[0001] The present application relates generally to systems and methods for submodeling, and more particularly, to systems and methods for simulating attributes of a submodel for additive manufacturing applications using finite element analysis.

[0002] Additive manufacturing encompasses various manufacturing and prototyping techniques such as freeform fabrication, 3D printing, rapid prototyping/tooling, and the like in which stock material (such as a feed wire or powder) is melted across underlying substrates layer-by-layer to fabricate a freestanding object. Generally, the article of manufacture can be fabricated from a computer aided design (CAD) model stored in memory that is provided to the additive manufacturing system. The processes use an energy beam to sinter or melt a powder material, creating a solid three-dimensional object in which particles of the powder material are bonded together.

[0003] The layering cycle includes rapid heating and rapid solidification with simultaneous melting of the top powder layer and re-melting of underlying previously solidified layers, in which the article experiences steep temperature gradients and high cooling rates. Residual stresses caused by the thermal cycle can result in distortion or deformation of the article, which may cause the article to solidify out of specification tolerances.

[0004] Finite element analysis (FEA) systems and methods are commonly used to model physical properties and attributes of the article prior to fabrication. Computing devices and FEA software implement virtual modeling simulations to determine physical attributes such as residual stress, deformation, displacement of the article, and the like. Simulation of a coarse-mesh model of the article may result in a low-resolution FEA simulation of the physical attributes, and simulation of a fine-mesh model of the article generally results in a high-resolution FEA simulation. However, FEA simulations of fine- mesh models require greater computational power and time. [0005] Accordingly, it is desirable to reduce computational time for high- resolution, fine-mesh finite element analysis.

[0006] In one aspect, a method for implementing communications between a computer aided design (CAD) system and a multiphysics modeling module for use in simulating one or more mechanical physical attributes resulting from an additive manufacturing process of a submodel of a geometric CAD model of an object using a discretization method is disclosed. The method includes applying an inherent strain simulation for the object and applying a submodeling method for each submodel time step S’ of the inherent strain simulation of an area of interest defining the submodel. In some embodiments, extracting at least one value for a cut boundary condition for a given submodel time step S’ from a time step S of the model, the at least one value for a cut boundary condition extracted at a model distance Z. The model distance Z is the distance to a reference plane of the model normal to a build direction. In some embodiments, applying the at least one value for a cut boundary condition to at least one position of the cut boundary, the at least one position located away from a reference plane of the submodel by a submodel distance Z’ for the given submodel time step S.’ The submodel distance Z’ is the distance to the reference plane of the submodel normal to the build direction.

[0007] In a second aspect, a system for simulating mechanical physical attributes resulting from an additive manufacturing process of a submodel of a geometric CAD model of an object using a discretization method is disclosed. The system includes a user input; and, a processor connected to the user input and media output. The processor is programmed to apply an inherent strain simulation for the object; and apply a submodeling method for each submodel time step S’ of the inherent strain simulation of an area of interest defining the submodel. In some embodiments, the processor further programmed to extract at least one value for a cut boundary condition for a given submodel time step S’ from a time step S of the model, the at least one value for a cut boundary condition extracted at a model distance Z, wherein the model distance Z is the distance to a reference plane of the model normal to a build direction. In some embodiments, the processor further programmed to apply the at least one value for a cut boundary condition to at least one position of the cut boundary, wherein the at least one position located away from a reference plane of the submodel by a submodel distance Z’ for the given submodel time step S’, wherein the submodel distance Z’ is the distance to the reference plane of the submodel normal to the build direction.

[0008] The subject-matter of the disclosure will be explained in more detail in the following text with reference to exemplary embodiments which are illustrated in the attached drawings.

[0009] FIG. 1 illustrates an exemplary computing device including a processor for executing instructions;

[0010] FIG. 2 illustrates a perspective view of an exemplary article of manufacture;

[0012] FIG. 3B illustrates a perspective view of the model of FIG. 3A segmented into a matrix of coarse elements;

[0013] FIG. 3C illustrates a perspective view of the model of FIG. 3A segmented into a matrix of fine elements;

[0014] FIG. 3D illustrates an exemplary submodel of the model illustrated in FIG. 3A with emphasis on REGION A;

[0015] FIG. 4A illustrates a side view of the model of FIG. 3 A;

[0016] FIG. 4B illustrates an enlarged view of DETAIL A of FIG. 4A;

[0017] FIG. 5 A illustrates an enlarged view of DETAIL A of FIG. 4A with emphasis on an exemplary target region;

[0018] FIG. 5B illustrates an embodiment where fine elements irregularly fit within the coarse elements such that top edges do not align; [0019] FIG. 6 illustrates the simulation of a first row of fine elements in accordance with a first embodiment;

[0020] FIG. 7 A illustrates the simulation of a second row of fine elements in accordance with a first embodiment;

[0021] FIG. 7B illustrates the simulation of the second row of fine elements in accordance with a second embodiment;

[0022] FIG. 8 illustrates the simulation of a fourth row of fine elements;

[0023] FIG. 9 illustrates the simulation of an n-th row of fine elements; and,

[0024] FIGS. 10A through 10C are a block diagram illustrating an exemplary method for simulating one or more mechanical physical attributes of a submodel of a geometric CAD model for additive manufacturing applications using finite element analysis.

