherent material properties can be obtained from the test results.

[0006] The disadvantage of all the above-known solutions is the insufficient information provided. This insufficient information cannot determine the inherent mechanical properties such as temperature- and strain-rate-dependent stiffness, yield stress, and / or failure strain.

[0007] For example, the deformability of a material may vary under different loading conditions. Therefore, understanding the deformation behavior of a material is an important criterion for material evaluation or material selection. For example, many cases have shown that even materials that meet the requirements in conventional strength tests (e.g., static tensile tests) may still fail in practice due to brittle fracture under multiaxial loading and low temperatures.

[0008] Toughness (ductility), stiffness, and brittleness are properties that depend not only on the material itself but also on loading conditions such as stress state, deformation rate, and temperature. Due to these correlations and the occurrence of multiaxial and / or impact loading in engineering practice, the mechanical response of materials can only be accurately represented by temperature-dependent and rate-dependent elastoplastic material models (also known as thermo-viscoelastic-viscoplastic material models).

[0009] For example, products, components, and materials used in the automotive industry need to remain constant and stable over a wide temperature range (e.g., between -30°C and +120°C). However, mechanical properties, especially those of polymers, are highly temperature-dependent and sensitive. For example, polymethyl methacrylate is a brittle material at a temperature of 4°C but mainly exhibits ductile behavior at higher temperatures.

[0010] It is also considered a problem that the known concepts require a large amount of time and computational resources to provide test results.

[0011] Therefore, there is a need for a method that can determine and output material parameters that describe at least one elastoplastic mechanical response of one or more materials in a more accurate, simpler, and more efficient automated manner. Specifically, the output material parameters should describe the inherent material properties to have a dynamic material response. For example, it should also cover the strain rate and temperature-dependent mechanical responses of the material. SUMMARY OF THE INVENTION

[0012] The present application solves the above problems and needs through the features of the independent claims. Advantageous embodiments can be derived from the dependent claims.

[0013] On the one hand, a computer-implemented method for outputting parameter values that describe at least one elastoplastic mechanical response of one or more materials is disclosed. The method includes the following steps: inputting a set of data values of one or more experimental force-displacement signals obtained from a mechanical impact test into an optimization algorithm; through the optimization algorithm, searching for a combination of parameter values of a material model that represents one or more material properties, wherein the combination of parameter values causes a difference between the set of data values input in the input step and the prediction result based on a prediction preferably performed by a trained artificial neural network, and the artificial neural network is trained using one or more finite element simulations based on one or more mechanical tests; and outputting from the optimization algorithm the combination of parameter values that causes the difference between the set of data values input in the input step and the finite element simulation or its prediction performed by the artificial neural network to reach a predetermined minimum difference.

[0014] In other words, the computer-implemented method for outputting parameter values that describe at least one elastoplastic mechanical response of one or more materials according to the present application includes the following steps: inputting a set of data values of one or more experimental force-displacement signals obtained from a mechanical impact test into an optimization algorithm; through the optimization algorithm, searching for a combination of parameter values of a material model that represents one or more material properties, wherein the combination of parameter values causes a difference between the set of data values input in the input step and the prediction result based on a prediction preferably performed by a trained artificial neural network, and the artificial neural network is trained using one or more finite element simulations based on one or more mechanical tests; and outputting from the optimization algorithm the parameter values that cause the difference between the set of data values input in the input step and the finite element simulation or its prediction performed by the artificial neural network to reach a predetermined minimum difference.

[0015] The computer-implemented method according to the present application can also be referred to as a computer-implemented method for outputting parameter values describing at least one elastoplastic mechanical response of one or more materials, and includes the following steps: inputting a data value set of one or more experimental force-displacement signals obtained from one or more mechanical tests into an optimization algorithm; searching, through the optimization algorithm, for a combination of parameter values of a material model, the combination of parameter values representing one or more material properties, wherein the combination of parameter values causes a difference to occur between the data value set input in the input step and a prediction result based on the combination of parameter values, preferably, the prediction result is obtained through a trained artificial neural network, and the artificial neural network is preferably trained using one or more finite element simulations based on one or more mechanical tests; and outputting, from the optimization algorithm, the combination of parameter values that causes the difference between the data value set input in the input step and the finite element simulation or its prediction performed by the artificial neural network to reach a predetermined minimum difference.

[0016] In other words, the computer-implemented method according to the present application for outputting parameter values describing at least one elastoplastic mechanical response of one or more materials includes the following steps: inputting a data value set of one or more experimental force-displacement signals experimentally obtained from one or more mechanical impact tests into an optimization algorithm; searching, through the optimization algorithm, for a combination of parameter values of a material model, the combination of parameter values representing one or more material properties; calculating the difference between the data value set input in the input step and a prediction result based on the combination of parameter values; and outputting, from the optimization algorithm, the combination of parameter values that causes the difference between the data value set input in the input step and the prediction result to reach a predetermined minimum difference, wherein the prediction result is the result of a finite element simulation or its prediction performed by an artificial neural network based on the combination of parameter values. In this method, the search and calculation of the difference are preferably performed repeatedly in the optimization algorithm.

[0017] In addition, the computer-implemented method according to the present application for outputting parameter values describing at least one elastoplastic mechanical response of one or more materials can be defined as including the following steps: inputting a data value set of one or more experimental force-displacement signals obtained from one or more mechanical impact tests into an optimization algorithm; searching, through the optimization algorithm, for a combination of parameter values of a material model, the combination of parameter values representing one or more material properties; calculating the difference between the data value set input in the input step and a prediction result based on the combination of parameter values, wherein the prediction result is the result of a finite element simulation or its prediction performed by an artificial neural network; and outputting, from the optimization algorithm, the combination of parameter values that causes a predetermined minimum difference to be reached. In this method, the search and calculation of the difference are preferably performed repeatedly in the optimization algorithm.

[0018] Therefore, an intelligent optimization scheme needs to be implemented, preferably a multi-objective optimization algorithm, for example, a multi-objective optimization algorithm based on the genetic algorithm (GA), which searches for combinations or performances of parameter values to achieve the best fit (such as the predefined minimum difference) between the input value set and the predicted result, for example, an experimental curve simulated using these best-fit output parameters. Incorporating such optimization into the method can further increase the accuracy of the output parameters and further speed up the method.

[0019] The optimization algorithm can be constructed as an optimization loop using comparison steps, where the input data set is compared with the (initial) prediction made by the artificial neural network. Subsequently, the optimization algorithm determines whether one or more stopping criteria (such as the minimum difference) are met. If the stopping criteria are not met, another loop (round) in the optimization algorithm is carried out, and the comparison and determination steps are repeated. If the stopping criteria are met, the optimization algorithm is stopped, and the output parameter values that caused this stop are used to describe at least one elastoplastic mechanical response of one or more materials, and this elastoplastic mechanical response will result in an input data value set of one or more experimental force-displacement signals in the mechanical shock test.

[0020] The optimization scheme can utilize external formulas during the (parameter) optimization process. The optimization scheme (optimization algorithm) can use, for example, the NSGAII genetic algorithm from the Platypus Python library.

