Patent Publication Number: US-2022226897-A1

Title: High Fatigue Strength Porous Structure

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a divisional of U.S. patent application Ser. No. 15/982,704, filed on May 17, 2018, which claims the benefit of the filing date of U.S. Provisional Patent Application No. 62/508,058, filed on May 18, 2017, the disclosures of which are hereby incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to three-dimensional porous structures and, in particular, to three-dimensional structures with porous surfaces having high fatigue strength and a process for the preparation of such structures. 
     BACKGROUND OF THE INVENTION 
     The field of additive layer manufacturing (ALM) has seen many important recent advances in the fabrication of articles directly from computer controlled databases. These advances have greatly reduced the time and expense required to fabricate articles, particularly in contrast to conventional machining processes in which a block of material, such as metal, is machined to engineering drawings. 
     Additive layer manufacturing has been used to produce various porous structures including, for example, medical implants. These structures are built in a layer-by-layer fashion in which individual layers often form portions of unit cells that have regular geometric shapes or irregular shapes having varied sides and dimensions. Various methods for producing a three-dimensional porous tissue ingrowth structure are disclosed in U.S. Pat. No. 9,180,010 filed Sep. 14, 2012 disclosing conformal manipulation of a porous surface; U.S. Pat. No. 9,456,901 filed Jul. 29, 2010 (“the &#39;901 Patent”) disclosing methods of creating porous surfaces having unit cells; and U.S. Pat. No. 7,537,664 filed Nov. 7, 2003 disclosing methods of beam overlap; the disclosures of each of which are incorporated herein by reference. 
     Advantageously, ALM allows for a solid substrate, e.g., a core of an implant, and an outer porous layer to be manufactured simultaneously, reducing manufacturing steps and materials, and thus costs, compared to conventional machining processes. However, current ALM techniques that form solid substrates and then porous layers onto the substrates create rough surfaces on the substrates that act as stress risers and result in an overall structure having relatively low fatigue strength. Due to their low fatigue strength, structures formed in this manner have an increased risk of fracture during use. Avoiding porous surfaces in high stress regions serves to increase the fatigue strength of such structures, but this approach leads to other undesirable properties of produced articles, e.g., by reducing available surfaces for bone in-growth in a medical implant which causes suboptimal implant fixation in the body. 
     Polishing the surfaces of devices is known to increase the fatigue strength of the devices. One well-known technique for polishing internal surfaces is abrasive flow machining, a process for polishing internal surfaces using a pressurized flow of a paste. The abrasive fluid flows through the interstices of the subject device and smooths its rough surfaces. 
     Porous layers of solid-porous layer combinations formed by current ALM techniques have at least one of varying pore shapes and sizes, such as may be caused by the use of randomization techniques including those described in the &#39;901 Patent, and relatively small pore sizes which may result in uneven or insufficient flow, respectively, of abrasive fluids during polishing. Such pore formations may lead to preferential polishing of a path through the largest pores which may not be along the interface of the solid and porous volumes, where the best surface finish is needed. 
     Thus, there is a need for a new process to form highly porous structures without sacrificing fatigue strengths. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with an aspect, a computer-aided design (CAD) first model build structure may include unit cells that may be populated with porous geometries, each of the porous geometries may be made up of struts that extend to vertices of the unit cells and collectively define faces and intersect at nodes at the vertices. The porous geometries can be used to control the shape, type, degree, density, and size of porosity within the structure. The first model build structure may be subjected to conformal manipulation such that certain nodes lying outside a boundary are repositioned to lie on the boundary. The first model build structure may include connection elements, which may be a set of equally spaced-apart joining struts, extending from the nodes repositioned on the boundary. The connection elements may connect the first model build structure to a mating model build structure, which may be a solid CAD model build structure. 
     The porous geometries may include first faces that at least partially confront, i.e., face, the mating model build structure, in which the first faces may extend in a direction parallel to a central axis of the mating model build structure or the faces may extend in any non-parallel direction, and each first face is positioned directly in front of and projects onto the mating building structure. Each of the first faces may be connected to the mating model build structure by a single connection element extending from one of the nodes of the first faces on the boundary. In some arrangements, the first model build structure may be uniformly spaced from the boundary such that connection elements may have substantially equal lengths. 
