Simulating additive manufacturing

Abstract

A method is provided of simulating additive manufacturing in which powder is used to additively manufacture an object The method comprises using a particle model to model application of powder, for example in form of a deposited powder bed, over a substrate layer during the additive manufacture, initiating a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, and executing the simulation model to obtain at least a 3D phase field and a 3D temperature field at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure.

Description

[0001] SIMULATING ADDITIVE MANUFACTURING

[0002] TECHNICAL FIELD

[0003] The invention relates to a method of simulating additive manufacturing in which powder bed deposition is used to additively manufacture an object. The invention further relates to a computer-readable medium comprising data representing instructions for causing a processor system to perform any one of the methods. The invention further relates to a processor system configured to perform the method.

[0004] BACKGROUND

[0005] Additive manufacturing (AM) is significantly impacting the manufacturing industry by introducing new capabilities for producing complex structures. One of the key advantages of AM is the ability to fabricate parts directly from digital models, which is particularly beneficial in environments where traditional manufacturing methods are impractical. For instance, additive manufacturing may be used in aerospace applications to produce lightweight components for spacecraft and may even allow for the manufacturing of parts on-demand during space missions, reducing the need for large numbers of spare parts and decreasing overall mission costs.

[0006] Among the various techniques of additive manufacturing, several utilize powder bed deposition, including Selective Laser Melting (SLM) and Electron Beam Melting (EBM). These techniques involve layer-by-layer deposition of a powder bed, and using a laser or electron beam to selectively fuse deposited powder particles according to a digital blueprint. In other techniques, such as Directed Energy Deposition (DED), powder may be ejected from a nozzle and the ejected powder may be fused. The aforementioned techniques allow for precise control over material properties and enables the production of parts with complex geometries that are often challenging or impossible to achieve with traditional manufacturing methods.

[0007] In applications such as those in the aerospace sector, it is crucial to ensure that each manufactured part meets specific performance and lifetime requirements to guarantee the quality and longevity of the component. Traditional approaches to verifying these requirements can involve destructive testing or advanced imaging techniques, which are not only costly but also time-consuming. Additionally, such methods may be impractical in remote environments like space.

[0008] To address these challenges, simulations may be employed. For example, simulations can predict the formation of pores within the material during its manufacture, which adversely affect the integrity and performance of the part. Besides assisting in the prediction of lifetime or fatigue, simulations may also serve other purposes such as the validation of design accuracy, digital twinning, and estimation of material properties in manufactured parts.

[0009] US2020089826A1 describes a process-structure-property prediction framework for metal additive manufacturing, with an implementation for selective electron beam melting (SEBM) of Ti-6AI-4V. In this framework, each model incorporates basic material information and data provided directly from previous models in the framework to predict the mechanical response and estimated fatigue life of critical microstructures given machine-relevant processing conditions.

[0010] Disadvantageously, US2020089826A1 is insufficiently accurate. It would be advantageous to obtain an improved method for simulating additive manufacturing in which powder bed deposition is used to additively manufacture an object.

[0011] SUMMARY

[0012] In accordance with a first aspect of the invention, a method is provided of simulating additive manufacturing in which powder is used to additively manufacture an object, comprising:

[0013] - accessing a 3D model of the object to be manufactured;

[0014] - determining control parameters for an energy beam to selectively melt and fuse powder regions during additive manufacturing of at least part of the object, wherein the control parameters are indicative of a beam path of the energy beam;

[0015] - simulating the additive manufacturing of the at least part of the object by: using a particle model to model application of powder over a substrate layer during the additive manufacture; initiating a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, wherein the 3D volumetric fields include at least a phase field and a temperature field, wherein initiating the simulation model comprises: importing a geometry and particle size distribution of the powder from the particle model; representing boundary surfaces of the powder as reflective surfaces in the simulation model; configuring the simulation model with emission and absorption coefficients and with phase change coefficients of at least a vapor-to- liquid phase transition of powder and substrate materials to model vapor condensation during the additive manufacture; executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure.

[0016] In accordance with a further aspect of the invention, a transitory or non- transitory computer-readable medium comprising data representing a computer program, the computer program comprising instructions for causing a processor system to perform any of the methods described in this specification.

[0017] In accordance with a further aspect of the invention, a processor system is provided, the processor system comprising a memory and one or more processors, wherein the memory comprises instructions for causing the one or more processors to perform any of the methods described in this specification.

[0018] The above measures involve simulating the additive manufacturing of an object, in which powder is used to additively manufacture the object. The method may involve accessing a 3D model of the object to be manufactured. The 3D model may for example be a geometric 3D model which defines at least a shape of the object, e.g., using vertices and edges. For example, the 3D model may define a component of a space craft. The method may further involve determining control parameters for an energy beam to selectively melt and fuse powder regions to additively manufacture of at least part of the object. The control parameters may be indicative of a beam path of the energy beam, for example by defining how the energy beam should be controlled to follow the beam path. For that purpose, similar techniques may be used as for actual (i.e., non-simulated) additive manufacturing. For example, the method may involve obtaining the control parameters of an energy beam from slicing software which uses layer decomposition to slice the 3D model into a plurality of slices and which generates a beam path for the energy beam to follow to manufacture at least part of a respective slice. In some examples, the control parameters may, in addition to parameters which control the beam to follow the beam path, include other parameters, such as energy level, scan speed, hatch distance, etc.

[0019] The additive manufacturing of at least a part of the object may then be simulated. In some examples, the part of the object of which the manufacture is to be simulated may be selected before start of the simulation. For example, the part may be selected to correspond to a region of interest in the object. In a specific example, the region of interest may be a region which is deemed critical in the manufacture of the object, for example by being a stress concentration point or by being prone to manufacturing artifacts. The simulation may involve providing a particle model and using the particle model to model an application of powder over a substrate layer. For example, in SLM and EBM, the powder may be applied by deposition of a powder bed over the substrate layer, while in DED, powder may be ejected from a nozzle and the ejected powder may accumulate over the substrate layer. The powder may thus be simulated as discrete particles. In addition, a separate simulation model may be initiated which uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing. In particular, the simulation model may simulate at least a phase field which may represent the state of a medium, such as whether it is in a solid, liquid, or gaseous state, and a temperature field which may represent the distribution of temperature. Both fields may be volumetric fields, e.g., 3D fields, and may therefore represent the phase and temperature at a plurality of spatial points in a certain region (of interest), e.g., throughout a 3D region. The term ‘medium’ may include any medium which may be present in the 3D region, such as the powder material, the substrate material and surrounding ambient gas. By also simulating the volumetric fields at different time instances during the additive manufacture, e.g., at different times while the energy beam travels along the beam path, the simulation may provide a 4D phase field and 4D temperature field as output, with the four dimensions (4D) comprising three spatial dimensions, e.g., expressed in x,y,z, and a time dimension, e.g., t.