[0025] The reference symbols used in the drawings, and their meanings, are listed in summary form in the list of reference symbols. In principle, identical parts are provided with the same reference symbols in the figures.

[0026] In the following specification and the claims, reference will be made to a number of terms, which shall be defined to have the following meanings.

[0027] As used herein, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. The terms “optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where the event occurs and instances where it does not. [0028] Unless otherwise indicated, approximating language, such as “generally,” “substantially,” and “about,” as used herein indicates that the term so modified may apply to only an approximate degree, as would be recognized by one of ordinary skill in the art, rather than to an absolute or perfect degree. Accordingly, a value modified by a term or terms, such as “about,” “approximately,” and “substantially,” is not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be identified. Such ranges may be combined and/or interchanged and include all the sub-ranges contained therein unless context or language indicates otherw ise.

[0029] Additionally, unless otherwise indicated, the terms “first,” “second,” etc. are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the items to which these terms refer. Moreover, reference to, for example, a “second” item does not require or preclude the existence of, for example, a “first” or lower-numbered item or a “third” or higher-numbered item.

[0030] As used herein, references to “example embodiment” or “one embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.

[0032] Computing device 10 also includes at least one media output component 16 for presenting information to a user 18. Media output component 16 is any component capable of conveying information to user 18. In some embodiments, media output component 16 includes an output adapter such as a video adapter and/or an audio adapter. An output adapter is operatively coupled to processor 12 and operatively couplable to an output device such as a display device (e.g., a liquid crystal display (LCD), organic light emitting diode (OLED) display, cathode ray tube (CRT), or “electronic ink” display) or an audio output device (e.g., a speaker or headphones).

[0033] In some embodiments, computing device 10 includes an input device 19 for receiving input from user 18. Input device 19 may include, for example, a keyboard, a pointing device, and a mouse. A single component such as a touch screen may function as both an output device of media output component 16 and input device 19.

[0034] The processor 12 receives input parameters such as a three- dimensional virtual model, a mesh resolution, and a selection of a target region for submodeling. The processor 12 is further configured to execute the method described herein as instructions to be executed by the processor 12. The processor 12 is also programmed to retrieve FEA applications (such as a multiphysics modeling module 24) from memory 14 and store instructions in memory 14. The processor 12 also outputs simulations resulting from the user inputs onto the media output 16, or stores the output simulation in memory 14.

[0035] A CAD system 22 and a multiphysics modeling module 24, are both stored in memory 14 and both are accessible by the processor 12. The CAD system 22 is a three-virtual environment in which a CAD model is represented. The multiphysics modeling module 24 executes multiphysics mathematical calculations and performs FEA simulations of CAD models.

[0036] In one embodiment, a computer program is provided, and the program is embodied on a computer readable medium (such as memory 14). In some embodiments, the system includes multiple components distributed among a plurality of computing devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium. As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory 14 for execution by the processor 12, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are example only, and are thus not limiting as to the types of memory usable for storage of a computer program. [0037] FTG. 2 illustrates an exemplary article of manufacture 30 (hereinafter referred to as “article 30”). In some embodiments, the article 30 is manufactured by inputting instructions from memory 14 into an additive manufacturing system such as a Laser Power Bed Fusion (LPBF) system, Direct Metal Laser Melting (DMLM) system, a Selective Laser Sintering (SLS) system, a Direct Metal Laser Deposition (DMLD) system, a Direct Metal Laser Deposition (DMLD) system, a binder jetting additive manufacturing (BJAM), and/or a powder blown additive system, and/or a LasergCusing system. As used herein, the terms “additive manufacturing” or “additive manufacturing techniques or processes” refer to manufacturing processes in which successive layers of material are deposited across underlying layers to build-up, layer-by-layer, a three-dimensional component. A first layer is deposited and fused onto a build plate, and successive layers are then partially melted or fused together to form a monolithic or integral component, such as article 30.

[0038] As a result of the repetitive melting and fusing of successive layers, residual stresses and distortion may be imparted to article 30. The melting and fusing also causes underlayers to expand or deform due to the temperature differential with the layer being applied across it. The residual stresses, distortion, and temperature differential may be simulated by FEA applications and methods.

[0039] One such method of simulating thermal and mechanical properties as disclosed herein uses an inherent strain simulation method. The inherent strain simulation method is a thermal-mechanical finite element method model that yields an approximation of the manufacturing-induced residual stresses and distortion (and other mechanical and thermal physical attributes generally). A three-dimensional virtual model of the article is imported into, or created in, FEA software. A three-dimensional mesh is applied across the model to segment into a matrix of cuboid elements. The matrix of cuboid elements is oriented in a three-dimensional space such that layers of cuboid elements are substantially parallel to the build plate and such that a sum of the layers defines a total height of the model.