[0021] Therefore, a thermo-viscoelastic-viscoplastic material model calibrated based on the artificial neural network and the multi-objective optimization scheme can be obtained.

[0022] In a preferred embodiment, before the output step, the method further includes a step of predicting one or more force-displacement signals using the trained artificial neural network, where the artificial neural network includes one or more neural processing units, and through the trained artificial neural network, the material properties representing the constitutive model are mapped to the data value set based on one or more mechanical shock tests.

[0023] In a preferred embodiment, the output parameter values describe at least one strain rate-related mechanical response and / or at least one temperature-related mechanical response. Preferably, the at least one strain rate-related mechanical response and / or at least one temperature-related mechanical response are considered in the optimization algorithm described below.

[0024] Although it is known that mechanical shock tests can be used to extract the material response under shock loading, the information directly obtained from these tests cannot determine the inherent material properties such as temperature and strain rate-related stiffness, yield stress, and failure strain. The solution of this application now allows the automatic determination of the parameters describing the strain rate and temperature-related mechanical response of the material under shock loading.

[0025] Therefore, a thermo-elasto-viscoplastic material model calibrated based on an artificial neural network can be obtained.

[0026] Although input data values are obtained from one or more mechanical shock tests, searching and / or mapping can be performed based on one or more mechanical shock tests. In this regard, the trained artificial neural network can include multiple neural models, each neural model representing a different mechanical shock test. By using this mapping step, real-time calculations of finite element (FE) simulations (which are time-consuming and may require parameter adjustment in further simulation iterations) can be avoided, thus obtaining output parameters more quickly.

[0027] Here, a trained artificial neural network is introduced to replace the usually required FE simulations, thus greatly reducing the calculation time for obtaining output parameters, for example, by several orders of magnitude. Here, material properties can be mapped to input data values, which can include the results of one or more mechanical tests. This new setup expands the temperature, strain rate, and geometric conditions that the method can cover, thus increasing its application range and accuracy.

[0028] The method provides parameter values describing the elasto-plastic mechanical response of one (or more), and an additional model considering the material temperature and strain rate correlation can be further used. In this way, information about the underlying physical laws describing the inherent material properties can be obtained, thus having higher value for further evaluation and testing based on these output parameters.

[0029] This means that the solution provided by this application can provide output parameters (as a result of the trained artificial neural network) faster and more reliably.

[0030] The core concept behind this application is that the material parameter values that best describe the mechanical shock behavior of one or more materials are the parameter values that produce the smallest difference between the simulation and experimental input data when simulating the mechanical shock tests of these materials. To avoid time-consuming simulations (for example, when iterations are required to obtain the best fit results), these simulations are now replaced by a trained artificial neural network, which is trained from a database of these finite element simulations, where one or more mechanical shock tests are used as surrogate models, and its calculation speed is at least one order of magnitude higher.

[0031] More specifically, this is achieved by inputting experimental data (a set of data values) into a trained artificial neural network (for example, as part of a computer program product) that has been pre-trained to map mechanical properties to the stress-displacement signals recorded during one or more shock loading experiments / tests. The output value is the constitutive parameter of the material model, or in other words, the mechanical properties of the material.

[0032] Therefore, the material data generated by this application can be used to predict the behavior of materials under conditions beyond the input experimental conditions. Such information is particularly useful for designing new components through computer-aided simulations (e.g., using finite element analysis, etc.) and comparing specific values of the mechanical properties of different materials.

[0033] The method provides a tool that can predict material responses under specific and arbitrary loading scenarios, more precisely, predict material responses under mechanical shock loading and under different component geometries, different temperatures, and different strain rates. Thus, this method can support engineers in developing new materials and components.

[0034] In a preferred embodiment, the trained artificial neural network includes one or more feedforward multi-layer perceptron neural network models. For each mechanical shock test, a neural network model with its own hyperparameters is generated, and each model has at least two hidden layers for neurons. In this way, the method performs optimally, and different neural models can be used to apply different shock tests. These neural models can be run in parallel and the test results can be combined to obtain the best-fitting output parameters.

[0035] The multi-layer perceptron neural network model can be implemented using the Scikit-Learn Python library.

[0036] One or more mechanical tests can be any mechanical test conducted under high-speed or non-quasi-static conditions.

[0037] One or more mechanical tests can be, for example, high-speed tensile tests or high-speed three-point (or four-point) bending tests, instrumented Charpy impact tests (e.g., according to the ISO 179-2:2020 standard), instrumented Izod impact tests (e.g., according to ASTM D256 or ISO 180 standard), instrumented puncture tests (e.g., according to the ISO 6603-2:2002-04 standard), instrumented drop weight tests, and / or tensile tests, and each test is preferably conducted at different temperatures.

[0038] The Charpy impact test can be a notched impact test also known as the Charpy V-notch test or unnotched Charpy impact test, which is a standardized high-strain-rate test used to determine the energy absorbed by a material during fracture. The absorbed fracture energy is often used as a measure of the toughness of the material. Due to its ease of performance and the ability to obtain results quickly at low cost, the Charpy impact test is widely used in industry. The apparatus for performing the Charpy impact test consists of a pendulum of known mass and length that is dropped from a known height to strike a material specimen (sample or specimen). The energy transferred to the material can be inferred from the difference in the height of the pendulum head before and after fracture (the energy absorbed by the fracture event). The material specimen includes a V-notch. The notch on the sample affects the results of the impact test, so the size and geometry of the notch must be regular. The impact test can be used to measure the toughness of materials. In addition, the ductile-to-brittle transition temperature (DBTT) can be obtained from the temperature at which there is a sharp change in the energy required to fracture the material.

[0039] The Izod impact test, also known as the Izod impact strength test, is another standard method for determining the impact resistance of materials. The swinging arm is raised to a specific height (constant potential energy) and then released. The swinging arm swings downward and strikes the notched sample, breaking the specimen. The energy absorbed by the sample is calculated based on the height to which the swinging arm swings after striking the sample. Notched samples are usually used to determine the impact energy and notch sensitivity. The Izod impact test is similar to the Charpy impact test, but the arrangement of the test specimen is different under the test. In the Izod impact test, the specimen has a cantilever beam configuration, while in the Charpy impact test, the specimen has a three-point bending configuration.

[0040] Instrumented puncture testing (IPT) is a class of test standards that focuses on measuring the ability of a specimen (usually a thin film, rubber, or paper) to withstand probe rupture when a force is applied at a constant speed.

[0041] Instrumented drop testing or drop testing (e.g., falling weight impact test or dart drop impact test (DDI)) is a mechanical test of a component in which the component is dropped from a defined height onto a defined surface.

[0042] In a preferred embodiment, the artificial neural network is trained using data from a database of multiple finite element (FE) simulations. In that database, there may be multiple data entries, and each data entry can represent the test result of one simulation of a (or multiple) mechanical test with fixed parameterization. The data entry is used to map one or more mechanical properties to the corresponding force-displacement signal.

[0043] The input data value set can be a numerical data set in the form of at least one multi-point force-displacement signal or a series of data values derived therefrom.