     A tangible, fabricated porous structure having a solid base or core and corresponding to a combination of the first and mating model build structures may be formed layer by layer using ALM. Notably, this tangible structure would provide for an even flow of abrasive fluid along the porous-solid interface because of the joining struts of equal length. In this manner, a higher fatigue strength of the tangible structure may be achieved. 
     In accordance with another aspect, a porous apparatus may include a first layer and a second layer having a plurality of struts. A portion of the plurality of struts may define a porous geometry. The porous geometry may define a plurality of faces, at least one of the plurality of faces at least partially confronting the first layer. Each of the faces may be bounded by intersecting struts at vertices. Less than all of the vertices of each face at least partially confronting the first layer may be connected to the first layer by a strut, in which each such strut may be a first attachment strut. 
     In some arrangements, the first and second layers may be made of a metal. The metal preferably may be titanium, titanium alloys, stainless steel, cobalt chrome alloys, tantalum and niobium, or any combination thereof. In some arrangements, the porous geometry may be in the form of an octahedron, a dodecahedron, or a tetrahedron. In some arrangements, the first layer may be solid. 
     In some arrangements, additional struts of the plurality of struts may define additional porous geometries that each may define additional faces at least partially confronting the first layer. Each of the additional faces may be bounded by intersecting struts at vertices. Less than all of the vertices of each of the additional faces at least partially confronting the first layer may be connected by additional attachment struts to the first layer. The first attachment strut and the additional attachment struts may have the same length. In some such arrangements, the additional attachment struts may extend in the same direction. In some such arrangements, the additional attachment struts may extend along axes extending through a central axis of the first layer. 
     In accordance with another aspect, a porous apparatus includes a first layer and a second layer having a plurality of struts. Some of the struts define a first porous geometry. The first porous geometry is connected to the first layer by only a first attachment strut. 
     In some arrangements, the first and second layers may be made of a metal selected from the group consisting of titanium, titanium alloys, stainless steel, cobalt chrome alloys, tantalum and niobium. In some arrangements, the first porous geometry may be in the form of an octahedron, a dodecahedron, or a tetrahedron. In some arrangements, the first layer may be solid. 
     In some arrangements, additional struts of the plurality of struts may define additional porous geometries each connected to the first layer by only an additional attachment strut. The first attachment strut and the additional attachment struts may have the same length. In some such arrangements, the additional attachment struts may extend in the same direction. In some such arrangements, the additional attachment struts may each extend along an axis extending through a central axis of the first layer. 
     In some arrangements, the porous apparatus may be a medical implant. 
     In accordance with another aspect, a porous structure may be produced. In producing the porous structure, a first layer of a metal powder may be deposited onto a substrate. The first layer of the metal powder may be scanned with a high energy beam to form either one or both of a portion of a first section of the structure and a portion of a plurality of struts. The struts may define a porous geometry. The struts and the porous geometry may form a second section of the structure. Successive layers of the metal powder may be deposited onto respective previous layers of powder. Each of the successive layers of the powder may be scanned with the high energy beam until the first and second sections and the portion of the plurality of struts defining the porous geometry. The porous geometry may be attached to the first section by only a first attachment strut. 
     In some arrangements, the substrate may be separable from the porous structure. In some other arrangements, the substrate may be integral with the porous structure such that the substrate is inseparable from the porous structure. In some arrangements, the porous apparatus may be a medical implant. 
     In some arrangements, the high energy beam may be an electron beam. In some arrangements, the high energy beam may be a laser beam. In some arrangements, the first section of the structure may be solid. In some arrangements, additional struts may define additional porous geometries each attached to the first section by only an additional first attachment strut. The first attachment strut and the additional attachment struts may have the same length. In some such arrangements, the additional attachment struts may extend in the same direction. In some such arrangements, the additional attachment struts may each extend along an axis extending through a central axis of the structure. 
     In accordance with another aspect of the invention, a porous structure may be produced. In producing the porous structure, a first layer of a metal powder may be deposited onto a substrate. The first layer of the metal powder may be scanned with a high energy beam to form either one or both of a portion of a first section of the structure and a portion of a plurality of struts. The struts may define a porous geometry. The struts and the porous geometry may form a second section of the structure. Successive layers of the metal powder may be deposited onto respective previous layers of powder. Each of the successive layers of the powder may be scanned with the high energy beam until the portion of the first section and the portion of the plurality of struts defining the porous geometry are formed. The porous geometry may define a plurality of faces, at least one of the plurality of the faces at least partially confronting the first section of the structure. Each of the faces may be bounded by intersecting struts at vertices. Less than all of the faces of each face at least partially confronting the first section may be connected to the first section of the porous structure by a strut, in which each such strut may be a first attachment strut. 