[0040] In some embodiments, a first layer (the bottom-most layer disposed on the build plate) is constrained to represent the build plate stiffness. A negative strain is applied to an n-th layer (the top-most layer opposite the bottom-most layer), in which thermal strain associated with the metal cool-down and irreversible deformation is combined. For every successive intermediate layer applied across the first layer, a reduced mesh is obtained by discarding all later layers, and the finite element mathematical calculation provides stress and displacements associated with every successive intermediate layer. The final residual stresses and displacement are calculated by a summation of the results of each finite element mathematical calculation.

[0041] As used herein, the term “finite element analysis” or “FEA” shall denote a process, method or computer-implemented method whereby a simulation or approximation of one or more physical attributes of a geometric model is represented virtually (through software) as a finite element model. The model is segmented into a matrix of elements which, taken together, form the finite element model. The matrix of elements is simulated by calculating mathematical formulas such as partial differential equations to simulate physical attributes of each individual element and to simulate interactions between adjacent elements. Physical attributes of the model are illustrated in simulation, with elements shaded in color scale where regions of greater physical attributes values are color- shaded differently than regions of lesser physical attributes values.

[0042] As used herein, the term “simulate,” “simulating” and “simulation” shall denote calculating multiphysics mathematical formulas to determine a value of one or more mechanical physical attributes of fine elements and/or coarse elements, as well as simulating interactions between adjacent fine elements and/or coarse elements. In the multiphysics calculation, boundary conditions of adjacent fine and/or coarse elements are extracted and are applied to the fine elements and/or coarse elements being simulated. The simulation and calculations of multiphysics mathematical calculations are executed by a processor and/or an application (such as FEA software). Likewise, as used herein, the term “applying an inherent strain simulation” or “executing an inherent strain simulation” denotes executing calculating multiphysics mathematical formulas in accordance with the inherent strain simulation method.

[0043] As used herein, the term “coarse element” resulting from applying a coarse mesh to the finite element model denotes a virtual segment of the finite element model having a cuboid shape and a volume. As used herein, the term “fine element” resulting from applying a fine mesh to the finite element model denotes a virtual segment of the finite element model having a cuboid shape and a volume. The volume of the fine element is less than the volume of the coarse element, and executing a simulation of fine elements results in a higher resolution than executing a simulation of coarse elements.

[0044] In some embodiments, the elements are voxel elements used for displacement mapping and simulation, and the FEA systems and methods described herein utilize voxel-based modeling and voxel meshes for displacement mapping.

[0045] FIG. 3A is a perspective view of an exemplary finite element model 50 of the article 30 simulated by FEA. FIG. 3B illustrates a perspective view of the model 50 segmented into a matrix of coarse elements 52. FIG. 3C illustrates a perspective view of the model 50 segmented into a matrix of fine elements 54. FIG. 3D illustrates a submodel 60 of the REGION A of the matrix of coarse elements 52 shown in FIG. 3A. Each of the views shown in FIGS. 3A-3D are virtual representations displayed on the at least one media output component 16, and may be rotated or manipulated by the user 18. By way of example, the user 18 may rotate and/or selectively enlarge any of the views by providing inputs through the input device 19. The REGION A may also be arbitrarily selected by the user 18 by providing inputs through the input device 19. In the illustrated embodiments, the REGION A includes at least a portion of a channel 32 of the model 50. The channel 32 may be selected by the user 18 because the channel 32 may represent a weak area of the model 50 or because the user 18 may intend to optimize the shape of the channel 32. Each of the views shown in FIGS. 3 A through 3D are arbitrarily oriented in X-Y-Z planes.

[0046] In the exemplary embodiment, the submodel 60 shown in FIG. 3D is segmented into fine elements, and executing a simulation of the submodel 60 results in a higher resolution relative to the model 50, which is segmented into coarse elements. To obtain a higher resolution, the entire model 50 may be simulated with fine elements 54. However executing the simulation of fine elements 54 requires substantially more processing resources relative to executing the simulation of coarse elements 52. By way of example, in one embodiment, to perform a FEA simulation of the finite element model 50 with a fine mesh (with the matrix of fine elements 54), at least fifteen hours of computational time may be needed, whereas in comparison, to perform a FEA simulation of only the submodel 60, only about nine minutes of computational time may be needed. [0047] Embodiments of the present invention generally relate to systems and methods for simulating one or more mechanical physical attributes of a submodel of a geometric model of a physical object for additive manufacturing applications using FEA. The attributes may include, but are not limited to only including, structural, fluid or thermal behavior, as well as residual stresses, deformation, or displacement of the article. The method includes applying an inherent strain simulation for the object, and applying a submodeling method for each submodel time step S' of the inherent strain simulation of an area of interest defining the submodel. The matrix of coarse elements extends in at least two dimensions which define rows and columns of coarse elements. The submodel is defined as a target region from the matrix of coarse elements of the model, and therefore the target region includes a subset of the matrix of coarse elements. The method further includes extracting at least one value for a cut boundary condition for a given submodel time step S’ from a time step S of the model. The at least one value for a cut boundary condition is extracted at a model distance Z, and the model distance Z is the distance to a reference plane of the model normal to a build direction. The method further includes applying the at least one value for a cut boundary condition to at least one position of the cut boundary. The at least one position is located away from a reference plane of the submodel by a submodel distance Z’ for the given submodel time step S. The submodel distance Z’ is the distance to the reference plane of the submodel normal to the build direction. The described system and methods provide for modeling a finite element submodel of the CAD model at a higher resolution than a resolution of the model.

