Scaling method and system based on point-by-point superposition process

Abstract

A scaling method for simulating any manufacturing process employing a moving heat source is disclosed. The method is aimed at melting or sintering materials where the heat source is driven according to a defined path. The method requires a mesoscale model that evaluates physical quantities representative of the process-induced thermal history and residual stress and strain fields for each set of process parameters for a given material. The mesoscale results obtained by modeling one or more scan lines are transferred to the elements of a macro-scale finite element mesh based on the defined path. Scaling is performed point-by-point and subsequent averaging operations are performed on the values of the physical quantities calculated within each element of the macro-scale finite element mesh. Finally, a macro-scale simulation is performed for evaluating the residual stresses and deformations produced throughout the manufacturing process.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to a point-by-point superposition-based simulation method that is applicable to any manufacturing process employing a moving heat source, such as welding and powder bed fusion (PBF). More specifically, the present disclosure relates to a scaling process that links mesoscale and macroscale models, as better explained hereinafter. BACKGROUND

[0002] In the field of 3D printing, several techniques are available. For example, PBF includes all the processes that use a focused energy to melt or sinter a powder layer.

[0003] The main manufacturing issues related to these processes are porosity, cracking, delamination, residual stresses and deformations. In particular, residual stresses can reduce the mechanical strength, while deformations can lead to collisions between the overcoater and the out-of-tolerance parts or pieces.

[0004] Therefore, the availability of a reliable and fast simulation method would be useful and welcome in this field in order to predict possible failures, thus minimizing the impact of a trial-and-error procedure.

[0005] Generally speaking, mesoscale and macroscale models are best suited to study the impact of residual stresses, while microscale and granular scale models are mainly focused on the microstructure, porosity and surface roughness.

[0006] More specifically, mesoscale models are suitable for assessing the local thermal history resulting from the scanning process on a finite volume and the residual stress and strain fields. Such models can be used in combination with thermodynamic simulations and experimental procedures to optimize the process parameters and predict how the microstructure of the material can change during additive manufacturing. This is particularly important because the microstructure influences the static and fatigue strength of the printed parts.

[0007] On the other hand, macroscale models consist of thermal-structural or purely structural finite element (FE) analyses that can be used to predict the piece deformations, assess the stresses and locate possible failures throughout the manufacturing process.

[0008] The poor scalability of mesoscale models currently limits their use to small scanning volumes, mainly due to the computational cost. Since the scanning length of a PBF process usually exceeds 10 9 times the beam diameter, a scaling process is needed to overcome such limitations.

[0009] Therefore, an efficient physics-based method to compute the initial conditions of a FE model aimed at predicting the residual stresses and piece deformations induced by the manufacturing process would be welcome in this field. SUMMARY

[0010] In one aspect, the subject matter disclosed herein is a computer-implemented method for simulating a manufacturing process using a mobile heat source intended to melt or sinter a material. The method comprises implementing a mesoscale model to compute physical quantities representative of process-induced thermal history and residual stress and strain fields for a given set of process parameters for the material. In addition, it defines a macro-scale FE model of all the parts involved in the manufacturing process, the model comprising a plurality of elements. Then, the method implements a scaling procedure linking the mesoscale and macro-scale models. More specifically, a point-by-point strain superposition (PSS) method is disclosed as such scaling procedure. The method computes the incompatible strains of the macro-scale structural model (i.e. the additive inverses of the initial elastic strains to be applied to the macro-scale model) and the initial state based on the results obtained from one or more mesoscale thermal structural simulations, thus reducing the total computational cost required to assess the residual stresses and part deformations induced by the process. In this way, an effective prediction of both the residual stresses and part deformations induced, for example, by a PBF additive manufacturing process is achieved. In addition, an assessment of the manufacturability and mechanical strength of the part that can result is also achieved.

[0011] Also disclosed herein is a system for simulating a manufacturing process, the system comprising a processing unit or computer having a processor operable to execute a computer-implemented simulation method. The system can comprise a database and a device for displaying, printing or storing the results obtained. BRIEF DESCRIPTION OF DRAWINGS

[0012] A more complete understanding of the disclosed embodiments and the many attendant features and advantages thereof will readily be had by reference to the following detailed description when considered in connection with the following drawings wherein:

[0013] Figure 1 A flowchart of the computer-implemented simulation method incorporating the new scaling procedure is shown;

[0014] Figure 2 A detailed flowchart of the simulation method of Figure 1 is shown;

[0015] Figure 3 A schematic representation of the mesoscale model according to the first embodiment is shown;