[0020] The simulation model may be configured before a start of the simulation. For example, a geometry and particle size distribution of the applied powder may be imported from the particle model into the simulation model. Having imported the geometry and particle size distribution of the powder, boundary surfaces of the powder may be identified and represented as reflective surfaces in the simulation model. For example, surfaces between the powder and surrounding ambient gas may be identified and their reflectivity properties may be adjusted to establish the surfaces as reflective surfaces. The simulation model may be further configured with emission and absorption coefficients of at least powder and substrate materials. By way of the emission coefficients, the simulation model may be configured with a material’s ability to emit thermal radiation, which may affect the material’s cooling rate after being heated by incoming radiation, e.g., from the energy beam. By way of the adsorption coefficients, the simulation model may be configured with a material’s ability to absorb incoming radiation, e.g., from the energy beam. The simulation model may be further configured with phase change coefficients of at least a vapor-to-liquid phase transition of powder and substrate materials. Thereby, the simulation model may model vapor condensation during the additive manufacture of the respective line structure.

[0021] The simulation model may then be executed to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer. This way, 4D volumetric fields may be obtained showing respectively temperature evolution and phase changes during the additive manufacture.

[0022] By way of the above measures, a more accurate simulation of the manufacture of (part of) the object may be obtained. The improved accuracy may be obtained due to the thermal behaviour of materials being more accurately modelled. The inventors have had the insight that the thermal behaviour may affect condensation, and that condensation is a significant contributor to anomalies in the manufactured product. Namely, condensation may increase porosity, cause inclusion defects by condensed material being trapped, cause thermal stresses and distortion due to uneven cooling, etc. The claimed measures take the vapor-to-liquid phase transitions into account in the simulation and are thereby able to model such condensation. In addition, the claimed measures provide a more accurate modelling of how thermal energies are managed and dissipated by way of the modelling of reflective surfaces and inclusion of appropriate emission and absorption coefficients. The thermal behaviour affects temperature distributions, which in turn is crucial for the condensation dynamics. By more accurately modelling the thermal behaviour during the additive manufacturing, the condensation dynamics may also be modelled more accurately. Advantageously, the 4D volumetric fields may be indicative of such condensation and in general may be indicative of the presence anomalies in the manufactured object. By analysing the 4D volumetric fields, such anomalies may be identified, which may for example be used for lifetime or fatigue prediction for the manufactured object.

[0023] Optionally, the method further comprises, after simulating the manufacture of the first line structure:

[0024] - using the particle model to model the deposition of a further application of powder to manufacture a second line structure;

[0025] - importing the geometry and particle size distribution of the further powder bed from the particle model into the simulation model;

[0026] - executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of the second line structure to simulate the temperature evolution and phase changes during the manufacture of the second line structure. The simulation model may be used to simulate the manufacture of a second line structure, and by repeatedly performing the above steps, also a third, fourth, etc line structure. For that purpose, the particle model may again be used to model the deposition of another powder bed, or another round of accumulation of ejected powder from a nozzle, the deposited or accumulated powder may again be imported into the simulation model, and boundary surfaces of the powder may again be modelled as reflective surfaces in the simulation model. This way, a longer part of the additive manufacturing process, and / or the manufacture of a larger part of the object, may be simulated, which may allow for more comprehensive follow-up analyses.

[0027] Optionally, the second line structure is horizontally or vertically connected to the first line structure.

[0028] Optionally, the simulation model is configured to model a remelting of solidified parts of the first line structure during the manufacture of the second line structure. By modelling the remelting of previously solidified parts of the first line structure, or in general of previous line structures, the accuracy of the simulation may be further improved since remelting may affect the microstructural properties of the line structure and thereby affect the performance and lifetime of the manufactured object.

[0029] Optionally, the simulation model is configured to, in the phase field, distinguish between at least:

[0030] - a solid phase;

[0031] - a liquid phase;

[0032] - a gas phase, for example of ambient gas;

[0033] - powder; and

[0034] - vapor, for example metal vapor.

[0035] The simulation model may thus be configured to model five different states of material, which may further contribute to the accuracy of the simulation model.

[0036] Optionally, the simulation model is configured with phase change coefficients of a liquid-to-vapor phase transition of the powder and substrate materials to model evaporation, during the additive manufacture. Evaporation, referring to vapor emission, is next to vapor condensation also a significant contributor to anomalies in the manufactured product. Namely, evaporation may lead to material depletion, porosity, and unstable melt pool dynamics, impacting the dimensional accuracy and mechanical properties of the final product. The claimed measures take the liquid-to- vapor phase transitions into account in the simulation and are thereby able to model such vapor evaporation. Advantageously, the 4D volumetric fields may be indicative of vapor evaporation. By analysing the 4D volumetric fields, such anomalies may be identified, which may for example be used for lifetime or fatigue prediction for the manufactured object.

[0037] Optionally, the method further comprises:

[0038] - performing a coarse scale simulation of the deposition of the first line structure without using the particle model to obtain a coarse temperature field; and

[0039] - using the coarse temperature field to set initial temperature boundary conditions for the simulation model.

[0040] The use of computational fluid dynamics to simulate the additive manufacturing may require significant computational resources. To reduce the required computational resources, initial temperature boundary conditions may be set for the simulation model. This may reduce the computational complexity since it may allow the simulation to start from a more stabilized thermal state, eliminating the need to calculate the thermal field from ambient conditions through all transitional states. The initial temperature boundary conditions may be obtained from a coarse scale simulation of the deposition of the first line structure. This coarse scale simulation may omit using the particle model and may instead primarily model the thermal effects of the electron beam. The coarse scale simulation may be coarser by providing a lower resolution volumetric temperature field as output. The computational complexity of determining the initial temperature boundary conditions may thus remain relatively limited.