     In some arrangements, the substrate may be separable from the porous structure. In some other arrangements, the substrate may be integral with the porous structure such that the substrate is inseparable from the porous structure. In some arrangements, the porous apparatus may be a medical implant. 
     In some arrangements, the first and second layers may be made of a metal. The metal preferably may be titanium, titanium alloys, stainless steel, cobalt chrome alloys, tantalum and niobium, or any combination thereof. In some arrangements, the high energy beam may be an electron beam. In some arrangements, the high energy beam may be a laser beam. In some arrangements, the first section of the structure may be solid. 
     In some arrangements, additional struts of the plurality of struts may define additional porous geometries that each may define additional faces at least partially confronting the first layer. Each of the additional faces may be bounded by intersecting struts at vertices. Less than all of the vertices of each of the additional faces at least partially confronting the first layer may be connected by additional attachment struts to the first layer. The first attachment strut and the additional attachment struts may have the same length. In some such arrangements, the additional attachment struts may extend in the same direction. In some such arrangements, the additional attachment struts may each extend along an axis extending through a central axis of the first layer. 
     In accordance with another aspect of the invention, a computer-generated model of a three-dimensional structure constructed of porous geometries may be prepared according to a process. In this process, a computer-generated component file including a porous CAD volume having a boundary may be prepared. A space may be populated by a processor. The space may include the porous CAD volume which may be populated by unit cells. The unit cells with porous geometries may be populated by a processor. A plurality of porous geometries may have a plurality of struts with nodes at each of the ends of the struts which may include a first strut overlapping the boundary. The first strut may have a length, a first node outside the porous CAD volume, and a second node inside the porous CAD volume. All struts entirely outside the porous CAD volume may be removed such that each of the remaining struts is connected at its corresponding node. The space may be populated, by a processor, with a second strut extending beyond the boundary from a node for connection with a mating structure. 
     In some arrangements, the node from which the second strut extends beyond the boundary may define an intersection of two struts of a porous geometry on or confronting the boundary. In some arrangements, during the process, the first strut overlapping the boundary may be removed, by a processor, when the first node at the first end of the strut is further from the boundary than the second node at the second end of the first strut. 
     In some arrangements, the second node at the second end of the first strut may be connected to an adjacent strut inside the porous CAD volume. A closer of the first and the second nodes may be moved to a position along the boundary during the process. When the first node is the closer node, the length of the first strut may be changed such that the first strut remains connected to the first node. When the second node is the closer node, the length of the adjacent strut may be changed such that the first strut remains connected to the second node. When the second node is the closer node, the first node and the first strut overlapping the boundary may be removed. 
     In some arrangements, the second strut may be connected with the mating structure. In some arrangements, the mating structure may correspond to a solid or substantially solid structure. In some arrangements, a method of fabricating a porous structure may include three-dimensional (3-D) printing a three-dimensional structure having a shape and dimensions corresponding to the computer-generated model prepared. 