[0016] Figure 4 A 3D cross-section of the residual von Mises equivalent stress field resulting from the mesoscale simulation of a single scan line is shown;

[0017] Figure 5 A cross-section of the transversal component of the residual stress field resulting from the mesoscale simulation of a single scan line is shown;

[0018] Figure 6a cross-section showing the longitudinal component of the residual stress field resulting from the mesoscale simulation of a single scan line;

[0019] Figure 7 a macro-scale simulation process is shown;

[0020] Figure 8A a cantilever-shaped sample used to validate the simulation method is shown, as well as a wire cut performed on the support after the build process;

[0021] Figure 8B the deformed shape of the sample after cutting is shown;

[0022] Figure 9 a comparison between the simulated top profile and the measured top profile of the sample after cutting is shown; and

[0023] Figure 10 a system configured to perform computer-implemented simulations of Figure 1 and Figure 2 is shown. DETAILED DESCRIPTION

[0024] A method for simulating any manufacturing process using a heat source moving along a predetermined path, such as a welding process or an additive manufacturing process, has been conceived. The method processes a solid model of the workpiece to be manufactured or welded. The mechanical and thermal response of the material to the heating process is simulated by a suitable mesoscale model. The results of such model are then scaled to simulate the structural behavior of the entire workpiece to be manufactured (or welded) in order to predict the residual stresses and deformations generated during the entire process.

[0025] In general, the simulation method disclosed herein comprises three main steps: a mesoscale simulation, a scaling process and a macro-scale simulation. The mesoscale simulation reproduces the scanning process on a finite volume (even a single scan line) and evaluates physical quantities representative of the process-induced residual stress-strain field. Then, the scaling process transfers the mesoscale results to a macro-scale FE mesh according to the given scanning path. Finally, the macro-scale simulation reproduces the entire manufacturing process evaluating the residual stresses and deformations of the entire workpiece. In this way, the entire process can be simulated with a very limited computational cost.

[0026] In the following description and in the embodiments given below, a PBF process is considered, but it is clear that the method described herein is not limited to this particular use.

[0027] The simulation method is shown in Figure 1 and Figure 2 and is generally indicated with reference number 100.

[0028] Reference is made to Figure 1The above three main steps of the simulation method 100 and the input data required to perform these steps are illustrated. Process-related input data, referred to as scan strategy 140, comprises process parameters 141 and a definition path 142, as better defined hereafter. Material-related input data, referred to as given material 143, comprises all thermophysical and mechanical properties required by the simulation method 100. Finally, discretization-related input data, referred to as FE mesh 144, comprises a list of element and node positions obtained by discretizing a solid model of the workpiece whose manufacturing process has to be simulated.

[0029] Still referring to Figure 1 and Figure 2 The mesoscale simulation step 110 of the simulation method 100 comprises a sub-step of computing the process-induced thermal history and the residual stress and strain fields for each set of process parameters 141 of the given material 143. Moreover, the mesoscale simulation 110 comprises a step of storing the results in step 112.

[0030] More specifically, as part of the scan strategy 140, the mesoscale simulation step 110 receives as input the process parameters previously retrieved and read in step 141. These parameters are the control variables of the manufacturing or welding process to be simulated, such as beam power, scan speed, beam diameter, layer thickness and pre-heat temperature.

[0031] The results of the mesoscale simulation step 110, i.e. the residual elastic strain, plastic strain and maximum temperature fields, are sampled and used to define one or more interpolation functions. In particular, in some embodiments, the results are sampled on a plane perpendicular to the scan direction and stored in step 112 as two-dimensional interpolation functions by a suitable storage means, which can be a hardware-based storage means (memory, hard disk or any other storage means) and / or a software-based storage means.

[0032] The scaling step 120 comprises four sub-steps. The first sub-step 121 is to define sampling points for each element of the macro-scale FE mesh 144. The second sub-step 122 is the initialization of the selected physical quantities at each sampling point.

[0033] Then, in sub-step 123, the values of the physical quantities, in this embodiment the incompatible strain and the initial equivalent plastic strain, at each sampling point are computed. This computation follows the definition path 142, which is part of the scan strategy and is pre-set, as mentioned above. Then, in averaging sub-step 124, the values of the physical quantities are transferred to the elements of the FE mesh 144.

[0034] In this way, the results of the mesoscale simulation 110 are scaled to each element of the macro-scale FE mesh 144, providing the initial state 131 of the macro-scale model 132.