[0041] Optionally, the particle model is a discrete element simulation model.

[0042] While the following optional aspects refer to the analysis of the 3D volumetric fields, it will be appreciated that they may equally refer to the analysis of the 3D volumetric fields at the respective time instances, and thereby to the analysis of the 4D volumetric fields. Since the 4D volumetric fields are indicative of the temperature evolution and phase changes over time, the 4D volumetric fields may be even more indicative of anomalies forming during the additive manufacture of the object.

[0043] Optionally, the method further comprises analysing the 3D volumetric fields to identify anomalies in said manufactured object, for example by quantifying bead and / or pore formation during the additive manufacturing.

[0044] Optionally, the method further comprises performing lifetime or fatigue prediction for the manufactured object based on said identified anomalies.

[0045] Optionally, the method further comprises analysing the 3D volumetric fields to validate the 3D model of the object and / or the control parameters for the manufacture of the object, and after validation, manufacturing the object using the 3D model and the control parameters. The simulation of the additive manufacturing may be a precursor to the actual manufacturing of the object. For example, the simulation may be performed, its output may be analysed to determine whether the manufactured object meets certain requirements, for example performance and / or lifetime requirements, and if so, the 3D model of the object and / or the control parameters may be validated, with the term ‘validate[ing]’ referring to the approval to be used in the actual manufacturing. If the analysis of the simulation output indicates that the manufactured object does not meet these requirements, the design of the object and / or the control parameters may be modified, and the simulation may be repeated. The modification and simulation steps may be alternately repeated until the manufactured object meets the requirements. This may allow for a quicker and / or less costly design process of an object, compared to a design process in which the designed the object is actually manufactured, then tested, and then redesigned based on the test results, etc.

[0046] Optionally, the method further comprises using the 3D volumetric fields to establish a digital twin of the object. A digital twin may for example be used for virtual testing of manufactured objects, which may be advantageous in environments where the actual testing of manufactured objects is not (easily) possible, e.g., in space.

[0047] Optionally, the method further comprises training a machine learning model, for example a graph neural network, on the 3D volumetric fields obtained from the simulation model and on sets of simulation parameters, a set of simulation parameters characterizing a configuration of the simulation model by which a respective 3D volumetric field is obtained, to be able to predict a 3D volumetric field for an input set of simulation parameters. The use of computational fluid dynamics to simulate the additive manufacturing may require significant computational resources. To reduce the computational complexity, a machine learning model, such as a graph neural network, may be trained to predict the 3D volumetric fields given the simulation parameters, e.g., the control parameters including the beam path, beam power, and generic material properties as input. The execution of a trained machine learning model may be much more computational efficient than the execution of the simulation model. Thereby, the advantages of the simulation model may be largely maintained while greatly reducing the computational complexity compared to a direct use of the simulation model.

[0048] Optionally, the method further comprises using the trained machine learning model to predict 3D volumetric fields and analysing the predicted 3D volumetric fields to identify anomalies in said manufactured object. Instead of using the simulation model to obtain 3D volumetric fields for the manufacture of the object, the machine learning model may be used instead to obtain these fields. Thereby, the advantages of the simulation model may be largely maintained while greatly reducing the computational complexity compared to a direct use of the simulation model.

[0049] In a further aspect of the invention, a method is provided of simulating additive manufacturing in which powder bed deposition is used to additively manufacture an object, comprising:

[0050] - accessing a 3D model of the object to be manufactured;

[0051] - determining control parameters for an energy beam to selectively melt and fuse powder regions during additive manufacturing of at least part of the object, wherein the control parameters are indicative of a beam path of the energy beam;

[0052] - simulating the additive manufacturing of the at least part of the object by: using a particle model to model deposition of a powder bed over a substrate layer during the additive manufacture; initiating a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, wherein the 3D volumetric fields include at least a phase field and a temperature field, wherein initiating the simulation model comprises: importing a geometry and particle size distribution of the powder bed from the particle model; representing boundary surfaces of the powder bed as reflective surfaces in the simulation model; configuring the simulation model with emission and absorption coefficients and with phase change coefficients of at least a vapor-to- liquid phase transition of powder and substrate materials to model vapor condensation during the additive manufacture; executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure.

[0053] Optionally, the method further comprises, after simulating the manufacture of the first line structure:

[0054] - using the particle model to model the deposition of a further powder bed;

[0055] - importing the geometry and particle size distribution of the further powder bed from the particle model into the simulation model;

[0056] - executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a second line structure to simulate the temperature evolution and phase changes during the manufacture of the second line structure.

[0057] In a further aspect of the invention, a method is provided of simulating additive manufacturing in which powder is ejected from a nozzle, comprising:

[0058] - accessing a 3D model of the object to be manufactured;

[0059] - determining control parameters for an energy beam to selectively melt and fuse ejected powder during additive manufacturing of at least part of the object, wherein the control parameters are indicative of a beam path of the energy beam;

[0060] - simulating the additive manufacturing of the at least part of the object by: using a particle model to model accumulation of the ejected powder over a substrate layer during the additive manufacture; initiating a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, wherein the 3D volumetric fields include at least a phase field and a temperature field, wherein initiating the simulation model comprises: importing a geometry and particle size distribution of accumulated powder from the particle model; representing boundary surfaces of the accumulated powder as reflective surfaces in the simulation model; configuring the simulation model with emission and absorption coefficients and with phase change coefficients of at least a vapor-to- liquid phase transition of powder and substrate materials to model vapor condensation during the additive manufacture; executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure.