[0044] The set of input data values for optimizing an algorithm can represent elastic data. This elastic data can have information about the ability of a material to resist the effects of distortion and return to its original size and shape when the effect or force is removed. When a sufficient load is applied to a solid object, the solid object will deform; if the material is elastic, the object will return to its initial shape and size after the removal. Elasticity and elastic modulus are defined as the force per unit area, usually a unit of measurement for pressure, which corresponds to stress in mechanics.

[0045] The set of input data values for optimizing an algorithm can represent plastic data. This plastic data can have information about the ability of a material to undergo permanent deformation (i.e., an irreversible change in shape in response to the applied force). Thus, plasticity is the opposite of elasticity.

[0046] The transition of a material from elastic behavior to plastic behavior is called yielding. The set of input data values (i.e., the set of input data values) can represent (rate-dependent) yield data. This yield data can have information about the yield point, which is the point on the stress-strain curve that indicates the limit of the elastic behavior of the material and the start of plastic behavior. Below the yield point, the material undergoes elastic deformation and returns to its original shape when the applied stress is removed. Once the yield point is exceeded, part of the deformation will be permanent and irreversible, which is called plastic deformation.

[0047] When the yield strength depends on the rate of strain (i.e., the strain rate) and the expected strain rate is significant, the rate-dependent yield data may have information to accurately define the yield behavior of the material. By providing tabular data for the isotropic hardening metal plasticity model, the isotropic component of the non-linear isotropic / kinematic plasticity model, and the extended Drucker-Prager plasticity model, the rate-dependent yield data can be conveniently defined based on the work hardening parameters and field variables. In addition, the rate-dependent yield data can also be defined by the description of user-defined overstress power-law parameters, yield stress ratios, or Johnson-Cook rate-dependent parameters. The rate-dependent yield data should be specified such that the yield stress increases with the increase in strain rate, especially in dynamic analysis.

[0048] The set of input data values for optimizing an algorithm may represent damage and / or failure data. This data may be information about the ability of a ductile material to evolve damage. Damage may be a gradual reduction in the stiffness of the material, leading to material failure. The damage and / or failure data may be based on mesh-independent measurements (plastic displacement or physical energy dissipation) to indicate the damage evolution after damage initiation. This data may consider the combined effects of different damage mechanisms acting on the same material simultaneously and may include options for specifying how each mechanism contributes to the overall material degradation.

[0049] Before the input step, the method may include a characterization step to reduce the number of input data values for the optimization algorithm. The definition and determination of such features depend on whether these features are present in different experimental impact test results and whether they can be used as (target) output parameter values to reduce the computational effort.

[0050] In either case, since the experimental data are multi-point curves, it is advantageous to reduce this information to a smaller set of input data values that contain the most important information in a streamlined form, which allows the artificial neural model to be more compact, accelerates model calibration, eliminates artifacts, and allows parameter weight regularization.

[0051] Preferably, the ultimate load (e.g., labeled F max ) is used as one or more parameters to represent the input data values. The ultimate load is the maximum load that a material (structure) can safely bear. In other words, it is the load at which the structure is in an incipient plastic failure state. As the load on the structure increases, the displacement increases linearly within the elastic range until the load reaches the yield value. After exceeding the yield value, the load-displacement response becomes non-linear, and the plastic or irreversible part of the displacement steadily increases with the increase of the applied load. Plastic deformation spreads throughout the solid, and at the ultimate load, the plastic zone becomes very large and the displacement becomes unconstrained, at which point the component is considered to have failed.

[0052] More preferably, the deflection (e.g., labeled U max ) is the deflection at the ultimate load, which is used as one or more parameters to represent the input data values. Deflection refers to the degree of displacement of a part of a structural element due to deformation under a load (e.g., the ultimate load). It can refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating a function that mathematically describes the slope of the deflected shape of the member under that load. More preferably, the deflection is calculated directly from sensor measurements of one or more experimental force-displacement signals.

[0053] In addition, preferably, when the strain energy (e.g., labeled E br ), especially the area under the force-displacement signal drops by up to 5% from the peak load, the strain energy is used as one or more parameters to represent the input data values.

[0054] These parameters are particularly preferred as input data values when one or more mechanical tests are instrumented Charpy impact tests or instrumented puncture tests.

[0055] If one or more of the mechanical tests are quasi-static tensile tests, the slope of the stress curve within a predetermined strain range (e.g., labeled as E), particularly the slope corresponding to the least squares regression between 0.05% and 0.25% strain, can be used as one or more parameters to represent the input data values.

[0056] In the latter case, the yield strength can also be used as one or more parameters to represent the input data values. The yield strength is the stress value σ at the yield point y , preferably the initial yield stress at zero offset strain. The yield point is the point on the stress-strain curve that indicates the limit of elastic behavior and the onset of plastic deformation. Below the yield point, the material will exhibit elasticity and return to its original shape when the applied stress is removed. Once the yield point is exceeded, part of the deformation will be permanent and irreversible, which is called plastic deformation.

[0057] The material properties as output parameters can be based on a thermo-viscoelastic-viscoplastic model. Viscoplasticity describes the rate-dependent inelastic properties of materials. In addition, viscoelasticity is the property of materials that exhibits both viscous and elastic characteristics when undergoing deformation. The output parameters of this model describe two material properties related to temperature, thus having a model that describes the inherent material properties related to temperature and strain rate.

[0058] The output parameter values can be one or more of the following: geometrically related (meaning a specific state of stress / strain multiaxiality), temperature related, and strain rate related stiffness, yield stress, and failure strain.

[0059] The output parameter values can include at least one inherent material property, and the output parameter values can describe characteristics suitable for predicting material properties under conditions beyond the set of input data values. Thus, this method becomes a useful tool for predicting material properties in different industries (e.g., the automotive industry), where the environmental parameters within the industry may vary over a wide range.

[0060] The material model is preferably the constitutive model of the material. The constitutive model of the material can be based on a nonlinear elastic model or a nonlinear plastic model, and preferably there is failure parameter calibration (meaning considering the failure behavior).

[0061] The constitutive model of the material can be based on a nonlinear elastic model. Materials generally exhibit elastic behavior only when a certain load is reached. After exceeding a certain load, the deformation becomes plastic. Materials can have a nonlinear elastic stress-strain curve, in which case the nonlinear elastic model best describes the material. Such models are, for example, the Blatz-Ko rubber model, the Mooney-Rivlin rubber model, and the viscoelastic model. In the inelastic domain, different materials react differently.

[0062] The constitutive model of the material can additionally or alternatively be based on a non-linear plasticity model. In a model undergoing inelastic deformation, both the normal stress and shear stress components of the stress will undergo changes under a combined stress field, which corresponds to the increments of the normal stress or shear stress components of the strain.

[0063] The constitutive model can be one or more models described in "ABAQUS Analysis User's Guide, Part V: Materials" (Dassault Systemes Simulia, Inc).

[0064] The constitutive model can be one or more models described in "LS-DYNA Keyword User's Manual, Volume II - Material Models" (2021, Livermore Software Technology Corporation).