[0035] The macro-scale simulation 130 reads the initial state 131 and evaluates the residual stresses and deformations generated during the whole manufacturing process through a macro-scale model 132.

[0036] Eventually, the scaling step 120, which constitutes the main disclosure, links the two finite element models of different length and time scales. In particular, it computes the incompatible strains and initial state of the macro-scale structural model based on the results obtained from the meso-scale thermal structural model, thus, as mentioned above, reducing the overall computational cost required to assess the residual stresses and part deformations induced by the evaluation process.

[0037] In other words, the scaling step 120 uses the results of a more refined but slower simulation model (i.e. the meso-scale model 111 described above) to define the input of a more coarse but faster simulation model (i.e. the macro-scale model 132).

[0038] The simulation method 100 is intended to be executed by a processing device or apparatus, similar to a computer or any other processing device suitably programmed to execute software implementing the simulation method 100. Examples of such apparatus are shown in Figure 10 and will be described in more detail hereinafter.

[0039] In the following, an embodiment of the simulation method 100 applied to a PBF process is described in detail. More specifically, examples of the meso-scale model of step 111 and of the macro-scale model of step 132 are set forth in order to better disclose the operation of the scaling step 120.

[0040] 1. Mesoscale model

[0041] The meso-scale model of step 111 of the present embodiment evaluates the temperature, stress and strain fields generated by a single scan line (from point A to point B) of a powder layer 204. Figure 3 It comprises a one-way coupled FE thermal-structural simulation.

[0042] As shown in Figure 3 , the domain 200 of the meso-scale model 111 comprises a substrate 203 and one powder layer 204. For ease of reference, a Cartesian coordinate system x, y and z is provided. In particular, the z-axis is aligned with the build direction (i.e. the direction along which the powder layers are added) and the x-axis is aligned with the scan direction, which is perpendicular to the sampling plane 201, which is parallel to the y-z plane. The single scan line 202 taken between the two points A and B as described above is parallel to the x-axis. In the domain 200 of the meso-scale model, the substrate 203 and the powder layer 204 are also shown.

[0043] The domain 200 is symmetric with respect to the plane containing the scan and build directions.

[0044] In the present embodiment, the thermal and structural FE equations for the mesoscale model 111 are as follows:

[0045]

[0046] [K u ]{u}={F u}-[K uT ]{T-T ref}

[0047] where:

[0048] [C T ] is the thermal specific heat matrix;

[0049] {T} and are the nodal temperature vector and its time derivative;

[0050] [K T ] is the thermal conductivity matrix;

[0051] {F q} is the thermal body force vector (resulting from the integration of moving volumetric heat sources);

[0052] {F g} is the thermal gradient force vector (which encompasses the effects of evaporation, radiation, convection, and all surface conduction of heat through boundary conditions subjected to constant temperature);

[0053] [K u ] is the structural stiffness matrix;

[0054] {u} is the nodal displacement vector;

[0055] {F u} is the structural nodal load vector (resulted from iperstatic boundary conditions);

[0056] [K uT ] is the thermoelastic stiffness matrix; and

[0057] T ref is the reference temperature employed for the calculation of thermal strains.

[0058] In other embodiments, other approximation procedures or methods can be used, such as other numerical solutions, or even analytical solutions (whenever available) in specific cases.

[0059] The volumetric heat source models the beam-matter interaction and advection phenomena occurring within the melt pool, which is the region of molten material. The heat source moves from the start point (point A) to the end point (point B) of the scan line 202 at a speed defined by the considered set of process parameters retrieved in step 141, and it is calibrated to minimize the difference between the simulated and measured melt zone.

[0060] In other embodiments, the beam-matter interaction can be modeled differently, depending on the environment and boundary conditions.

[0061] In the computer-implemented simulation model, melting and solidification are simulated by changing the thermal conductivity (for thermal simulation) and stiffness (for structural simulation) of the elements undergoing phase change.

[0062] The nodal temperatures, i.e. the temperature at each node of the FE mesh 144, are initialized to the pre-heat temperature according to the set of process parameters retrieved and read in step 141.

[0063] During the thermal simulation (see Figure 3 ), the surface z = 0 is subjected to evaporation, radiation and convection. The surface y = 0 is adiabatic (for symmetry), while all other boundary surfaces are kept at the pre-heat temperature.

[0064] During the structural simulation (see Figure 3 ), the surface z = 0 is stress-free, the surface y = 0 is subjected to a symmetric constraint u y = 0, where u y is the displacement in the y direction, while all other boundary surfaces are fully constrained according to the half-infinite assumption, i.e. the displacement at high distances from the scanned region is negligible.