[0048] FIG. 4A illustrates a side view of the model 50 of REGION A (shown FIG. 3A) meshed with a coarse mesh to produce a resulting matrix of coarse elements 100. The matrix of coarse elements 100 is arbitrarily oriented in a two-dimensional F-Z plane. The coarse mesh applied results in a low resolution relative to applying a fine mesh, and the shape of the channel 32 can only be approximated by the matrix of coarse elements 100, wherein a matrix of fine elements results in higher resolution and a more accurate approximation of the shape of the channel 32.

[0049] FIG. 4B illustrates an enlarged view of DETAIL A of FIG. 4A. In the exemplary embodiment, the coarse elements 100 are stacked in rows and columns, with the rows being substantially parallel to the Y-plane and the columns being substantially perpendicular to the Y-plane It should be understood that the matrix of coarse elements 100 extends in the three-dimensional X-Y-Z plane (not shown) and that each coarse element 100 has a node 102 positioned at a comer boundary 104 of each coarse element 100. The node 102 for each coarse element 100 is arbitrarily positioned within the coarse element 100, and in the exemplary embodiment, is along a boundary of the coarse element 100, or on a comer boundary 104. Positioning the node 102 is application-specific and is uniform across the model, and consistent during FEA modeling and simulations. In some embodiments, the node may be a point, a comer, an edge, a point along the edge, a middle of the edge, and/or a center of the coarse element 100. In some embodiments, nodes 102 are assigned only to coarse elements 100 that are adjacent to other coarse elements 100.

[0050] Each node 102 represents a cartesian coordinate of the coarse element 100, and each coarse element 100 has boundary condition values that are attributed to the node 102 and that may be extracted from for executing simulations. The boundary conditions are values for mechanical and thermal physical attributes (also referred to as “physical properties”) of each coarse element 100. The numerical values represented as boundary conditions and the cartesian coordinate of the nodes 102 may be inputs used in calculating the multiphysics mathematical formulas for executing one or more simulations. By way example, the residual stress of a coarse element 100 (or a group of coarse elements 100) is simulated from extracted boundary conditions of coarse elements 100 that are adjacent to the coarse element 100 (or that are adjacent to the group of coarse elements 100).

[0051] A simulation of the matrix of coarse elements 100 for one or more mechanical physical attributes of the model 50 is executed and boundary conditions for the matrix of coarse elements 100 are extracted and applied to respective nodes 102. From the simulation of the model 50, a user 18 may observe a high-stress region and the user 18 may select an exemplary target region 200 as shown in FIG. 5A. Alternatively, the user 18 may elect to optimize the shape and/or the design of the model 50 and may select the target region 200 to determine physical attributes of the target region 200. The user 18 thus defines the target region 200 for submodeling from the coarse mesh of the model 50.

[0052] FIG. 5 A illustrates an enlarged view of DETAIL A of FIG. 4A with emphasis on the exemplary target region 200 wherein the channel 32 requires a fine mesh simulation to obtain a higher resolution of the channel 32. A coarse mesh is initially applied to the model 50 (as shown in FIGS. 4A and 4B) to define a matrix of the coarse elements 100. The matrix of coarse elements 100 extends in at least two dimensions (defined by the two-dimensional T-Z plane) that define rows and columns of coarse elements 100.

[0053] The target region 200 includes a subset of the matrix of coarse elements 100, and a fine mesh is applied to the target region 200, resulting in a matrix of fine elements 110. In applying the matrix of fine elements 110, coarse elements 100 of the target region 200 are replaced with fine elements 110 (illustrated as replaced coarse elements 100’). In the illustrated embodiments, coarse elements 100, through which the channel 32 pass through, are subdivided into the fine elements 110 to better approximate the virtual shape of the channel 32.

[0054] The fine elements 110 are stacked into rows and columns, with rows being substantially parallel to the Y -plane and the columns being substantially perpendicular to the Y-plane. In the exemplary embodiment, each fine element 110 has a subnode 112 positioned at a comer boundary 114 of each fine element 110. The subnode 112 for each fine element 100 is arbitrarily positioned within the fine element 110, generally along a boundary of the fine element 110, or on a comer boundary 114 Positioning the subnode 112 is application-specific and is uniform across the model and consistent during FEA modeling and simulations. Positioning the subnodes 112 is also uniform and consistent with positioning of the nodes 102. In some embodiments, the subnode may be a point, a comer, an edge, a point along the edge, a middle of the edge, and/or a center of the fine element 110. In some embodiments, subnodes 112 are assigned only to fine elements 110 that are adjacent to coarse elements 100 or that are adjacent to other fine elements 110.