[0065] The constitutive model can be one or more of the following models: a linear elastic model based on Hooke's law; a linear viscoelastic model; a hyperelastic model (e.g., Arruda-Boyce model, Ogden model, Marlow model, Mooney-Rivlin model, Neo-Hookean model, polynomial model); a linear elastic isotropic strain hardening plasticity model (Mises or Hill yield surfaces and their associated plastic flow, allowing isotropic and anisotropic yielding respectively); an ABAQUS model (such as ABAQUS perfect plasticity model, ABAQUS isotropic hardening model, ABAQUS kinematic hardening model or ABAQUS direct input test data model (e.g., ABAQUS direct input test data model, ABAQUS bilayer viscoplastic model, ABAQUS yield stress ratio model, ABAQUS ductile metal progressive damage and failure model or ABAQUS fiber-reinforced material progressive damage and failure model)); Johnson-Cook isotropic hardening model; Drucker-Prager model; Mohr-Coulomb plasticity model; crushable foam plasticity model; Ramberg-Osgood plasticity model; LS-DYNA MAT_24 model; Johnson-Cook rate-dependent model; Bergstrom-Boyce model; Bergstrom three-network model; Bergstrom hybrid model; LS-DYNA SAMP-1 model; and / or LS-DYNA models (such as MAT_81, MAT_105, MAT_107 or MAT_120 volumetric damage models (Lemaitre), metal non-volumetric damage models (Gurson), plastic non-volumetric damage models (SAMP), crack modeling)).

[0066] In a preferred embodiment, one or more experimental force-displacement signals are recorded during an impact loading experiment.

[0067] According to another aspect, a non-transitory computer-readable storage medium is provided for tangibly storing computer program instructions executable by a processor, the computer program instructions defining the steps of the above method. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Embodiments of the present application are illustrated by way of example and are not limited by the figures in the drawings, where the same reference numerals represent similar elements.

[0069] Figure 1 An exemplary flowchart showing the method steps of a computer-implemented method according to the present application;

[0070] Figure 2 An exemplary structure of an artificial neural network for performing the method steps of a computer-implemented method according to the present application;

[0071] Figure 3a An exemplary input data set according to the present application is shown;

[0072] Figure 3b An exemplary output parameter set according to the present application is shown;

[0073] Figure 4 An exemplary optimization scheme is shown;

[0074] Figures 5a to 5c Illustrates the corresponding experimental IPT, INC, and tensile curves of polymer material A at different temperatures from -30°C to 50°C;

[0075] Figures 6a to 6c Illustrates the corresponding experimental IPT, INC, and tensile curves of polymer material B at different temperatures from -30°C to 50°C;

[0076] Figures 7a to 7d Illustrates the output parameters representing the material properties of material A in a graphical form; and

[0077] Figures 8a to 8d Illustrates the output parameters representing the material properties of material B in a graphical form.

[0078] REFERENCE NUMERALS

[0079] 100: Method

[0080] 101 - 109: Method steps

[0081] 200: Artificial Neural Network (ANN)

[0082] 201: ANN input neuron

[0083] 202: ANN intermediate (hidden) neuron

[0084] 203: ANN output neuron

[0085] 301: Input data (value) set

[0086] 302: Output parameter (value) set

[0087] 400: Optimization scheme

[0088] 401: Target / fitting unit

[0089] IPT: Instrumented impact penetration test

[0090] INC: Instrumented (V-notch) Charpy test

[0091] TEN: Tensile test

[0092] F max : Ultimate load

[0093] U max : Deflection under F max

[0094] E br : Peak load

[0095] σ y : Yield stress Detailed implementation manners

[0096] Figure 1 An exemplary flowchart showing the method steps of the computer-implemented method 100 according to the present application is presented. The optional steps in method 100 are represented by dashed lines.

[0097] This method is used to output parameter values describing at least one elastoplastic mechanical response of one or more materials.

[0098] In step 101, an input step is shown. In step 101, an input step is shown. Here, a data value set of one or more experimental force-displacement signals obtained in a mechanical impact test is input into an optimization algorithm, which further includes a trained artificial neural network (ANN) 200 (see Figure 2 ), which includes one or more neural processing units.

[0099] In an optional step ( Figure 1 not shown), a characterization step is shown, in which several input data values input in step 101 are further reduced.

[0100] ​In step 102, an optimization algorithm (optimization scheme) is shown. In this optimization algorithm, combinations of parameter values are searched for to make the difference between the input parameters (step 101) and the prediction results of the artificial neural network 200 for these parameter values as small as possible (best fit).

[0101] In step 108, an output step is shown. In this step, the optimization algorithm 102 outputs a combination of parameter values 302 (e.g., as listed in Figure 3b ), and this combination of parameter values 302 makes the difference between the set of input data values based on the experimental force-displacement signal 101 and the prediction results of these signals obtained from the ANN 200 using the combination of parameter values guessed in step 106 reach a predetermined minimum difference. If multiple experimental signals are used as inputs (e.g., INC, IPT, and TEN, as well as different test temperatures), the optimization loop will simultaneously generate sets of optimized parameter values 301, each corresponding to a specific strain rate and temperature of the corresponding input signal (as shown in Figure 4 ). These sets of parameter values are constrained by Formulas 1 and 2, such that the optimization algorithm generates the parameter sets shown in Table 4. Therefore, the optimization can determine the temperature-viscoplastic-viscoelastic material properties.

[0102] The optimization algorithm includes a comparison step 103. Here, the set of input data values obtained experimentally (step 101) is compared with the predicted (force-displacement) signals obtained from the ANN 200. Initially, these predicted signals of the ANN 200 are generated using the initial guess results of the parameters 301.

[0103] After the comparison step 103 is a decision step 104, where the comparison result (providing the difference between the input and the prediction) is compared with one or more stopping criteria (e.g., the minimum difference (best fit) criterion). If it is determined in step 104 that the stopping criteria are met (the "yes" case), the optimization algorithm ends, and the obtained parameter values are output in step 108.

[0104] If it is determined in step 104 that the stopping criteria are not met (the "no" case), the optimization algorithm continues. Then, the ANN 200 obtains new guess results of the input values 301 in step 106 (these guess results are automatically generated by the optimization algorithm), and predicts the corresponding force-displacement signals based on these input data values 301 in step 107. This step 106 can also be referred to as the "local input" of the artificial intelligence (AI) model executed by the optimization algorithm. Then, in step 107, the AI model predicts the force-displacement signals as the "local output". This prediction result is generated based on the ANN 200 that has been trained in advance using finite element simulations. Then, the output (prediction result) of step 107 is fed back to the comparison step 103.

[0105] As long as the stop criterion in step 104 is not satisfied, the optimization algorithm utilizes the prediction results from step 107 and calculates the output parameters. Thus, the optimization algorithm is an optimization loop, preferably a multi-objective optimization algorithm, and most preferably a genetic multi-objective optimization algorithm, which is used to iteratively search for a combination of material properties that best fits the input data set. The input data set represents one or more force-displacement signals obtained from a mechanical shock test. In the optimization algorithm 102 with steps 103 and 104, a combination of parameter values of the material model is searched for by the optimization algorithm. This combination of parameter values of the material model results in a minimum difference (referred to as "best fit") between the input data value set 101 and the simulation obtained by using the guessed results of the parameter values 301 of the material model.