[0065] Excluding the domain region close to the end points, the thermal-structural problem is quasi-stationary. Therefore, since the domain 200 under consideration tends to infinity over time, approaching a stationary state, the residual stress (see Figure 4 , Figure 5 and Figure 6 ) and strain fields are constant along the scanning direction x.

[0066] The residual stress field generated by a single scanning line typically shows a tensile hydrostatic component on the surface. In response, the stresses become compressive in the region below the surface to ensure self- balancing.

[0067] Figure 4 A 3D section of the residual von Mises equivalent stress field generated by a meso-scale simulation of a single scanning line along the x-axis on a nickel-based alloy 718 (Inconel is a registered trademark) according to the first embodiment is shown. The von Mises equivalent stress is defined as follows:

[0068]

[0069] where σ1, σ2and σ3are the principal stresses.

[0070] In addition, Figure 5 A 3D section of the residual von Mises equivalent stress field generated by a meso-scale simulation of a single scanning line along the x-axis on a nickel-based alloy 718 Cross section of the transverse component of the residual stress field generated by mesoscale simulation of a single scan line along the x-axis (values in MPa - megaPascal).

[0071] Figure 6 shows a cross section of the longitudinal component of the residual stress field generated by mesoscale simulation of a single scan line along the x-axis (values in MPa - megaPascal) according to the first embodiment.

[0072] 2. Scaling procedure

[0073] The scaling process 120 links the mesoscale model 111 and the macroscale model 132 by defining incompatible strains and initial state 131 of the macroscale simulation 130 based on the mesoscale results.

[0074] Incompatible strains are the additive inverse of the initial elastic strains to be applied to the macroscale model 132.

[0075] A mesoscale simulation 110 of a single scan line 202 (again, refer to Figure 3 ) is performed with each combination of parameters 141 (e.g. power, speed, beam diameter, layer thickness) for processing a given material 143.

[0076] The residual elastic strains The plastic strains and the maximum temperature T max field are sampled on a plane 201 perpendicular to the scan direction, which is the x-axis in the Cartesian coordinate system of Figure 3 These results, as physical quantities, are stored in the database 112 in the form of three interpolation functions and T max(p) , where p is the position on the sampling plane 201. Such interpolation functions can be called by the respective material-parameter combination.

[0077] Referring to Figure 2 , the scaling process 120 is started in step 144 by defining sampling points 121 within the elements of the defined macroscale FE mesh.

[0078] The list of scan lines is extracted from the scan path in step 142, and each line is associated with a respective set of process parameters 141 (see Figure 2 ). These data are stored in three arrays (where n l is the total number of scan lines):

[0079] - whose coordinates

[0080] - whose coordinates​

[0081] - It collects a reference for the interpolation function for each scan line.

[0082] In this implementation, the PSS process 123 calculates the incompatible strain at each sampling point generated in step 121. and initial equivalent plastic strain In other implementation schemes, different physical quantities may be considered.

[0083] The following is a pseudocode report of the implementation schemes for initialization step 122 and superposition algorithm 123.

[0084]

[0085] and Both are initialized at 0 (line 1, line 2) for each sample point generated in step 121, and are updated if the projection of the sample point on the scan line under consideration is between and below its start and end points (line 9).

[0086] If this is the case, the sampling points are projected onto a plane perpendicular to the scanning direction (line 10). Then, the elastic strain generated by the considered scan line is retrieved using the corresponding interpolation function 112. Plastic strain and maximum temperature T max .

[0087] By changing To obtain symbols The first-order approximation is given, in which the maximum trace (line 18) is evaluated after the last relaxation (lines 14-17) and represented in the global reference frame (line 19).

[0088] The initial equivalent plastic strain is the maximum calculated after the last relaxation (line 14-17). Approximate (line 21) is:

[0089]

[0090] By averaging the values ​​calculated at sampling points within each element of the above grid (step 124), the incompatible strain and the initial equivalent plastic strain are transferred to the elements of the macroscale grid 144:

[0091]

[0092] Where n e It is the element field Ω generated in step 121. e The number of sampling points.

[0093] 3. Macroscopic scale model

[0094] The macro-scale simulation 130 consisting of structural FE simulations estimates the displacement field and all derived quantities throughout the build process.

[0095] The part volume is sliced with planes perpendicular to the build direction.

[0096] With reference to Figure 7 All elements belonging to the manufactured part are initially deactivated, i.e. their stiffness is made negligible with respect to their original value. Then, the slices are sequentially activated by restoring the original stiffness of their elements.