     In accordance with another aspect of the invention, a non-transitory computer-readable storage medium may have computer readable instructions of a program stored on the medium. The instructions, when executed by a processor, may cause the processor to perform a process of preparing computer-generated model of a three-dimensional structure constructed of porous geometries. In this process, a computer-generated component file including a porous CAD volume having a boundary may be prepared. A space including the porous CAD volume with unit cells may be populated by a processor. The unit cells may be populated, by a processor, with the porous geometries. A plurality of the porous geometries may have a plurality of struts that may have opposing ends. Each of the ends may be connected at a corresponding node. A first strut of the plurality of struts may overlap the boundary. The first strut may have a length, a first node at a first end outside the porous CAD volume, and a second node at a second end inside the porous CAD volume. All struts entirely outside the porous CAD volume may be removed, by a processor, such that each end of the remaining struts remains connected at its corresponding node. The space may be populated, by a processor, with a second strut extending beyond the boundary from a node for connection with a mating structure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of the subject matter of the present invention and the various advantages thereof may be realized by reference to the following detailed description, in which reference is made to the following accompanying drawings: 
         FIG. 1  is a functional diagram of a system in accordance with an exemplary embodiment; 
         FIG. 2A  illustrates a wireframe of porous geometries created within unit cells that intersect a boundary of a porous CAD volume, which models the porous portion of the structure to be manufactured up to the outer boundary of the porous portion, as known in the prior art; 
         FIG. 2B  illustrates the nodes and the struts of the porous geometries within the unit cells of  FIG. 2A ; 
         FIGS. 3A and 3B  illustrate the wireframe of the porous geometries of  FIG. 2  after removing the full length of struts lying entirely outside the boundary of the porous CAD volume and removing the full length of struts overlapping the boundary that have outer nodes further from the boundary than their corresponding inner nodes as known in the prior art; 
         FIGS. 4A and 4B  illustrate the wireframe of the porous geometries of  FIG. 3  after repositioning of the nodes closest to the boundary to positions along the boundary of the porous CAD volume through conformal manipulation, as known in the prior art; 
         FIGS. 5A and 5B  are plan and side cross-sectional views of a solid CAD volume surrounded by a porous CAD volume of a cylindrical geometry, in accordance with an embodiment; 
         FIG. 6  is a partial cross-sectional side view of a porous CAD volume along an edge of a solid CAD volume aligned along a Z-axis, in accordance with another embodiment; 
         FIG. 7  is a partial cross-sectional side view of a porous CAD volume along an edge of a solid CAD volume aligned along a Z-axis in accordance with another embodiment; and 
         FIG. 8  is a process flow diagram in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  depicts system  105  that may be used to generate, store and share three-dimensional models of structures. System  105  may include at least one server computer  110 , first client computer  120 , and in some examples, second client computer  130 . These computers may send and receive information via network  140 . For example, a first user may generate a model on first client computer  120  which may be uploaded to server  110  and distributed via network  140  to second client computer  130  for viewing and modification by a second user. 
     Network  140 , and intervening communication points, may comprise various configurations and protocols including the Internet, World Wide Web, intranets, virtual private networks, wide area networks, local networks, private networks using communication protocols proprietary to one or more companies, Ethernet, WiFi, and HTTP, and various combinations of the foregoing. Such communication may be facilitated by any device capable of transmitting data to and from other computers, such as modems (e.g., dial-up, cable or fiber optic) and wireless interfaces. Although only a few devices are depicted, a conventional system may include a large number of connected computers, with each computer being at a different communication point of the network. 
     Each of computers  110 ,  120 , and  130  may include a processor and memory. For example, server  110  may include memory  114  which stores information accessible by processor  112 , computer  120  may include memory  124  which stores information accessible by processor  122 , and computer  130  may include memory  134  which stores information accessible by processor  132 . 
     Processors  112 ,  122 ,  132  may be any conventional processor, such as commercially available CPUs. Alternatively, the processors may be dedicated controllers such as an ASIC, FPGA, or other hardware-based processor. Although shown in  FIG. 1  as being within the same block, the processor and memory may comprise multiple processors and memories that may or may not be stored within the same physical housing. For example, memories may be a hard drive or other storage media located in a server farm of a network data center. Accordingly, references to a processor, memory, or computer will be understood to include references to a collection of processors, memories, or computers that may or may not operate in parallel. 
     The memories may include a first part storing applications or instructions  116 ,  126 ,  136  that may be executed by the respective processor. Instructions  116 ,  126 ,  136  may be any set of instructions to be executed directly (such as machine code) or indirectly (such as scripts) by the processor. In that regard, the terms “applications,” “instructions,” “steps” and “programs” may be used interchangeably herein. 
     The memories may also include a second part storing data  118 ,  128 ,  138  that may be retrieved, stored or modified in accordance with the respective instructions. The memory may include any type capable of storing information accessible by the processor, such as hard-drive, memory card, ROM, RAM, DVD, CD-ROM, write-capable, and read-only memories or various combinations of the foregoing, where applications  116  and data  118  are stored on the same or different types of media. 
     In addition to a processor, memory and instructions, client computers  120 ,  130  may have all of the components used in connection with a personal computer. For example, client computers  120 ,  130  may include respective electronic displays  129 ,  139  (e.g. a monitor having a screen, a touch screen, a projector, a television, a computer printer, or any other electrical device that is operable to display information), one or more user inputs (e.g. a mouse, keyboard, touch screen and/or microphone), speakers, and all of the components used for connecting these elements to one another. 