[0106] For the implementation of the present application, the computer program product may include the following three key elements: (1) a neural network-based model NNM, which includes one or more neural processing units and can predict the necessary characteristics of a shock test for any given set of material parameters; (2) a neural network parameter set NNS, which stores the parameter values learned by the NNM. The NNS is trained using a database that is generated through a large amount of calculations (e.g., through finite element simulations); and (3) a multiple optimization scheme, which uses the NNM to find the set of material parameters that best fits a given experiment according to a selected criterion.

[0107] The input data value set 101 of the optimization loop (step 102) is based on experimental data, and the material properties should be determined according to this experimental data.

[0108] The experimental data most preferably used as the basis of the present application is, for example, obtained from quasi-static tensile tests (TEN) at two different temperatures (i.e., -30 °C and +23 °C).

[0109] The experimental data most preferably used as the basis of the present application is, for example, obtained from an instrumented impact piercing test (hereinafter referred to as IPT).

[0110] The experimental data most preferably used as the basis of the present application is, for example, obtained from an instrumented Charpy impact test (hereinafter referred to as INC). In principle, the Charpy impact test can be a V-notch Charpy impact test or an unnotched Charpy impact test.

[0111] These tests (TEN, INC, IPT) generate numerical data in the form of force-displacement signals (curves). In method 100, a combination of material properties that best fits these experimental results obtained from the TEN, INC, and IPT tests can be found by reducing the computational and time workload.

[0112] Since the experimental data is represented in the form of multi-point force-displacement signals (curves), it is advantageous to reduce the input value set of step 101 to a smaller input value set that contains the most important information in a condensed form. This allows for a more compact artificial intelligence model, speeds up model calibration, eliminates artificial traces, and allows for parameter weight regularization. This feature extraction step requires domain knowledge and an understanding of the entire test system.

[0113] Exemplarily, for IPT and INC, the defined features are:

[0114] ● Ultimate load F max

[0115] ● Deflection U max (at F max )

[0116] ● Area under the force-displacement signal when the force drops by up to 5% at the peak load E br .

[0117] Exemplarily, for TEN, the defined features are:

[0118] ● Slope E of the least squares regression corresponding to between 0.05% and 0.25% strain

[0119] · Yield stress σ y .

[0120] The purpose of the constitutive material model is to describe the mechanical behavior of the material. In the example shown, a linear elastic isotropic strain hardening Mises plastic model has been used, and its input parameters can be input in tabular form in ABAQUS. These input parameters are the input data set 301 of ANN 200. As mentioned above, other constitutive material models can also be used to describe the mechanical behavior of the material.

[0121] The specific material model shown is neither strain rate dependent nor temperature dependent. However, since the strain rate of each of the three types of experimental data (TEN, INC, IPT) considered is different, and each test providing the experimental data is conducted at a different temperature, it is necessary to have a strain rate dependent and / or temperature dependent material model.

[0122] In this example, the nonlinear elastic model

[0123]

[0124] and the nonlinear plastic model

[0125]

[0126] It is implemented in the optimization loop, as shown in 400.

[0127] Equation (1) represents the strain rate and temperature-dependent elastic additional model, and Equation (2) represents the strain rate and temperature-dependent plastic additional model.

[0128] As shown in the figure, the implemented material model also calibrates the failure parameters by implementing a ductile damage model related to temperature and stress triaxiality:

[0129]

[0130] where, is the equivalent plastic strain at the occurrence of ductile damage. As shown in the figure, the complete definition of the implemented material model requires a total of five temperature and strain rate correlation parameters and six failure parameters to be determined, as shown in Table 1 below:

[0131] Table 1 - Temperature and Strain Rate Correlation Parameters and Failure Parameters

[0132]

[0133] The "Boundary" column in Table 1 reflects the boundaries of each individual parameter. Parameters with only a single value listed in this column are fixed, so there is no need to determine the boundaries of that parameter.

[0134] As described above, the calculated FE simulations are used to generate (form) a database to train the ANN 200. Then, the ANN 200 replaces (substitutes) these FE simulations by providing a faster response in the mapping step 107.

[0135] As described above, the FE simulations only consider the elastoplastic response, while the calibration of the strain rate dependence, temperature dependence, and failure parameters is considered through Equations (1) to (3), for example, in the optimization step 104. 36,878 INC simulations and 22,755 IPT simulations have been run separately. Each simulation involves different parameter combinations based on the values shown in Table 2 below:

[0136] Table 2 - Elastoplastic Material Parameters for Creating the FE Simulation Database Used in the Mapping Step 103

[0137]

[0138] Figure 2 Shows the exemplary structure of the artificial neural network 200 used in method 100 (specifically for the mapping step 103 as Figure 1 shown).

[0139] An artificial neural network (ANN) uses a network of neurons 201, 202, 203 to process a set of input values input to the ANN 200 and generate output parameters 302 from the ANN 200. For example, in Figure 1 In step Figure 1 102, each neuron 201, 202, 203 in the ANN 200 receives the input data set 301. Some of the input data values 301 of the neurons may be the outputs of some other neurons in the ANN 200. Some of the inputs to the neurons may be the inputs provided to the ANN 200. The input / output relationships between the neurons 201, 202, 203 in the ANN 200 represent the neuron connections in the ANN 200.

[0140] For example, each neuron 201, 202, and 203 may have a set of biases, activation functions, and synaptic weights 204 for its inputs respectively. The activation function can be in the form of a step function, a linear function, a log-sigmoid function, etc. Different neurons 201, 202, 203 in the ANN 200 may have different activation functions.

[0141] For example, each neuron 201, 202, 203 can generate a weighted sum of its inputs and a bias, and then produce an output that is a function of the weighted sum and is calculated using the activation function of the neuron 201, 202, 203.

[0142] The relationship between the inputs and outputs of the ANN 200 is typically defined by an ANN model that includes data representing the connections of the neurons 201, 202, 203 in the ANN 200, as well as the bias, activation function, and synaptic weights of each neuron 201, 202, 203. Based on a given model, a computing device can be configured to calculate the output of the ANN 200 according to a given set of inputs provided to the ANN 200.

[0143] Typically, the ANN 200 can be trained using a supervised method, where the parameters in the ANN 200 are adjusted to minimize or reduce the error between a known output associated with or produced by a corresponding input and a calculated output generated by applying the input to the ANN 200. Examples of supervised learning / training methods include reinforcement learning and learning with error correction.

[0144] Optionally or in combination, the ANN 200 can be trained using an unsupervised method, where the exact output produced by a given set of inputs is unknown until the training is complete. The ANN 200 can be trained to classify an item into multiple categories, or to classify data points into multiple clusters.

[0145] For complex machine learning / training paradigms, multiple training algorithms can be employed.