[0097] The activated elements receive initial elastic strains

[0098]

[0099] and initial equivalent plastic strains (see step 131), which are defined by the PSS process 123 in the scaling step 120.

[0100] The structural FE equations to be solved have the following form:

[0101] [K u ]{u} = {F u}- [K uT ]{T - T ref}

[0102] where:

[0103] [K u ] is the structural stiffness matrix;

[0104] {u} is the nodal displacement vector;

[0105] {F u} is the nodal load vector of the structure (resulting from the iperstatic boundary conditions);

[0106] [K uT ] is the thermo-elastic stiffness matrix;

[0107] {T} is the nodal temperature vector; and

[0108] T ref is the reference temperature adopted for the calculation of thermal strains.

[0109] The substrate is at least isostatically constrained to prevent rigid motion during the build process.

[0110] All nodes not belonging to the active elements are fully constrained (see Figure 7) to maintain the top surface of each slice at its nominal shape and size until activation.

[0111] 4. Validation of the simulation method

[0112] The simulation method 100 has been tested on cantilever-shaped samples represented in Figure 8A and Figure 8B Samples were manufactured in selective laser melting 718. Wire-cut supports were removed before the top profile was measured with a 3D scanner.

[0113] Wire-cutting causes the cantilever to bend ( Figure 8B ) due to the x-z stress gradient generated during the build.

[0114] The comparison between the simulated top profile and the measured top profile is shown in Figure 9 Overall, the simulation overestimates the upward displacement with a maximum absolute error of 0.2 mm. This accuracy is comparable to the fluctuations of the measured data between different samples.

[0115] Since the cantilever deformation after support removal is mainly driven by the release of the bending stress accumulated during the build process, the simulation method seems to correctly reproduce the stress field of the whole top flange of the sample.

[0116] 5. Conclusions

[0117] The method 100 can be applied to simulate any manufacturing process employing a moving heat source, such as welding, direct energy deposition, laser metal deposition, fused deposition modeling, PBF and other additive manufacturing processes.

[0118] The PSS process 123 is either equivalent to or more efficient than similar structure scaling strategies. Indeed, it requires the mesoscale model step 111 of a single scan line 202, while other methods simulate one or more layers 204. Moreover, the PSS process 123 is faster to produce than all simulation strategies that perform a full-scale thermal analysis. This saves computational resources and also improves processing speed.

[0119] Reference is now made to Figure 10 , showing a system 300 for performing the method 100. The system 300 comprises a computer or processing unit 301 provided with a processor 301' configured to perform the method 100 and to simulate, for example, a production or welding process by a moving heat source, wherein the heat source is driven according to a manufacturing path. The computer 301 is operable to execute a computer program that performs the simulation method.

[0120] The software implementing the simulation method 100 can be executed by different computer systems. For example, a computer system having a processor 301' and a memory 302' can be used. The memory 302' can be a volatile memory, such as a RAM, or a non-volatile memory, such as a ROM, a hard disk, or a combination thereof. The memory 302' can store the computer program that performs the simulation method 100. or A common laptop computer (e.g. Dell® Optiplex® 7010, Lenovo® ThinkCentre® M70e, HP® Pavilion® 17-f2000, Apple® iMac®, equipped with a suitable RAM memory package, such as, by way of example only, 1 GB RAM.

[0121] Moreover, a server can be used, which can be installed on site or be cloud-based. Furthermore, due to the fact that a processing device is required, a computer network can be used, even if it is remote with respect to the place where the processing is started. Moreover, a hand-held device such as a tablet or a smartphone, properly programmed, can in principle be used to perform the simulation method 100. Theoretically, even a quantum computer or any other processing device can be programmed in order to process the simulation method 100.

[0122] As for the software language used to implement the simulation method, a compiled language such as C++, Fortran, etc. should be preferred, but depending on the specific case, even an interpreted language such as Python, Java, etc. can be suitable.

[0123] The system 300 further comprises a database 302 configured to store the interpolation functions 112. The database 302 can be a hardware-based database (memory, hard disk or any other storage device) and / or a software-based database, and it is coupled with the computer processor. The interpolation functions can be called from the database 302 by the respective material- parameter combination.

[0124] The system 300 further comprises devices for a display 303, a printer 304 and an additional storage device 305 to store the computation results, all of which are connected to and controlled by the computer 301. Such devices are configured to display the results of the simulation.