[0061] The presently disclosed measures are not only applicable to additive manufacturing in which powder bed deposition is used to additively manufacture an object, for example to techniques such as SLM and EBM, but also to additive manufacturing in which powder is ejected from a nozzle, for example as in Directed Energy Deposition (DED). In additive manufacturing which uses powder ejection, powder may be fed into a nozzle and ejected therefrom. As the powder is ejected, it may be heated by an energy beam, such as laser or electron beam, which is directed at the point of deposition. The powder may then melt upon contact with the targeted surface, where the melted powder may solidify to form a new material layer. The nozzle may move according to a predefined path, allowing layers to be built up successively to manufacture (the part of) the object. The advantages described elsewhere in relation to additive manufacturing in which powder bed deposition is used equally apply to the simulation of additive manufacturing in which powder is ejected from a nozzle. In particular, any examples, embodiments and optional aspect described in this specification also apply to the method of simulating additive manufacturing in which powder is ejected from a nozzle, unless precluded for technical reasons.

[0062] It will be appreciated by those skilled in the art that two or more of the above-mentioned embodiments, implementations, and / or aspects of the invention may be combined in any way deemed useful.

[0063] Modifications and variations of any one of the above-mentioned entities (e.g., method, processor system, computer-readable medium), which correspond to the described modifications and variations of another one of these entities, may be carried out by a person skilled in the art on the basis of the present description.

[0064] BRIEF DESCRIPTION OF THE DRAWINGS

[0065] These and other aspects of the invention are apparent from and will be elucidated with reference to the embodiments described hereinafter. In the drawings, Fig. 1 shows an example of additive manufacturing in which powder bed deposition is used to additively manufacture an object;

[0066] Fig. 2 shows the use of a plurality of software modules to simulate additive manufacturing of at least part of an object;

[0067] Figs. 3A-3D show a detailed workflow to simulate additive manufacturing; Fig. 4 shows a flowchart of a method to simulate additive manufacturing; Fig. 5 shows a non-transitory computer-readable medium comprising data.

[0068] Reference signs list

[0069] The following list of references and abbreviations is provided for facilitating the interpretation of the drawings and shall not be construed as limiting the claims.

[0070] 1-8 subphases

[0071] 100 processor system

[0072] 110 control parameters

[0073] 120 energy source (laser) 130 energy beam (laser beam)

[0074] 140 steerable mirror

[0075] 150 focusing lens

[0076] 160 platform

[0077] 170 powder bed

[0078] 180 manufactured line structures

[0079] 200-250 software tools / libraries

[0080] 200 g-code path generation

[0081] 210 coarse mesh-based boundary condition simulation

[0082] 220 discrete element simulation

[0083] 230 multiphase-multiphysics solver

[0084] 240 preparation for high performance computing

[0085] 250 simulation state monitoring on computing platform

[0086] 260 framework to simulate additive manufacturing

[0087] 300 analyze design, assign simulation domain

[0088] 302 choose default or specific

[0089] 304 choose specific

[0090] 306 internal action

[0091] 308 internal action & scale / coordinate transform

[0092] 310 design

[0093] 312 processing parameters

[0094] 314 property and performance requirements

[0095] 316 geometry sizes

[0096] 318 processing times, spaces, velocities

[0097] 320 select region of interest

[0098] 322 create simulation domain

[0099] 324 design of experiment

[0100] 400 compose simulation cases / chains

[0101] 402 boundary condition and initial condition parameters

[0102] 404 dependency graph

[0103] 406 create case / chain

[0104] 408 create process scan pattern

[0105] 410 create mesh 412 create materials model

[0106] 414 material database

[0107] 416 create boundary conditions and initial conditions

[0108] 418 create powder layer

[0109] 420 configure simulation cases / chains

[0110] 422 configure software environment

[0111] 424 simulation configuration set

[0112] 500 run & iterate

[0113] 502 performance requirements

[0114] 504 build software environment

[0115] 506 create and execute run

[0116] 508 spawn child process

[0117] 510 create process monitor

[0118] 512 transform local laser pattern

[0119] 514 simulation configuration sequence

[0120] 600 evaluation and post-processing

[0121] 602 visualization parameters

[0122] 604 set of geometrical visualization objects

[0123] 606 create serial post-processing sequence

[0124] 608 render all serial post-processing cases / chains

[0125] 610 compose post-processed data

[0126] 612 4D temperature profile

[0127] 614 4D porosity field

[0128] 616 virtual test confidence metric

[0129] 700 simulating additive manufacturing

[0130] 710 accessing 3D model of object to be manufactured

[0131] 720 determining control parameters for energy beam

[0132] 730 simulating the additive manufacturing of part of object

[0133] 740 using particle model to model application of powder

[0134] 750 initiating simulation model of the additive manufacturing

[0135] 760 importing applied powder from the particle model

[0136] 770 representing boundary surfaces as reflective surfaces

[0137] 780 further configuring the simulation model 790 executing the simulation model to simulation output

[0138] 800 non-transitory computer readable medium

[0139] 810 data

[0140] DESCRIPTION OF EMBODIMENTS

[0141] Fig. 1 shows an example of additive manufacturing in which powder bed deposition is used to additively manufacture an object. In this example, a laser is used as an energy beam to selectively melt deposited powder particles. The example of Fig. 1 may therefore represent an example of an additive manufacturing technique known as Selective Laser Melting (SLM). It will be appreciated, however, that the measures described in the present disclosure equally apply to other additive manufacturing techniques in which powder bed deposition is used to additively manufacture an object, such as Electron Beam Melting (EBM) and Directed Energy Deposition (DED).

[0142] In the example of Fig. 1 , a processor system 100, which may for example be a personal computer (PC) or a workstation, may generate and transmit control parameters 100 to a laser 120. These control parameters 110 may define the trajectory or path that the laser beam 120 is to follow and the intensity or power level at which the laser is to operate. The laser 120 may produce a coherent light beam, referred to as the laser beam 130. In this example, the path of the laser beam 130 may be manipulated by a steerable mirror 140. This mirror 140 may have the capability to pivot or rotate, thereby allowing the direction of the laser beam 130 to be dynamically adjusted in accordance with the control parameters 110. After reflection, the beam may pass through a focusing lens 150, which may concentrate the laser beam 130 to a precise point on the target surface. The target of the focused laser beam may be a layer of metallic or polymer powder, laid out on a powder bed 170 (with the powder depositing mechanism not being depicted in Fig. 1). The heat of the focused laser beam 130 may be sufficient to melt the targeted regions of the powder, creating a molten pool that solidifies upon cooling. By moving the laser beam 130 methodically across the surface of the powder bed, solid line structures may be created. These lines may be oriented horizontally (along the x-axis) or vertically (along the y-axis) and may be referred to as hatch lines. Additionally, a platform 160 may be provided which may be incrementally lowered as each successive layer is solidified. The platform 160 may support the formation of subsequent layers atop the previously solidified material, marked as 180 in Figure 1. Through the repetitive application of this process, with each successive layer, the system shown in Fig. 1 may be capable of fabricating complex three-dimensional objects in a layer-wise, additive manufacturing manner. The system of devices and other entities of Fig. 1 may collectively be referred to as a 3D printer.