     Instructions  126 ,  136  of first and second client computers  120 ,  130  may include building applications  125 ,  135 . For example, the building applications may be used by a user to create three-dimensional structures, described further herein. The building applications may be associated with a graphical user interface for displaying on a client computer in order to allow the user to utilize the functions of the building applications. 
     A building application may be a CAD three-dimensional modeling program or equivalent as known in the art. Available CAD programs capable of generating such a structure include Autodesk® AutoCAD®, Creo® by Parametric Technology Corporation (formerly Pro/Engineer), Siemens PLM Software NX™ (formerly Unigraphics), and CATIA® by Dassault Systemes. 
     Data  118 ,  128 ,  138  need not be limited by any particular data structure. For example, such data may be stored in computer registers, in a relational database as a table having a plurality of different fields and records, or XML documents. The data may also be formatted into any computer-readable format, which preferably may be binary values, ASCII or Unicode. Further, the data may comprise any information sufficient to identify the relevant information, such as numbers, descriptive text, proprietary codes, pointers, references to data stored in other memories (including other network locations) or information that is used by a function to calculate the relevant data. For example, data  128  of first client computer  120  may include information used by building application  125  to create three-dimensional models. 
     In addition to the operations described above and illustrated in the figures, various other operations will now be described. It should be understood that the following operations do not have to be performed in the exact order described below. Instead, various steps may be handled in a different order or simultaneously. Steps may also be omitted or added unless otherwise stated herein. 
     An overall three-dimensional representation of a component may first be generated by preparing a CAD model. This overall CAD model may include one or more distinct CAD volumes, e.g., solid and porous CAD volumes, that are intended to be modeled by a model build structure which in turn used to manufacture a part as either solid or porous geometries or a combination of the two. 
     Solid CAD volumes may be sliced into layers of a predetermined thickness ready for hatching, re-merging with the porous volume (post-lattice generation) and subsequent manufacture. 
     Porous CAD volumes (the basic principles of which are detailed in  FIGS. 2A and 2B ) may be processed using bespoke software. In some examples, a model structure, such as model build structure  50  identified in  FIGS. 3A and 3B  is made up of a plurality of struts defining individual porous geometries which are organized within tessellated unit cells, e.g., porous geometries  55  identified in  FIG. 2A  which are organized within tessellated unit cells  60 . Many designs of porous geometries are possible to impart various strength, surface, and/or other characteristics into the porous CAD volume. For example, these porous geometries can be used to control the shape, type, degree, density, and size of porosity within the structure. Such porous geometry designs may be bounded by unit cells that may be dodecahedral, octahedral, tetrahedral (diamond), as well as many other various shapes. Besides such regular geometric shapes, the cells of the present invention may be configured to have irregular shapes where various sides and dimensions have little if any repeating sequences. The cells, including the unit cells, may be configured to constructs that closely mimic the structure of trabecular bone, for instance. Porous geometries can be space filling, in which all the space within a three-dimensional object is filled with porous geometries but do not always fill the space of an object they are used to produce. 
     The first step in creating a porous CAD volume is to calculate a bounding box, a box with x, y, and z dimensions corresponding to, or slightly larger than, a predefined boundary of the porous CAD volume, which may be the entire boundary or a portion of a boundary. The bounding box is then divided into a number of cells, such as unit cells  60 , defined by x, y, and z dimensions. Calculations are then performed during an interrogation on each individual cell  60  to ascertain if each cell is within or intersects the boundary of the porous CAD volume. If these conditions are satisfied for an individual cell, that cell is retained such as in the example of  FIG. 2A , and if they are not satisfied, that cell is discarded. Once all cells have been interrogated, the overall porous geometry is populated within cells that have been retained, such as in the example of  FIGS. 2A and 2B  in which a collection of porous geometries  55 , which together form model build structure  50 , are populated within unit cells  60  that have been retained in a porous CAD volume. 
     Each of the individual porous geometries  55  is made up of struts, i.e., segments having a length. Nearly all of the struts meet at a node or intersection. The position of the nodes may be identified within an array of the data of the processor according to Cartesian, polar coordinates, or other user-defined coordinates. 