[0146] Deep learning uses multiple layers of machine learning to gradually extract features from input data. For example, the lower layers can be configured to identify image edges; the higher layers can be configured to identify the items captured in the image, such as faces, objects, events, etc., based on the edges detected using the lower layers. Deep learning can be implemented by an ANN 200 such as a deep neural network, a deep belief network, a recurrent neural network, and / or a convolutional neural network.

[0147] At least some embodiments disclosed herein provide a general integrated circuit device configured to perform the calculations of ANN 200. The integrated circuit device may include a deep learning accelerator (DLA) and a random access memory (RAM) and / or a direct media access (DMA) controller. The integrated circuit device may be configured with separate connections for concurrent access to the RAM.

[0148] The DLA may include a set of general-purpose programmable hardware computing logics that are specialized or optimized for performing parallel vector and / or matrix calculations, including but not limited to the multiplication and accumulation of vectors and / or matrices. In addition, the DLA may include one or more arithmetic logic units (ALUs) for performing arithmetic and bitwise operations on integer binary numbers.

[0149] The DLA can be programmed through a set of instructions to perform the calculations of ANN 200.

[0150] The granularity at which the DLA operates on vectors and matrices corresponds to the maximum unit of vectors / matrices that the DLA can operate on during the execution of one instruction. During an instruction that performs a predefined operation on vector / matrix operands, the DLA can operate on the elements of the vector / matrix operands in parallel to reduce the execution time and / or energy consumption associated with memory / data access. The operations performed on the vector / matrix operands at the DLA granularity can be used as building blocks to implement the calculations on larger-sized vectors / matrices.

[0151] Typical / practical implementations of ANN 200 involve vector / matrix operands whose sizes are larger than the operation granularity of the DLA. To implement such ANN 200 using the DLA, the calculations involving large-sized vector / matrix operands can be decomposed into calculations of vector / matrix operands at the DLA granularity. The DLA can be programmed through instructions to implement the calculations involving large vector / matrix operands. For example, the atomic calculation capabilities of the DLA in manipulating vectors and matrices at the DLA granularity in response to instructions can be programmed to implement the calculations in ANN 200.

[0152] A typical ANN 200 can be described / specified in a standard format (e.g., Open Neural Network Exchange (ONNX)). A compiler can be used to convert the description of the ANN 200 into an instruction set for the DLA to execute the calculations of the ANN 200. The compiler can optimize the instruction set to improve the performance of the DLA in implementing the ANN 200.

[0153] For example, the input data stream 301 to the ANN 200 can be configured in the form of a series of input data sets. Each input data set is the input set to the ANN within a time slot. When the DLA calculates the output of the current input set, the DMA controller can store the next input set in the RAM, and the CPU can concurrently retrieve the output generated for the previous input set from the RAM. Thus, the task of preparing and processing the input data to the ANN 200 can be offloaded from the CPU. The combination of the DLA, RAM, and DMA controller can act as an independent provider for supplying the results from the ANN 200 to the CPU. The CPU can retrieve the output set when the output is needed. When the output from the ANN 200 is not required, the CPU can instruct the DMA controller to pause the operation of supplying inputs to the ANN. Subsequently, when the output from the ANN 200 is needed, the CPU can instruct the DMA controller to resume the operation of loading the input data into the RAM.

[0154] To model the IPT and INC tests of the ANN 200 as shown Figure 2 to perform the mapping step 107 in Figure 1 , a feedforward multi-layer perceptron neural network model can be implemented, preferably using the Scikit-Learn Python library here. Each test (IPT, INC) generates an ANN model with its respective hyperparameters.

[0155] As shown Figure 2 , the network input neurons 201 are fed with the material parameters defined in Table 2. Figure 3a Lists the preferred input data sets for predicting material properties based on IPT and INC tests.

[0156] The network uses neurons 203 to output (predict) the characteristics of TEN, IPT, and INC listed above as output parameters 302, as follows:

[0157] For the IPT and INC tests, the output parameters 302 are (see also Figure 3b ):

[0158] · Ultimate load F max

[0159] · Deflection U max (at F maxwhen)

[0160] · At the peak load E br the area under the force-displacement signal when the force drops by up to 5%.

[0161] As Figure 2 shown, ANN 200 has two hidden layers, containing N (1) and N (2) neurons 202 respectively. For each layer, the rectified linear unit activation function can be used to introduce non-linearity.

[0162] For training INC and IPT of ANN 200, an optimization algorithm (e.g., direct grid search method) can be adopted to determine the model hyperparameters, as listed in Table 3 below:

[0163] Table 3 - AI model hyperparameters

[0164]

[0165] To calibrate the material model, which means determining the material properties that best fit the experimental results of the input data 301, a multi-objective optimization algorithm as Figure 1 shown is adopted, and more detailed details are as Figure 4 shown.

[0166] Thus, when the algorithm searches for the optimal solution (= the predetermined minimum difference between the set of data values 301 input in the input step 102 and the finite element simulation performed with the combination of parameter values 302), this search must be performed simultaneously for all mechanical shock tests (such as INC, IPT, tensile test) at all temperatures, while also satisfying the additional constraints imposed by the strain rate and temperature correlations described by formulas (1) to (3).

[0167] Figure 4 Illustrates a framework that allows any number of experiments to be performed in a grid of representative strain rates and temperatures, i.e., mechanical shock tests (e.g., INC, IPT, TEN). It can be found that formulas (1), (2), and (3) define the combined constitutive output parameters 302. The entire scheme generates a table of material properties, as shown in Table 4:

[0168] Table 4 - Material properties determined in this application

[0169]

[0170] These material properties in Table 4 have been calibrated for different temperatures and strain rates. The set of output parameters 302 according to Table 4 are the thermo-viscoelastic-viscoplastic model parameters.

[0171] Figure 4Illustrates the complete parameter determination scheme using ANN 200 in the optimization scheme 400. The feedback loop provides the elastic and plastic parameters to ANN 200 and compares the output values of ANN 200 with the target / fitting unit 401.

[0172] The generalization performance of ANN 200 is listed in Table 5. This generalization performance is quantified by the coefficient of determination (R2) and the mean absolute error (MAE).

[0173] Table 5 - Generalization Performance of ANN 200

[0174]

[0175] To run the optimization scheme 400, six calibration experiments were conducted, namely the IPT experiment at 23 °C, the IPT experiment at -30 °C, the INC experiment at 23 °C, the INC experiment at -30 °C, the TEN experiment at -30 °C, and the TEN experiment at 30 °C. The remaining IPT and INC experiments conducted at 0 °C, 30 °C, and 50 °C were only used for verification to evaluate the accuracy of ANN 200 in predicting these experimental curves. The optimization scheme 400 was configured to run for 100 generations with a population of 200 individuals per generation, which represents the set within the range of Table 1.