[0143] The presently disclosed measures simulate such and other examples of additive manufacturing in which powder bed deposition is used, or in which powder is ejected from a nozzle, to additively manufacture an object. Figs. 2 and 3A-3D show detailed embodiments of such a method, with the method itself being described with reference to Fig. 4. It is noted that the embodiments shown and described with reference to Figs. 2 and 3A-3D show various specific features and optional features, both of which do not limit the general applicability of the presently disclosed measures.

[0144] Fig. 2 shows a functional diagram illustrating the use of a plurality of software modules to simulate the additive manufacturing of at least part of the object. The framework to simulate the additive manufacturing, e.g., as implemented by the system and method described in this specification, may be represented by the reference numeral 260, with the framework 260 invoking various software tools / libraries 200-250. Input data to the simulation may include a design 310 of the object to be manufactured, for example in form of a CAD model, processing parameters 312 describing characteristics of the used manufacturing process such as the number of lasers, laser focal radius, laser velocity range, and properties such as the powder size and shape statistics. As further input, performance requirements 314 may be used, such as available computing resources and available compute time. The simulation may involve the invocation of software tools / libraries. For example, a g-code path generation software 200 may generate a beam path, a coarse mesh-based boundary condition simulation software 210 may provide a coarse scale simulation to obtain initial boundary conditions for the simulation model, a discrete element simulation software 220 may model deposition of a powder bed over a substrate layer during the additive manufacture as in SLM or EBM, or the ejection of powder from a nozzle over the substrate layer as in DED, and a multiphase-multiphysics solver software 230 may be use computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing. Moreover, Fig. 2 shows a software 240 being used to prepare for high performance computing (HPC), while a simulation state monitoring software 250 may be implemented on the chosen computing platform.

[0145] In a specific example of Fig. 2, the g-code path generation 200 may use pySLM which is a Python-based software tool designed for the simulation and modelling of selective laser melting (SLM) processes. In a specific example, the coarse mesh-based boundary condition simulation 210 may use deal. II which is a C++ library that provides tools for solving partial differential equations using finite element methods. In a specific example, the discrete element simulation 220 may use Liggghts (LAM MPS Improved for General Granular and Granular Heat Transfer Simulations) which is a software designed for discrete element method simulations. In a specific example, the multiphase-multiphysics solver 230 may be OpenFOAM which is a computational fluid dynamics (CFD) software, with pyLightFoam 235 being used to interact with OpenFOAM. In a specific example, the simulation state monitoring 250 may use pyFoam which is a Python library designed for managing, controlling, and analyzing OpenFOAM simulations. It will be appreciated that the above-identified software tools / libraries are merely exemplary and that they may be substituted by any other software tools / libraries, or the simulation may be implemented in any other way.

[0146] Figs. 3A-3D show a workflow showing a detailed embodiment to simulate the additive manufacturing. In these figures, arrows 302 may represent “choose default or specific”, with ‘default’ referring to the pre-selection of one hatch line to explore basic porosity features of the material and without using the detailed CAD geometry of an object to be manufactured, while ‘specific’ refers to the use of the detailed CAD geometry. Moreover, arrows 304 may represent “choose specific”, arrows 306 may represent an internal action, and arrows 308 may represent an internal action and a scale and / or coordinate transformation. It is noted that the workflow represents a specific embodiment and includes various optional features, of which the presence in the workflow is not to be interpreted as limiting the scope of the invention as claimed.

[0147] Fig. 3A illustrates an initial phase 300 of the workflow which may encompass the analysis of the design and assignment of the simulation domain. This phase 300 may use as input data a design 310 of the object to be manufactured, for example in form of a CAD model, the processing parameters 312 describing characteristics of the used manufacturing process such as the number of lasers, laser focal radius, laser velocity range, powder size and shape statistics, and properties such as the powder size and shape statistics. As further input, performance requirements 314 may be used, such as available computing resources and available compute time. From the input data, intermediate data may be generated for defining the simulation scope, for example geometry sizes 316 and processing times, spaces, and velocities, respectively, with the latter being collectively referenced by numeral 318. In step 320, the region of interest for the simulation may be selected, while in step 322 a simulation domain may be created where specific simulations may be performed. In step 324, an experiment may be designed, which may establish a framework for the simulation.

[0148] Fig. 3B shows a second phase 400 which may involve composing simulation cases / chains. A case may be defined as a granular simulation, while a chain may be a composition of multiple cases. The second phase 400 may use as additional input data the boundary condition (BC) and initial condition (IC) parameters, which may be collectively referenced by numeral 402 and used for setting up the simulation environment, and a dependency graph 404 which may map relationships between various simulation parameters. In step 406, cases or chains for the simulation may be created. The second phase 400 may further comprise creating 408 a process scan pattern, creating 410 a mesh, creating 412 a materials model using a materials database 414, creating 416 boundary and initial conditions, creating 418 the powder layer, and configurating 420 the simulation cases / chains. As output of step 420, a simulation configuration parameter set 424 is obtained, which may be used together with the dependency graph 404 to configure the simulation environment in step 422.

[0149] Fig. 3C shows a third phase 500 which may involve running the simulation in an iterative manner. The third phase 500 may use as additional input data performance requirements 502, such as time, computing resources, and power budget. In a step 504, the software environment may be built, and in a step 506, simulation runs may be created and executed. Child processes may be spawned as part of the iterative simulation process, as shown by numeral 508. A process monitor, indicated by numeral 510, may be created to oversee the simulation progression. Local laser pattern transformations may be executed, indicated by numeral 512. In step 514, a specific sequence of simulation steps may be created based on the available set from step 424, for example to ensure numerical stability and robustness of the simulation, as well as precision of the mesh-based results.