     In one example, a porous CAD volume is bounded by predefined boundary  100  that corresponds to the intended surface of a part to be formed. As shown in  FIGS. 2A and 28 , some unit cells along predefined boundary  100  have overlapping struts that cross over the boundary. The struts have inner nodes within boundary  100  and outer nodes outside the boundary. To produce a porous structure having struts that terminate at boundary  100 , each strut that intersects the boundary is either fully retained or removed depending on the distance of its nodes from boundary  100 . Each strut having an outer node farther from boundary  100  than its inner node is fully removed. Whereas, each strut having an outer node closer to boundary  100  than its inner node is fully retained. In this example, with reference to  FIGS. 2B, 3A, and 3B , struts  9 - 12 ,  16  and  19  are fully removed because their outer nodes are farther from the boundary than their inner nodes. Whereas, struts  8 ,  13 - 15 ,  17 - 18 , and  20 - 21  are fully retained because outer nodes  25 ,  30 ,  32 ,  34 , and  35 , although outside the boundary  100 , are still closer than their corresponding inner nodes. 
     Still referring to this example, as shown in  FIGS. 4A and 4B , after removal of the appropriate struts, the nodes closest to boundary  100 , nodes  25 - 35 , may be repositioned to lie on the boundary, and as such nodes  25 - 35  are conformal nodes. In some examples, the conformal nodes may be repositioned based on a mathematical calculation based on the original position of each of these nodes, the distance from the boundary of each of these nodes, or based on the original length of the struts attached to these nodes that overlap the boundary, or based on both of these values. In this way, the shape of the structure may be maintained or at least substantially maintained when having conformal nodes along the boundary. 
     Upon repositioning of nodes  25 - 35 , the struts connected to these nodes may be lengthened or shortened to maintain connectivity with the repositioned nodes. Alternatively, nodes  25 - 35  may not be repositioned but rather discarded and replaced by new nodes. Likewise, the struts originally connected to nodes  25 - 35  may be discarded and replaced by new struts that are longer or shorter than the original struts to provide connectivity with the corresponding repositioned nodes. In this manner, the unit cells and nodes experience conformal manipulation. 
     In another example, only struts having both nodes inside the boundary may be retained. The node closest to the boundary may then be repositioned to lie on the boundary and any adjacent strut previously connected to the repositioned node may be lengthened or shortened to maintain connection with the repositioned node, as described above. Alternatively, the nodes and struts may be replaced with new nodes and struts, as above. 
     The use of polar or spherical coordinates may be preferred to the use of Cartesian coordinates when a surface of a model build structure to be formed is curvate or cylindrical. In this manner, nodes repositioned on a boundary may be positioned at the same angle defining a replaced node but at a different radius from the origin of a polar coordinate system being used to create a model build structure. However, other user-defined node positioning system also may be used to form a model build structure having nodes along an outer boundary that fit the contours of the outer boundary of the component being modeled. 
     Referring now to  FIGS. 5A and 5B , porous structure  210 , which in some arrangements may be in the form of a medical implant, includes first layer or section  220  and porous model build structure  250  that connects to the first layer at interface  225 . First layer  220  forms a base or core of structure  210  and, as in this example, may be solid, although in alternative arrangements the first layer may be at least partially porous. Porous model build structure  250  includes porous layer  230  and joining struts  240  that connect the model build structure to first layer  220  at interface  225 . Porous layer  230  includes a plurality of porous geometries  255 . 
     Porous geometries  255  may be modeled using available CAD programs, which preferably may be any of those described previously herein, through the use of cells in the manner described previously herein. In the example shown, octahedral unit cells may be used to form porous geometries  255 . In alternative arrangements, other cell designs may be utilized, which may, in some arrangements, be either or both octahedral and dodecahedral unit cells. In the example shown, each porous geometry  255  includes a plurality of struts  245  that intersect at vertices defining boundary nodes  270  along circular boundary  200  and at vertices defining nodes  275  at positions away from the boundary to define faces  285  of the unit cells facing away from first layer  220  and faces  295  at least partially confronting first layer  220 . 
     Porous geometries  255  along boundary  200  define faces  295  that at least partially confront first layer  220  and have struts  245  connected at one of their ends to boundary nodes  270 , which in this example have been repositioned onto porous boundary  200  in the same manner as nodes  25 - 35  were repositioned along boundary  100  as described above with respect to model build structure  50 . Each face  295  at least partially confronting first layer  220  is connected to the first layer by single joining strut  240  extending from one of the boundary nodes  270 . In this manner, as boundary  200  is equidistant about its circumference from first layer  220 , boundary nodes  270  are set at substantially equal distances from first layer  220 , and as a result, joining struts  240  connecting porous layer  230  to first layer  220  are all of substantially equal lengths. 