[0176] Figures 5a to 5c Illustrates the corresponding IPT, INC, and tensile experimental curves of polymer material A at two different temperatures. The composition of material A is: 59.7 wt.-% post-consumer recycled polypropylene (commercially available from Borealis AG, density according to ISO1183 is 915 kg / m 3 , melt flow rate 2 (MFR2) at 230 °C according to ISO 1133 is 20.0 g / 10 min) + 40 wt.-% HECO1 (multi-phase polypropylene, commercially available from Borealis AG, MFR2 at 230 °C according to ISO 1133 is 11.0 g / 10 min, and intrinsic viscosity is 2.1 dl / g) + 0.3 wt.-% Irganox B225 (antioxidant, commercially available from BASF). Whenever material A is mentioned hereinafter, it refers to this composition.

[0177] Figures 6a to 6c Illustrates the corresponding IPT, INC, and tensile experimental curves of polymer material B at two different temperatures. The composition of material B is: 79.7 wt.% post-consumer recycled plastic blend PE / PP (commercially available from Borealis AG, density according to ISO 1183 is 940 kg / m 3, the MFR2 at 230 °C according to ISO 1133 is 5.5 g / 10 min) + 20 wt.% - Queo 8201 (ethylene-1-octene plastomer, commercially available from Borealis AG, density according to ISO 1183 is 883 kg / m 3 , the MFR2 at 190 °C according to ISO 1133 is 1.1 g / 10 min) + 0.3 wt.-% Irganox B225 (antioxidant, commercially available from BASF). When referring to Material B below, this composition is meant.

[0178] Figure 5a and Figure 6a show the corresponding IPT experimental curves of Materials A and B at different temperatures from -30 °C to 50 °C.

[0179] Figure 5b and Figure 6b show the corresponding INC experimental curves of Materials A and B at different temperatures from -30 °C to 50 °C.

[0180] Figure 5c and Figure 6c show the corresponding tensile experimental curves of Materials A and B at the temperatures of -30 °C and 23 °C.

[0181] According to Figures 5a - 5c and Figures 6a - 6c , the IPT, INC, and TEN curves at different temperatures from -30 °C to 50 °C are given as the corresponding input data value sets. Based on these input data value sets, the material properties in a relatively wide temperature and strain rate range can be extracted as described above. Here, the term "material properties" should be understood as the set of constitutive output parameters that define the thermo-viscoelastic-viscoplastic response and failure response of the material listed in Table 4.

[0182] Figures 5a - 5b and Figures 6a - 6b show the experimental force-displacement signals of the IPT and INC impact tests of Materials A and B respectively. The x and y coordinates of the dot symbol (·) correspond to the experimental ultimate load F max and the experimental deflection U max characteristics respectively. The x and y coordinates of the x symbol (x) correspond to the predicted ultimate load F max and the predicted deflection U max characteristics respectively.

[0183] Figures 5a - 5b and Figures 6a - 6b The numerical values at the bottom of each chart in brThe force decline amplitude of the feature, where the calibration value is shown by an asterisk (*). For this example, the fitting accuracy and extrapolation ability of the present application can be evaluated by comparing the positions and amplitudes of the experimental features with those of the predicted features. For the experimental curves at -30°C and +23°C, the result is fitting (the best fit as the difference is the smallest). However, for all other curves (0°C, +30°C, and +50°C - shown with a gray background), the results are actually predictions as these experimental curves were not used to extract the constitutive output parameters.

[0184] Figures 7a to 7d Illustrates the output parameters representing the material properties of Material A in graphical form. Figures 8a to 8d Illustrates the output parameters representing the material properties of Material B in graphical form. This information can be directly used to represent the thermo-viscoelastic-viscoplastic response and failure response of Material A or Material B when designing components, typically using the finite element method for simulation.

[0185] Figure 7a Illustrates the functional relationship of the Young's modulus (elastic modulus in MPa) of Material A with temperature (in degrees Celsius) and strain rate (in 1 / s). Figure 7b Illustrates the functional relationship of the initial yield stress (yield stress in MPa) of Material A with temperature (in degrees Celsius) and strain rate (in 1 / s). Figure 7c Illustrates the functional relationship of the yield hardening (hardening parameter in MPa) of Material A with the plastic equivalent strain. Figure 7d Illustrates the functional relationship of the initial damage strain (failure strain) of Material A with temperature (in degrees Celsius) and the stress / strain multiaxial state.

[0186] Figure 8a Illustrates the functional relationship of the Young's modulus (elastic modulus in MPa) of Material B with temperature (in degrees Celsius) and strain rate (in 1 / s). Figure 8b Illustrates the functional relationship of the initial yield stress (yield stress in MPa) of Material B with temperature (in degrees Celsius) and strain rate (in 1 / s). Figure 8c Illustrates the functional relationship of the yield hardening (hardening parameter in MPa) of Material B with the plastic equivalent strain. Figure 8d Illustrates the functional relationship of the initial damage strain (failure strain) of Material B with temperature (in degrees Celsius) and the stress / strain multiaxial state.

[0187] The present disclosure includes methods, apparatuses for performing the above methods, including data processing systems for executing these methods, and computer-readable media containing instructions that, when executed on the data processing systems, cause the systems to execute these methods.

[0188] A non-volatile memory can be a local device directly coupled to the remaining components in a data processing system. A non-volatile memory that is remote from the system can also be used, such as a network storage device coupled to the data processing system through a network interface such as a modem or an Ethernet interface.

[0189] In this disclosure, for simplicity of description, some functions and operations are described as being performed or caused by software code. However, such an expression is also used to specify that these functions are the result of a processor, such as a microprocessor, executing code / instructions.

[0190] Alternatively or in combination, the functions and operations described herein can be implemented using special-purpose circuits such as application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs) with or without software instructions. Embodiments can be implemented using hardwired circuits without software instructions or in combination with software instructions. Thus, these techniques are not limited to any particular combination of hardware circuits and software, nor to any particular source of the instructions executed by the data processing system.

[0191] Although one embodiment can be implemented in a fully functional computer and computer system, various embodiments can be distributed as a computing product in a variety of forms and can be applied regardless of the particular type of machine or computer-readable medium used for actual distribution.

[0192] At least some aspects of the disclosure can be embodied, at least in part, in software. That is, these techniques can be implemented in a computer system or other data processing system in response to a sequence of instructions contained in a memory, such as a ROM, volatile RAM, non-volatile memory, cache, or remote storage device, being executed by its processor, such as a microprocessor.

[0193] The routines executed to implement an embodiment can be implemented as part of an operating system or a specific application, component, program, object, module, or sequence of instructions (referred to as a "computer program"). A computer program typically includes one or more instructions set at various times in various memories and storage devices in a computer, and when the instructions are read and executed by one or more processors in the computer, cause the computer to perform the operations required to involve elements of the various aspects.

[0194] A machine-readable medium can be used to store software and data, which, when executed by a data processing system, cause the system to perform various methods. The executable software and data can be stored in various locations, such as including ROM, volatile RAM, non-volatile memory, and / or cache. A portion of the software and / or data can be stored in any of these storage devices. Additionally, data and instructions can be obtained from a centralized server or a peer-to-peer network. Different portions of the data and instructions can be obtained from different centralized servers and / or peer-to-peer networks at different times, in different communication sessions, or in the same communication session. The data and instructions can be obtained in their entirety before the application is executed. Alternatively, portions of the data and instructions can also be obtained dynamically and on-the-fly when needed for execution. Thus, the data and instructions do not have to be stored in their entirety on the machine-readable medium at a particular moment.