[0150] Fig. 3D shows a fourth phase 600 which may involve evaluating and postprocessing the simulated additive manufacturing results. The fourth phase 600 may use as additional input data visualization parameters 602 and a set of geometrical visualization objects to represent the calculated physical fields 604. For example, the geometrical visualization set may comprise geometrical and configuration parameters to create a 3D representation of the physical data. The geometrical visualization set may be generated with a software tool such as Paraview. In step 606, the sequence of physical field to be visualized may be created and may be comprised of multiple serial renders, and in a step 608, the rendering calculations for each serial instance may be performed, and in a step 610, the connected serial instances (e.g., videos) may be grouped and connected based on the physical field that is to be represented. The postprocessed data may for example include a 4D temperature profile 612, a 4D porosity field 614, and a virtual test confidence metric 616. Here, ‘virtual test’ may generally refer to the simulated case / chain. The 4D porosity field 614 may for example be obtained by analysing a 4D phase field (not explicitly shown in Fig. 3D). In some examples, the fourth phase 400 may additionally output the 4D phase field.

[0151] Figs. 3A-3D further show various subphases using numerals 1-7 which relate to one or more of the aforementioned steps. These subphases may include a first subphase 1 (not shown in Figs. 3A-3D) which may involve initializing the simulation environment. A second subphase 2 may be summarized as ‘CAD design interpretation and laser strategy formation’. In this second subphase, the baseline for all subsequent tasks within the simulation may be established. A CAD design intended for production may be analysed, and a laser processing strategy may be chosen. Instead of directing this data to a physical 3D printer, e.g., of the type as shown in Fig. 1, the data may be utilized to generate a laser path for the simulation. This may involve aligning the spatial and temporal steps, as well as the underlying coordinate system for the simulation. These calculations may be used to define the 3D size of the simulation domain and determine the number of these domains. For example, a default scenario may involve printing a single horizontal hatch track for a specified material and supplementing this with a proximate additional horizontal track. Moreover, a vertical hatch track may be established on top of this assembly, which may provide insights into remelting and morphology alterations during the remelting of the initial tracks. Through this methodology, various combinations of laser processing paths and simulation domains may be constructed to analyse different regions of the initial CAD design.

[0152] As an optional third subphase 3, which may relate to step 324, a coarse- scale simulation, using the laser processing strategy as input and fed with initial boundary conditions and an analytical laser model as input, may yield a simplified temperature map. This temperature map may be optionally chosen to refine the initial temperature boundary conditions for the high-fidelity simulation and incorporate a floating temperature boundary field to account for precise processing conditions.

[0153] A fourth subphase 4 may be summarized as ‘powder geometry configuration’. In this fourth subphase, the simulation domain may be filled with powder from a Discrete Element (DEM) simulation code in order to reflect the real-life powder geometry, e.g., of a deposited powder bed or powder ejected from a nozzle, and particle size distribution, e.g., a distribution of the size of the powder particles. This subphase may provide granular information for local 3D heat dissipation (e.g., conduction, convention and radiation) as well as for local phase change (e.g., melting, evaporation, condensation, sublimation and solidification) of the material. Initially the powder statistics may be created, defined by for example particle size, shape / morphology and / or chemical composition. The first two properties may be included as statistical distributions, while the composition may be assumed to be fixed for the powder setup and without accounting for uncertainty. A contact model may be used to define how powder particles interact with one another, for example in terms of forces and positions. Finally, a geometrical representation of a powder re-coater may be added, for example to reflect the real-life process of powder spreading in this type of additive manufacturing process. The DEM simulation may allow the powder to be dropped under normal gravitational conditions into the simulation domain and may subsequently compact the powder with the re-coater and movement. The positional changes and forces enacted within the powder may be calculated and the subsequent movement and / or re-deposition of the powder may be processed. The outcome of the fourth subphase may be a final 3D powder field, including powder connection areas and powder gaps, e.g., filled with gas.

[0154] A fifth subphase, also identified by the reference numeral 5, may be summarized as ‘configuration of multiphysics CFD simulation’. The fifth subphase 5 may involve integrating the simulation domain with the powder field to configure the multiphysics CFD simulation. Thereby, intricacies of laser-material interaction physics, detailed temperature evolution, and phase transitions along the laser path may be captured, allowing the hatch line morphology and potential defects to be predicted with high precision. The fifth subphase 5 may involve various steps, such as transferring the laser path to the CFD simulation along with the powder field and substrate layer information, which may involve a transformation of coordinates and scales. The boundary surface between the powder and ambient gas may be defined and discretized to identify the initial reflective surface for the laser beam. A range of physical parameters may be calculated and set for the simulation. These physical parameters may include, but not be limited to, temperature-dependent emission and absorption coefficients and phase change properties.

[0155] A first part of the sixth subphase, also identified by the reference numeral 6, may be summarized as ‘simulation execution and monitoring’. The configured simulation may be discretized and processed using the OpenFOAM framework. Performance monitoring and numerical stability may be overseen by a state monitor (e.g. pyFOAM), and additional checks may be integrated to ensure consistency and reliability of the simulation output.

[0156] A further part of the sixth subphase 6 may be summarized as ‘sequential hatch line simulation and analysis’ and may involve, following the simulation of an initial hatch line, transitioning the different phase fields to accommodate the simulation of subsequent hatch lines. This step may enable the simulation to emulate complex shaping and phase transformations closely resembling real-life manufacturing processes, inclusive of defect formation analysis. If the new hatch line is to be horizontally aligned with the initial hatch line, the initial powder field setup may be augmented with processed field information, e.g., from temperature and / or phase fields. Conversely, for a vertical alignment of hatch lines, a new powder processing cycle may be initiated to reflect the interaction with the previously processed surface.