[0125] The solution is advantageous in that it allows a physics-based simulation of huge scan volumes at reasonable computational costs.

[0126] In addition, the solution disclosed herein is advantageous in that it minimizes the number of scan path-related configurations developed at a mesoscale level.

[0127] The simulation method according to the present disclosure is also advantageous in that it allows to reduce the number of trial-and-error procedures currently used for product development.

[0128] While aspects of the present application have been described in terms of various specific embodiments, it will be apparent to those with ordinary skill in the art that numerous modifications, variations, and alternatives can be employed without departing from the true spirit and scope of the present claims. Also, any process or method steps described herein can be performed in an alternative order or sequence, unless otherwise indicated herein. Moreover, unless specifically stated otherwise, the order or sequence of any process or method steps are not constrained.

[0129] Reference has been made throughout this disclosure in detail to particular embodiments of the disclosure, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation of the disclosure and not limitation thereof. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present disclosure without departing from the scope or spirit of the disclosure. References throughout this specification to "one embodiment" or "an embodiment" or "embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. Thus, the appearances of the phrase "in one embodiment" or "in an embodiment" or "in some embodiments" in various places throughout this specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0130] When introducing elements of various embodiments, the articles "a," "an," "the," and "said" are intended to mean that there are one or more of the elements. The terms "comprising," "including," and "having" are intended to be inclusive and mean that there can be additional elements other than the listed elements.

Claims

1. A computer-implemented method (100) for simulating a manufacturing process using a moving heat source intended to melt or sinter a material, wherein the heat source is driven according to a defined path, wherein the method (100) comprises the steps of: reading a plurality of process parameters for performing the manufacturing process; reading material properties for simulating the manufacturing process; computing, by a mesoscale model (111), physical quantities representative of process-induced thermal history and residual stress and strain fields for each set of process parameters for a given material; defining a macro-scale finite element mesh of all parts involved in the manufacturing process, the macro-scale finite element mesh comprising a plurality of elements; and scaling (120) mesoscale results to the macro-scale finite element mesh based on the defined path (142), wherein the scaling (120) step further comprises the steps of: computing values of the physical quantities at one or more sampling points of each element of the macro-scale finite element mesh based on the defined path (142), and averaging (124) the values of the physical quantities computed within each element of the macro-scale finite element mesh; and performing a macro-scale simulation (130) for determining displacements and all derived quantities throughout the manufacturing process.

2. The method (100) according to the preceding claim, wherein the mesoscale model (111) determines the physical quantities on a length scale comparable to the size of the heat source.

3. The method (100) according to any one of the preceding claims, wherein the physical quantities are obtained from a mesoscale simulation (110) of a single scan line (202).

4. The method (100) according to any one of claims 1-2, wherein the physical quantities are sampled or computed on a plane (201) perpendicular to the direction of movement of the heat source.

5. The method (100) according to claim 3, wherein the physical quantities are employed to define one or more interpolation functions (112).

6. The method (100) according to claim 5, wherein the interpolation functions compute elastic strain, plastic strain and maximum temperature based on a position relative to the scan line (202).

7. The method (100) according to claim 5, comprising the step of storing the interpolation functions (112) in a storage device.

8. The method (100) according to any one of claims 1-2, wherein the scaling process (120) further comprises the steps of: defining one or more sampling points (121) of each element of the macro-scale finite element mesh, and initializing (122) values of the physical quantities at each sampling point, prior to the step of computing values of the physical quantities at each sampling point of the elements of the macro-scale finite element mesh.

9. The method (100) according to any one of claims 1-2, wherein the sampling points are distributed randomly or regularly.

10. The method (100) according to any one of claims 1-2, wherein the heat source is an electromagnetic beam, and wherein the material is a powder to be layered.

11. The method (100) of any one of claims 1-2, wherein the process parameters include one or more of the following parameters: beam power, scan speed, beam diameter, layer thickness, and pre-heat temperature.

12. System (300) for simulating a manufacturing process using a moving heat source intended to melt or sinter a material, wherein the heat source is driven according to a predetermined path; the system (300) comprising: a processing unit or computer (301) comprising at least one processor (301') operable to execute a computer program that performs the steps according to any one of the preceding claims; a database configured to store the interpolation function (112); and at least one device (303, 304, 305) for displaying, printing or storing the results of the macro-scale simulation (130).

13. A computer program product comprising instructions which, when executed by a computer (301), cause the computer (301) to carry out the steps of the method according to any one of claims 1-11.

14. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method according to any one of claims 1-11. ​

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