[0195] Examples of computer-readable media include, but are not limited to, non-transitory, recordable, and non-recordable media such as: volatile and non-volatile memory devices, read-only memory (ROM), random access memory (RAM), flash memory devices, floppy disks, and other removable optical disks, magnetic disk storage media, optical storage media (e.g., compact disc read-only memory (CD ROM), digital versatile disc (DVD), etc.), and the like. The computer-readable medium can store instructions.

[0196] Instructions can also be embodied in digital and analog communication links for electrical, optical, acoustic, or other forms of propagated signals (such as carrier waves, infrared signals, digital signals, etc.). However, propagated signals such as carrier waves, infrared signals, digital signals, etc. are not tangible machine-readable media and are not configured to store instructions.

[0197] Generally, a machine-readable medium includes any mechanism that provides (i.e., stores and / or transmits) information in a form accessible by a machine (e.g., a computer, a network device, a personal digital assistant, a manufacturing tool, any device having one or more processor sets, etc.).

[0198] In various embodiments, hardwired circuitry can be used in combination with software instructions to implement these techniques. Thus, these techniques are not limited to any particular combination of hardware circuitry and software, nor to any source of the instructions executed by the data processing system.

[0199] The above description and the drawings are for illustrative purposes only and should not be considered limiting. The description of many specific details is intended to provide a thorough understanding. However, in some cases, well-known or conventional details have not been described to avoid obscuring the description. References to "one embodiment" or "an embodiment" in this disclosure do not necessarily refer to the same embodiment. Such references mean at least one.

[0200] In the foregoing specification, the present disclosure has been described with reference to specific exemplary embodiments. Obviously, various modifications can be made to it without departing from the broader scope set forth in the appended claims. Accordingly, the specification and drawings are to be regarded as illustrative rather than restrictive.

Claims

1. A computer-implemented method (100) for outputting parameter values that describe at least one elastoplastic mechanical response of one or more materials, preferably one or more polymers, characterized in that, The method includes the following steps: Input (101) a set of data values of one or more experimental force-displacement signals obtained in a mechanical shock test into an optimization algorithm (102); Through the optimization algorithm (102), search (103, 104) for a combination of parameter values (301) of a material model representing one or more material properties, wherein the combination of the parameter values (301) causes a difference between the set of data values input in the input step (101) and the prediction result (107) of the parameter values, and the prediction result is based on an estimation preferably performed by a trained artificial neural network (200), and the artificial neural network (200) is trained using a finite element simulation based on one or more mechanical tests; and Output (108) the parameter values from the optimization algorithm (102), and the parameter values cause the difference between the set of data values input in the input step (101) and the finite element simulation or its estimation performed by the artificial neural network (200) to reach a predetermined minimum difference.

2. The computer-implemented method (100) according to claim 1, wherein Before the output step (108), the method further includes: Predict (107) the one or more force-displacement signals using the trained artificial neural network, wherein the artificial neural network includes one or more neural processing units, and Based on one or more mechanical shock tests, map the material properties representing the constitutive model to the set of data values through the trained artificial neural network.

3. The computer-implemented method (100) according to claim 1 or 2, characterized in that The output parameter values describe at least one strain rate-dependent mechanical response and / or at least one temperature-dependent mechanical response, Wherein, preferably, the at least one strain rate-dependent mechanical response and / or the at least one temperature-dependent mechanical response are considered in the optimization algorithm.

4. The computer-implemented method (100) according to any one of the preceding claims, characterized in that The trained artificial neural network (200) includes one or more feedforward multi-layer perceptron neural network models, Wherein, for each mechanical test, a neural network model with its own hyperparameters is generated, and each model has at least two hidden layers for neurons (202).

5. The computer-implemented method (100) according to any one of the preceding claims, characterized in that The one or more mechanical tests are: Instrumented Charpy impact test; Instrumented Izod impact test; Instrumented piercing test; Instrumented drop weight test; and / or Tensile tests at different temperatures.

6. The computer-implemented method (100) according to any one of the preceding claims, characterized in that The artificial neural network (200) is trained using data from a database of multiple finite element simulations to map one or more mechanical properties to corresponding force-displacement signals.

7. The computer-implemented method (100) according to any one of the preceding claims, characterized in that The input data value set is a numerical data set in the form of at least one multi-point force-displacement signal. Preferably, the data value set represents one or more of the following data: elastic data, plastic data, rate-dependent yield data, damage data, and / or failure data.

8. The computer-implemented method (100) according to one of the preceding claims, characterized in that, Before the input step (101), the method further includes: A feature extraction step in which the number of input data values is reduced. Preferably, the input data values are represented by one or more of the following parameters: Ultimate load (F max ); Deflection (U max ); Peak load (E br ) force drops; The slope (E) of the least squares regression corresponding to a strain between 0.05% and 0.25%; and / or The stress at the yield point (σ y ).

9. The computer-implemented method (100) according to one of the preceding claims, characterized in that The material properties are based on a thermo-viscoelastic-viscoplastic model, and the parameter values are preferably one or more of the following: A specific geometry; Temperature; Strain rate-dependent stiffness; Yield; and Failure strain.

10. The computer-implemented method (100) according to one of the preceding claims, characterized in that The output parameter values include at least one intrinsic material property, and the output parameter values describe features suitable for predicting the material properties under conditions beyond the input data value set.

11. The computer-implemented method (100) according to any one of claims 2-10, characterized in that, The constitutive model is based on a nonlinear elastic model or a nonlinear plastic model. Preferably, there is failure parameter calibration.

12. The computer-implemented method according to any one of claims 2 to 10, characterized in that The constitutive model is one or more of the following models: A linear elastic model based on Hooke's law; A linear viscoelastic model; A hyperelastic model; A linear elastic isotropic strain hardening plastic model; An ABAQUS perfect plastic model; An ABAQUS isotropic hardening model; An ABAQUS kinematic hardening model; A Johnson-Cook isotropic hardening model; A Drucker-Prager model; A Mohr-Coulomb plastic model; A crushable foam plastic model; A Ramberg-Osgood plastic model; An LS-DYNA MAT_24 model; An ABAQUS direct input test data model; An ABAQUS bilayer viscoplastic model; An ABAQUS yield stress ratio model; A Johnson-Cook rate-dependent model; A Bergstrom-Boyce model; A Bergstrom three-network model; A Bergstrom hybrid model; An LS-DYNA SAMP-1 model; An ABAQUS ductile metal progressive damage and failure model; An ABAQUS fiber-reinforced material progressive damage and failure model; and An LS-DYNA model.

13. The computer-implemented method according to one of the preceding claims, characterized in that The one or more experimental force-displacement signals are recorded during an impact loading experiment.

14. A non-transitory computer-readable storage medium for tangibly storing computer program instructions executable by a processor, the computer program instructions defining the steps of one of the preceding method claims.

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