[0055] Each subnode 112 represents a cartesian coordinate of the fine element 110, and each fine element 110 has boundary condition values that are attributed to the subnode 112 and that may be extracted from for executing simulations. The boundary conditions are values for mechanical and thermal physical attributes (also referred to as “physical properties”) of each fine element 110. The numerical values represented as boundary conditions and the cartesian coordinate of the subnode 112 may be inputs used in calculating the multiphysics mathematical formulas for executing one or more simulations. By way example, the residual stresses of a fine element 110 (or a group or row of fine elements 110) are simulated from boundary conditions of coarse elements 100 and fine elements 110 adjacent to the fine element 110 (or adjacent to the group or row of fine elements 110).

[0056] In the illustrated embodiments, the matrix of fine elements 110 includes a first row of fine elements 1 10-1 that is adjacent to, and above, an underlying row of coarse elements 100-0, at least one intermediate row of fine elements (110-2, 110-3, 110- 4, etc.), and an n-nth row of fine elements 110-n, all of which combined define the matrix of fine elements 110. As will be explained in further detail below, in some embodiments, the underlying row of coarse elements 100-0 may be included in simulations of the submodel. Additionally, in some embodiments, coarse elements 100 that are adjacent to the matrix of fine elements 110 of the target region 200 may also be included in simulations of the submodel. In some embodiments, a first row of coarse elements 100-1 and a second row of coarse elements 100-2 may be included in executing simulations of the submodel and target region 200. The first row of coarse elements 100-1 is adjacent to, and above, an underlying row of coarse elements 100-0, and the second row of coarse elements 100-2 is adjacent to, and above, the first row of coarse elements 100-1. Generally, the target region 200 includes at least one row of fine elements 110 and a plurality of coarse elements 100 immediately adjacent to the at least one row of fine elements 110.

[0057] Each fine element 110 has a vertical unit (a height) Hf and each coarse element has a vertical unit (a height) H_c. The vertical unit Hf is smaller than the vertical unit (a height) H_c defining a ratio of fine elements to coarse elements. In the illustrated embodiments, the ratio is 1:4. Stated differently, the vertical unit Hf of four fine elements equals the vertical unit H_c of one fine element. As a result, a top edge 116 of a fourth row of fine elements 110-4 aligns with a top edge 106 of the first row of coarse elements 100-1. In some embodiments, the ratio may be larger or smaller than 1:4 depending on the resolutions of the coarse mesh and fine mesh. In some embodiments, the fine elements irregularly fit within the coarse elements such that top edges do not align.

[0058] As previously, set forth, boundary conditions for the matrix of coarse elements 100 are extracted and the values are applied to respective nodes 102 adj acent to the matrix of fine elements 110. To simulate the matrix of fine elements 110 and the submodel, an inherent strain simulation method is employed, wherein multiple simulations for each successive layer are executed to obtain mechanical phy sical attributes for each row of fine elements. The mechanical physical attributes of the row of fine elements are aggregated to output a simulation for the entire submodel.

[0059] FIG. 5B illustrates an embodiment where fine elements 110 irregularly fit within the coarse elements 100 such that top edges do not align. Tn such instances, an offset vector V having a magnitude is applied to multiphysics mathematical calculations and performs FEA simulations and to the inherent strain simulation as explained in further detail below. The offset vector V has cartesian coordinates and is defined by the distance between the node 102 of a coarse element 100 of a coarse layer of the model and at the subnode 112 of the fine element 110 of a given fine layer. As will also be explained in further detail below, the offset vector V may also be applied when nodes and subnodes do not align depending on which layer of fine elements are included in the simulation, even with regularly fitting coarse and fine elements.

[0060] The inherent strain simulation method generally includes one or more time step intervals. Each time step interval is defined the layering of a row of coarse elements over underlying layers, and/or the layering of a row of fine elements being layered over underlying layers A model time step S is defined as the layering of a layer of coarse elements and a submodel time step S’ is defined as the layering of a row of fine elements. The inherent strain simulation therefore has a number of submodel time step S’ equal to the number of layers of fine elements, and can be expressed as n’ submodel time steps S’, where n’ submodel time steps S’ includes n-layers of fine elements. In some embodiments, a first layer of the n-layers of fine elements is characterized as a zero or starting timestep, and therefore, a submodel time step S’ of n’ greater than two includes n’ -layers of fine elements layered over the first layer of fine elements. Similarly, inherent strain simulation has a number of model time step S equal to the number of layers of coarse elements.

[0061] The model time step S increases at a slower rate relative to the submodel time step S’, and is dependent on the ratio of fine elements to coarse elements. As the vertical unit Hf of layers of fine elements exceeds one vertical unit H_c of coarse elements, an additional layer of coarse elements is applied and therefore an additional model time step S elapses, defining an adjacent model time step S. The submodel time step S' is expressed as a function of S’ = fl(Z’, S’), where submodel distance Z’ is the distance from a first or zero layer of fine elements to a reference plane of fine elements. Likewise, the model time step S’ is expressed as a function of S = fl (Z, S), where model distance Z is the distance from the first or zero layer of fine elements to a reference plane of coarse elements.