[0157] A seventh subphase 7 may be summarized as ‘extraction and conversion of simulation data’. In the seventh subphase, 3D physical fields, such as phase fields, e.g., for all phases, temperatures, and densities, may be extracted and converted into a standardized file format such as HDF5. This may allow the processed data to be used for subsequent analysis of the structural and material properties of the virtually manufactured part. The conversion may include the temporal evolution of the manufacturing process, providing a 4D dataset that encapsulates the dynamics of mesoscale interactions characterizing the simulated additive manufacturing process.

[0158] The following provides a pseudocode of a specific embodiment while continuing to refer to the respectively numbered subphases as described above. Suffixes such as 'a', 'b', 'c', etc., may be appended to numerals to denote additional subphases within the corresponding subphases, while apostrophes such as ', ", etc., may denote optional subphases which may for example be involved if multiple hatch lines, or an entire CAD design, is printed. Where possible and appropriate, these additional subphases are also indicated in Figs. 3A-3D.

[0159] It will be appreciated that the output fields of the simulation, such as 3D temperature fields and phase fields or 4D fields constituted by the 3D fields at respective time steps, may be used for various purposes. For example, the volumetric fields may be analysed to identify anomalies in said manufactured object, for example by quantifying bead and / or pore formation during the additive manufacturing. Such anomalies may be determined from the temperature fields and phase fields in various ways. For example, the temperature field(s) may provide insights into areas of excessive or insufficient heat, which may lead to overflow or inadequate melting, respectively, while the phase field(s) may indicate rapid material state changes such as condensation and evaporation that can cause structural issues such as cracks or delamination. By analyzing these fields, places may be detected where material may not have properly fused (e.g., due to rapid solidification), which may create weak spots in the manufactured object. Quantitative analysis may allow for measuring the extent of these defects, and correlating them with specific process parameters, such as laser power or scan speed, enabling targeted adjustments. Accordingly, in some examples, the identified anomalies may be used to optimize the manufacturing process.

[0160] In other examples, the identified anomalies may be used to perform lifetime or fatigue prediction for the manufactured object. In yet other examples, the identified anomalies, or a lack thereof, may be used to validate the 3D model of the object and / or the control parameters for the manufacture of the object, and after validation, the object may be manufactured using the 3D model and the control parameters. In other words, the (lack of) identified anomalies may be used to approve the 3D design of the model for manufacturing, optionally after one or more design iterations in which the 3D design of the object and / or the control parameters used in the manufacture are adjusted. In yet other examples, the simulation, and in particular the volumetric fields generated by the simulation, may be used to establish a digital twin of the object. The digital twin may therefore be more realistic since it may take the presence of anomalies into account.

[0161] In some examples, a machine learning model, such as a graph neural network, may be trained on the 3D volumetric fields obtained from the simulation model and on sets of simulation parameters which characterize the configuration of the simulation model with which a respective 3D volumetric field is obtained. For example, simulation parameters such as the control parameters including the beam path, beam power, and generic material properties may be used as input, e.g., as features or predictors, while the simulated 3D volumetric fields may be used as prediction targets. This way, the machine learning model may be trained to predict a 3D volumetric field using a set of simulation parameters as input. In a specific example, a graph neural network may receive as input the 3D volumetric fields for discrete values of the laser power (e.g., at 10W, 50W, and 100W) and at constant laser velocity and the simulation parameters which include the laser power and the laser velocity. The 3D volumetric fields may then be extrapolated to laser power values in the proximity of the original ones (e.g., within a range of 5-15W, 40-60W, or 90-110W) without expensive recalculation of said 3D volumetric fields by the simulation model. After training, the machine learning model may be used to generate 3D volumetric fields, which may then be further analysed, for example to identify anomalies in said manufactured object. To be able to deal with the complexity of being able to predict 3D volumetric fields, a machine learning architecture capable of handling the spatial complexity of 3D data may be used. This may for example include a combination of traditional neural networks and specialized layers such as convolutional layers (e.g., 3D CNNs) or graph neural networks (GNNs) when representing the spatial domain as a graph.

[0162] Fig. 4 shows a flowchart of a method 700 to simulate additive manufacturing in which powder is used to additively manufacture an object. The method 700 may comprise, in a step titled “ACCESSING 3D MODEL OF OBJECT TO BE MANUFACTURED”, accessing 710 a 3D model of the object to be manufactured, in a step titled “DETERMINING CONTROL PARAMETERS FOR ENERGY BEAM”, determining 720 control parameters for an energy beam to selectively melt and fuse powder regions during additive manufacturing of at least part of the object, wherein the control parameters are indicative of a beam path of the energy beam. The method 700 may further comprise, in a step titled “SIMULATING THE ADDITIVE MANUFACTURING OF PART OF OBJECT”, simulating 730 the additive manufacturing of the at least part of the object by, in a step titled “USING PARTICLE MODEL TO MODEL APPLICATION OF POWDER”, using 740 a particle model to model application of powder over a substrate layer during the additive manufacture, and in a step titled “INITIATING SIMULATION MODEL OF THE ADDITIVE MANUFACTURING”, initiating 750 a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, wherein the 3D volumetric fields include at least a phase field and a temperature field. The step 750 of initiating the simulation model may comprise, in a step titled “IMPORTING APPLIED POWDER FROM THE PARTICLE MODEL”, importing 760 a geometry and particle size distribution of the powder from the particle model, in a step titled “REPRESENTING BOUNDARY SURFACES AS REFLECTIVE SURFACES”, representing 770 boundary surfaces of the powder as reflective surfaces in the simulation model, and in a step titled “FURTHER CONFIGURING THE SIMULATION MODEL”, configuring 780 the simulation model with emission and absorption coefficients and with phase change coefficients of at least a vapor-to-liquid phase transition of powder and substrate materials to model vapor condensation during the additive manufacture. The simulation 730 may further comprise, in a step titled “EXECUTING THE SIMULATION MODEL TO SIMULATION OUTPUT”, executing 790 the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure. It should be noted that the aforementioned steps or sub-steps may be executed in any suitable sequence, including simultaneously or with overlapping timing, provided that the necessary input-output relationships are preserved.