[0062] In some embodiments, for a given submodel time step S’, the reference plane of the submodel as a top layer of fine elements of the submodel at a given time step S’. In some embodiments, for a given submodel time step S, the reference plane of the model is defined as a top layer of coarse elements of the model at a given time step S. The reference planes may alternatively or additionally be the coarse and fine layers being simulated. In some embodiments, the model distance Z is equal to the submodel distance Z’, and in some embodiments, the model distance Z is unequal to the submodel distance Z’. In embodiments where the model distance Z is unequal to the submodel distance Z’, the offset vector V may be used in an interpolation calculation between the model distance Z is unequal to the submodel distance Z’

[0063] Additionally, for a given n’ submodel time step S’ for the submodel, n’-layers of fine elements include a first layer of fine elements, at least one intermediate layer of fine elements and an nth layer of fine elements. Likewise, for a given n model time step S for the model, n-layers of coarse elements which include a first layer of coarse elements, at least one intermediate layer of coarse elements and an nth layer of coarse elements. In some embodiments, the nth layer of fine elements of the submodel time step S’ of the submodel is defined as an uppermost fine layer of the submodel. Likewise, the nth layer of coarse elements of the model time step S of the model is defined as an uppermost coarse layer of the submodel.

[0064] For a given n’ submodel time step S’ of the inherent strain simulation of the submodel, boundary condition values from nodes of the model are extracted from a time step S of the model and from model distance Z. The extracted values are applied to a position of the submodel, and the position is located away from the reference plane of the submodel by the submodel distance Z.’

[0065] FIG. 6 illustrates the inherent strain simulation at model time step S = 0, and submodel time step S’ = 1. As previously set forth, each submodel time step S corresponds to the layering of a row of fine elements. In the illustrated embodiment, the first row of fine elements 110-1 are layered over the underlying row of coarse elements 100-0. Because the simulation simulates conditions of an additive manufacturing process, and according to the inherent strain method, the first row of coarse elements 100-1, at least one intermediate row of fine elements (110-2, 110-3, 110-4, etc.) and the n-nth row of fine elements 110-n are not included in the simulation for the given submodel time step S’ = 1.

[0066] In the illustrated step of submodel time step S’ = 1, a subnode 112- 1 of the first row of fine elements 110-1 located along a top edge of the first row of fine elements 110-1 has submodel distance Z’ which is equal to one vertical unit Hf, and a node 102-0 of the underlying row of coarse elements 100-0 located along a top edge of the underlying row of coarse elements 100-0 has a model distance Z vertical unit of zero.

[0067] For an additional model time step S to elapse, at least two additional submodel time step S’ first occur, and therefore the model time step S = 0 and the model distance Z are considered the most adjacent values for the submodel time step S’ = 1. For the given submodel time step S’=l, boundary condition values from nodes 102-0 are extracted from model time step S=0, and the extracted values are applied to node 102-0. Due to non- alignment of the node 102-0 and subnode 112-1, the values for the cut boundary conditions are interpolated relative to the subnode 112-1. The simulation of the first row of fine elements 110-1 for submodel time step S’=l results in a numerical value of one or more mechanical physical attributes for the first row of fine elements 110-1 and the value is stored in memory 14.

[0068] FIG. 7A illustrates the simulation of the second row of fine elements 110-2 at time step S = 0, and submodel time step S ’ = 2. As shown, the second row of fine elements 110-2 is layered across the first row of fine elements 110-1. In executing the simulation for the second row of fine elements 110-2, all underlying layers of fine elements (which have previously been simulated) are simulated with the second row of fine elements 110-2.

[0069] Similar to the simulation of the first row of fine elements 110-1, the submodel distance Z’ is attributed to a subnode 112-2 of the second row of fine elements 110-2 and the boundary conditions are extracted from node 102-0 of the underlying row of coarse elements 100-0. Due to non-alignment of the node 102-0 and subnode 112-2, the values for the cut boundary conditions are interpolated relative to the subnode 112-1. [0070] In some embodiments as shown in FIG. 7B, prior to executing the simulation for the second row of fine elements 110-2, a model time step S has elapsed such that model time step S = 1 and the first row of coarse elements 100-1 is layered across the underlying row of coarse elements 100-0. Here, the model distance Z is one vertical unit H_C3. Elapsing of the additional model time step S occurs when the subnode 112-2 of the second row of fine elements 110-2 is positionally closer to the node 102-1 of the first row of coarse elements 100-1. It is understood that the subnode 112-2 of the second row of fine elements 110-2 is equidistant from the node 102-0 of the underlying row of coarse elements 100-0 and from the node 102-1 of the first row of coarse elements 100-1, and therefore either of the nodes (102-0, 102-1) may be used for interpolation. Alternatively, the boundary condition values may be extracted from both of the nodes (102-0, 102-1) and can be applied by extrapolation between the nodes (102-0, 102-1) relative to the subnode 112-2 of the second row of fine elements 110-2.