[0163] In general, each entity described in this specification may be embodied as, or in, a device or apparatus. The device or apparatus may comprise one or more (micro) processors which execute appropriate software. The processor(s) of a respective entity may be embodied by one or more of these (micro)processors. Software implementing the functionality of a respective entity may have been downloaded and / or stored in a corresponding memory or memories, e.g., in volatile memory such as RAM or in non-volatile memory such as Flash. Alternatively, the processor(s) of a respective entity may be implemented in the device or apparatus in the form of programmable logic, e.g., as a Field-Programmable Gate Array (FPGA). Any input and / or output interfaces may be implemented by respective interfaces of the device or apparatus. In general, each functional unit of a respective entity may be implemented in the form of a circuit or circuitry. A respective entity may also be implemented in a distributed manner, e.g., involving different devices or apparatus.

[0164] It is noted that any of the methods described in this specification, for example in any of the claims, may be implemented on a computer as a computer implemented method, as dedicated hardware, or as a combination of both. Instructions for the computer, e.g., executable code, may be stored on a computer-readable medium 800 as for example shown in Fig. 5, e.g., in the form of a series 810 of machine-readable physical marks and / or as a series of elements having different electrical, e.g., magnetic, or optical properties or values. The executable code may be stored in a transitory or non-transitory manner. Examples of computer-readable mediums include memory devices, optical storage devices, integrated circuits, servers, online software, etc. Fig. 5 shows by way of example a memory card 800.

[0165] An abstract for the present specification may read as follows: a method is provided of simulating additive manufacturing in which powder bed deposition is used to additively manufacture an object. The method comprises using a particle model to model deposition of a powder bed over a substrate layer during the additive manufacture, initiating a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, and executing the simulation model to obtain at least a 3D phase field and a 3D temperature field at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure. It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims.

[0166] In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. Use of the verb "comprise" and its conjugations does not exclude the presence of elements or stages other than those stated in a claim. The article "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. Expressions such as “at least one of” when preceding a list or group of elements represent a selection of all or of any subset of elements from the list or group. For example, the expression, “at least one of A, B, and C” should be understood as including only A, only B, only C, both A and B, both A and C, both B and C, or all of A, B, and C. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

CLAIMSClaim 1. A method (700) of simulating additive manufacturing in which powder is used to additively manufacture an object, comprising: accessing (710) a 3D model of the object to be manufactured; determining (720) control parameters for an energy beam to selectively melt and fuse powder regions during additive manufacturing of at least part of the object, wherein the control parameters are indicative of a beam path of the energy beam; simulating (730) the additive manufacturing of the at least part of the object by: using (740) a particle model to model application of powder over a substrate layer during the additive manufacture; initiating (750) a simulation model of the additive manufacturing, wherein the simulation model uses computational fluid dynamics to simulate 3D volumetric fields at respective time instances during the additive manufacturing, wherein the 3D volumetric fields include at least a phase field and a temperature field, wherein initiating the simulation model comprises: importing (760) a geometry and particle size distribution of the powder from the particle model; representing (770) boundary surfaces of the powder as reflective surfaces in the simulation model; configuring (780) the simulation model with emission and absorption coefficients and with phase change coefficients of at least a vapor-to-liquid phase transition of powder and substrate materials to model vapor condensation during the additive manufacture; executing (790) the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of a first line structure on the substrate layer to simulate temperature evolution and phase changes during the manufacture of the first line structure.Claim 2. The method (700) according to claim 1 , further comprising, after simulating the manufacture of the first line structure:using the particle model to model a further application of powder to manufacture a second line structure; importing the geometry and particle size distribution of the further application of powder from the particle model into the simulation model; executing the simulation model to obtain the 3D volumetric fields at respective time instances during manufacture of the second line structure to simulate the temperature evolution and phase changes during the manufacture of the second line structure.Claim 3. The method (700) according to claim 2, wherein the second line structure is horizontally or vertically connected to the first line structure.Claim 4. The method (700) according to claim 2 or 3, wherein the simulation model is configured to model a remelting of solidified parts of the first line structure during the manufacture of the second line structure.Claim 5. The method (700) according to any one of claims 1 to 4, wherein the simulation model is configured to, in the phase field, distinguish between at least: a solid phase; a liquid phase; a gas phase, for example of ambient gas; powder; and vapor, for example metal vapor.Claim 6. The method (700) according to any one of claims 1 to 5, wherein the simulation model is configured with phase change coefficients of a liquid-to-vapor phase transition of the powder and substrate materials to model evaporation during the additive manufacture.Claim 7. The method (700) according to any one of claims 1 to 6, further comprising: performing a coarse scale simulation of the deposition of the first line structure without using the particle model to obtain a coarse temperature field; and using the coarse temperature field to set initial temperature boundary conditions for the simulation model.Claim 8. The method (700) according to any one of claims 1 to 7, wherein the particle model is a discrete element simulation model.Claim 9. The method (700) according to any one of claims 1 to 8, further comprising analysing the 3D volumetric fields to identify anomalies in said manufactured object, for example by quantifying bead and / or pore formation during the additive manufacturing.Claim 10. The method (700) according to claim 9, further comprising performing lifetime or fatigue prediction for the manufactured object based on said identified anomalies.Claim 11. The method (700) according to any one of claims 1 to 10, further comprising: analysing the 3D volumetric fields to validate the 3D model of the object and / or the control parameters for the manufacture of the object, and after validation, manufacturing the object using the 3D model and the control parameters; or using the 3D volumetric fields to establish a digital twin of the object.Claim 12. The method (700) according to any one of claims 1 to 11 , further comprising training a machine learning model, for example a graph neural network, on the 3D volumetric fields obtained from the simulation model and on sets of simulation parameters, a set of simulation parameters characterizing a configuration of the simulation model by which a respective 3D volumetric field is obtained, to be able to predict a 3D volumetric field for an input set of simulation parameters.Claim 13. The method (700) according to claim 12, further comprising using the trained machine learning model to predict 3D volumetric fields and analysing the predicted 3D volumetric fields to identify anomalies in said manufactured object.Claim 14. A transitory or non-transitory computer-readable medium (800) comprising data (810) representing a computer program, the computer program comprising instructions for causing a processor system to perform the method according to any one of claims 1 to 13.Claim 15. A processor system comprising a memory and one or more processors, wherein the memory comprises instructions for causing the one or more processors to perform the method according to any one of claims 1 to 13.

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