[0072] Interpolation and extrapolation may be used in simulating for any fine row of elements. For simulating rows that are vertically closer (along the Z-axis) to the node 102-0 of the underlying row of coarse elements 100-0 (such as the first row of fine elements 110-1), interpolating results in less approximation error relative to extrapolating. For simulating rows that are vertically closer (along the Z-axis) to the node 102-1 of the first row of coarse elements 100-1 (such as the third row of fine elements 110-3 and the fourth row of fine elements 110-4), extrapolating results in less approximation error relative to interpolating. The linear interpolation and linear extrapolation are in two dimensions, however it is understood that non-linear interpolation and non-linear extrapolation may be implemented in three dimensions. Interpolation and extrapolation utilize the ratio of fine elements to coarse elements to calculate the extracted boundary conditions.

[0073] Simulations for the n-nth row of fine elements 110-n is executed in the same manner, and the boundary condition values are interpolated from the node 102-1 of the first row of coarse elements 100-1 and the node 102-2 of the second row of coarse elements 100-1 as shown in FIG. 9. The simulation of the n-nth row of fine elements 110-n results in a numerical value of one or more mechanical physical attributes for n-nth row' of fine elements 110-n, and the value is stored in memory 14.

[0074] The values of the one or more mechanical physical attributes resulting from the simulations for each of the rows of fine elements (first row of fine elements 110-1, at least one intermediate row of fine elements (110-2, 110-3, 110-4, etc.) and an n- nth row of fine elements 110-n) are stored in memory 14. The values are aggregated to output a simulation for the entire submodel.

[0075] FIGS. 10A through 10C are a block diagram illustrating an exemplary method 300 for implementing communications between a computer aided design (CAD) system and a multiphysics modeling module for use in simulating one or more mechanical physical attributes resulting from an additive manufacturing process of a submodel of a geometric CAD model of an object using a discretization method. The method 300 includes applying 302 an inherent strain simulation for the object; and, applying 304 a submodeling method for each submodel time step S’ of the inherent strain simulation of an area of interest defining the submodel.

[0076] The method 300 further includes extracting 306 at least one value for a cut boundary condition for a given submodel time step S’ from a time step S of the model. The at least one value for a cut boundary condition is extracted at a model distance Z, and the model distance Z is defined as the distance to a reference plane of the model normal to a build direction. [0077] The method 300 further includes applying 308 the at least one value for a cut boundary condition to at least one position of the cut boundary. The at least one position is located away from a reference plane of the submodel by a submodel distance Z’ for the given submodel time step S’, and the submodel distance Z’ is defined as the distance to the reference plane of the submodel normal to the build direction. The method 300 further includes defining 310 the reference plane of the submodel as a top layer of fine elements of the submodel at a given time step S’ and, defining 312 a reference plane of the model as a top layer of coarse elements of the model at a given time step S. In some embodiments, the model distance Z is equal to the submodel distance Z’. In some embodiments, the model distance Z is unequal to the submodel distance Z’.

[0078] At the given submodel time step S ’ and for the at least one value for a cut boundary condition applied 308 at the at least one position of the cut boundary', the method 300 further includes calculating 314 from cut boundary condition values extracted from the model from one or more adjacent model time steps S at one or more model distances Z. Applying 302 the inherent strain simulation for the object defines a coarse mesh model of the object. The coarse mesh model defines a plurality of layers of coarse elements. Applying 304 the submodeling method for each model time step S to the area of interest defines a fine mesh submodel of the coarse mesh model, wherein the fine mesh submodel defines a plurality of layers of fine elements.

[0079] The method 300 further includes defining 316 a plurality of fine elements from a coarse element. Each fine element has a fine dimensional value parallel to the build direction of the submodel, and each coarse element has a coarse dimensional value parallel to the build direction of the submodel. The coarse dimensional value is greater than the fine dimensional value by a factor value.

[0080] The method 300 further includes defining 318, at a given submodel time step S’ for the submodel, n’ -layers of fine elements which include a first layer of fine elements, at least one intermediate layer of fine elements and an nth layer of fine elements. The method 300 further includes defining 320, for the model, at a given model time step S, n-layers of coarse elements which include a first layer of coarse elements, at least one intermediate layer of coarse elements and an nth layer of coarse elements. The method 300, further includes defining 322 the nth layer of fine elements of the submodel time step S’ of the submodel as an uppermost fine layer of the submodel; and, defining 324 the nth layer of coarse elements of the model time step S of the model as an uppermost coarse layer of the submodel.

[0082] The method 300 further includes executing 330 the inherent strain simulation at an nth submodel time step S’ for one or more mechanical physical attributes of at least one of the layers of fine elements. For the nth submodel time step S’, the method 300 further includes extracting 332 the values for a cut boundary condition from a coarse element of an n-layer of coarse elements adjacent to the area of interest.

[0083] For extracting 332 at least one value for a cut boundary condition for a given submodel time step S’, the method 300 further includes determining 334 an offset vector having cartesian coordinates. The offset vector is defined by the distance between a node of a coarse element of a coarse layer of the model at an adjacent time step S and a subnode of a fine element of a fine layer at the given submodel time step S’.

[0084] The method 300, further includes defining 336 the node as one of: a point, a corner, an edge, a point along the edge, a middle of the edge, and a middle of a coarse element. The method 300, further includes defining 338 the subnode as one of: a point, a comer, an edge, a point along the edge, a middle of the edge, and a middle of a fine element.

[0085] The method 300 further includes interpolating 340 the at least one value for a cut boundary condition from the coarse element at the adj acent time step S relative to the subnode of the fine element at the given submodel time step S’. In some embodiments, the method 300 further includes interpolating 342 the at least one value for a cut boundary condition from the coarse element at the adjacent time step S relative to subnodes of a fine element of each fine layer underlying the fine layer at the given submodel time step S’. [0086] In some embodiments, executing the simulation for each given submodel time step S’ determines a value of one or more mechanical physical attributes for the fine layer at the given submodel time step S’ and for the fine layer underlying the fine layer at the given submodel time step S’. In some embodiments, the method 300 further includes The method 300 further includes aggregating 344 the value of one or more mechanical physical attributes of each simulation to output a simulation of the submodel. Executing the simulation for the one or more mechanical physical attributes includes simulating 346 for at least one of residual stresses, strain, displacement, and temperature differential created as a result of an additive manufacturing process.

[0087] Embodiments of the disclosure provide an advantage over existing FEA systems and methods that do not have the capability to quickly simulate a fine element model. By implementing inherent strain simulation method for a submodel of the model, finite element simulations need only be executed on a submodel of the model. The described system and methods thus provide modeling a finite element submodel of the CAD model at a higher resolution in a manner that requires fewer processing resources than would be necessary simulating the entire model. By way of example, in one embodiment, to perform a FEA simulation of a finite element model with a fine mesh, up to about fifteen hours of computational time may be needed, whereas to perform a FEA simulation of only the submodel with a fine mesh, only up to about nine minutes of computational time may be needed.

[0088] The systems and processes are not limited to the specific embodiments described herein. In addition, components of each sy stem and each process can be practiced independent and separate from other components and processes described herein. Each component and process also can be used in combination with other assembly packages and processes.

[0089] Although specific features of various embodiments may be shown in some drawings and not in others, this is for convenience only. Moreover, references to “one embodiment” in the above description are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. In accordance with the principles of the disclosure, any feature of a drawing may be referenced and/or claimed in combination with any feature of any other drawing. [0090] This writen description uses examples, including the best mode, to enable any person skilled in the art to practice the disclosure, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the disclosure is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.

[0091] As used herein, a processor may include any programmable system including systems using micro-controllers, reduced instruction set circuits (RISC), application specific integrated circuits (ASICs), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are example only, and are thus not intended to limit in any way the definition and/or meaning of the term “processor.”

[0092] As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible computer-based device implemented in any method or technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data in any device. Therefore, the methods described herein may be encoded as executable instructions embodied in a tangible, non-transitory, computer readable medium, including, without limitation, a storage device and/or a memory device. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methods described herein. Moreover, as used herein, the term “non-transitory computer-readable media” includes all tangible, computer-readable media, including, without limitation, non- transitory computer storage devices, including, without limitation, volatile and nonvolatile media, and removable and non-removable media such as a firmware, physical and virtual storage, CD-ROMs, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being a transitory, propagating signal. [0093] Further aspects of the disclosure are provided by the subject matter of the following clauses:

[0094] A method for implementing communications between a computer aided design (CAD) system and a multiphysics modeling module for use in simulating one or more mechanical physical attributes resulting from an additive manufacturing process of a submodel of a geometric CAD model of an object using a discretization method, the method including applying an inherent strain simulation for the object; and, applying a submodeling method for each submodel time step S' of the inherent strain simulation of an area of interest defining the submodel.

[0095] The method according to the preceding clause further including extracting at least one value for a cut boundary condition for a given submodel time step S’ from a time step S of the model, the at least one value for a cut boundary condition extracted at a model distance Z, wherein the model distance Z is the distance to a reference plane of the model normal to a build direction.

[0096] The method of any preceding clause further including applying the at least one value for a cut boundary condition to at least one position of the cut boundary', the at least one position located away from a reference plane of the submodel by a submodel distance Z’ for the given submodel time step S’, wherein the submodel distance Z’ is the distance to the reference plane of the submodel normal to the build direction.

[0097] The method of any preceding clause further including defining the reference plane of the submodel as a top layer of fine elements of the submodel at a given time step S’; and, defining a reference plane of the model as a top layer of coarse elements of the model at a given time step S.

[0098] The method of any preceding clause, wherein the model distance Z is equal to the submodel distance Z’.

[0099] The method of any preceding clause, wherein the model distance Z is unequal to the submodel distance Z’. [00100] The method of any preceding clause wherein, at the given submodel time step S’, for the at least one value for a cut boundary condition applied at the at least one position of the cut boundary, the method further includes calculating from cut boundary condition values extracted from the model from one or more adjacent model time steps S at one or more model distances Z.