     With this configuration, abrasive polishing material can flow evenly along an interface of a fabricated structure corresponding to interface  225  of structure  210  at a junction of a core and a porous section of the fabricated structure corresponding to first layer  220  and porous model build structure  250 , respectively. In this manner, a higher fatigue strength of the fabricated structure corresponding to structure  210  may be achieved. 
     Unlike nodes  270 , nodes  275  are not connected to any joining strut  240  extending to first layer  220 . In this manner, less than all of the nodes of each porous geometry  255  are connected to first layer  220 . 
     Although the joining struts may be of substantially equal lengths, such as in the example of  FIGS. 5A and 5B , the joining struts may extend in any possible build direction. In the example of  FIGS. 5A and 5B , joining struts  240  extend in parallel planes perpendicular to a central axis of first layer  220  and in various directions ranging between approximately 0 degrees and 360 directions about a circumference of boundary layer  200  and first layer  220 . Alternatively, joining struts  240  may be defined as being oriented in directions defined by the intersection of a plane defined by a vector normal to their respective attachment points on the first layer  220  and orthogonal to boundary layer  200 , which may correspond to a build surface. As further shown in  FIG. 5A , in some such arrangements, joining struts  240  all extend along axes extending through a central axis of first layer  220 . 
     Referring to  FIGS. 6 and 7 , in other examples, the joining struts may extend in the same direction. As shown in  FIG. 6 , structure  310  includes joining struts  340  extending in an upward direction along the z-axis and connecting first layer  320  to porous layer  330 . In contrast, as shown in  FIG. 7 , structure  410  includes joining struts  440  extending in a downward direction along the z-axis and connecting first layer  420  to porous layer  430 . Alternatively, joining struts  340 ,  440  may be defined as being oriented in directions defined by the intersection of a plane oriented 45 degrees upward or downward from its attachment point on first layers  320 ,  420  towards the boundary nodes along boundaries  300 ,  400 , respectively. In another example, adjacent joining struts may extend in an alternating upward-downward pattern. In this manner, interconnecting pore size may be larger at the interface of the porous surface and the first layer, which may be a core. The larger interconnecting pore size may preferably allow a greater amount of abrasive material to flow along the interface. 
     In some arrangements, the joining struts, such as joining struts  240 ,  340 ,  440  may be larger or smaller in diameter than other struts of a model build structure, such as model build structure  250 . In some arrangements, the joining struts, such as joining struts  240 ,  340 ,  440  may be longer or shorter than other struts of a model build structure, such model build structure  250 . In some arrangements, more than a single joining strut, such as joining struts  240 ,  340 ,  440 , may extend from vertices of intersecting struts defining faces of a porous geometry at least partially confronting the first layer, e.g., core, of a structure, but in such arrangements, less than all of the vertices of each face of the porous geometry at least partially confronting the first layer may be connected by a strut to the first layer. 
     Each of structures  210 ,  310 , and  410  may be formed in a layer-by-layer fashion during an ALM, i.e., 3D printing, process using a high energy beam, which may be a selective laser sintering (SLS) or selective laser melting (SLM) process as described in U.S. Pat. Nos. 7,537,664; 8,728,387; and 9,456,901, the disclosures of each of which are hereby incorporated by reference herein. A first layer or portion of a layer of metal powder is deposited onto a substrate, which, in some arrangements, may be a core of a structure, a base, or a work platform, and then scanned with the high energy beam so as to sinter or melt the powder and create a portion of a plurality of predetermined porous geometries, such as porous geometries  255 ,  355 ,  455 . Successive layers of the metal powder are then deposited onto previous layers of the metal powder and also respectively scanned with the high energy beam prior to the deposition of subsequent layers of the metal powder. The scanning and depositing of successive layers of the metal powder continues the building process of the predetermined porous geometries. Such continuation of the building process refers not only to a continuation of a predetermined porous geometry from a previous layer but also a beginning of a new predetermined porous geometry as well as or instead of the completion of a predetermined porous geometry, depending on the desired characteristics of the structure to be fabricated. 
     The structures formed using this process may be partially porous and, if desired, have interconnecting pores to provide an interconnecting porosity. The base or core may be fused to the 3D-printed structure, which may be a porous layer or section of the fabricated structure. At least one of the base or core and the 3D-printed structure preferably may be made of any of cobalt chrome alloy, titanium or alloy, stainless steel, niobium and tantalum. Thus, a mixture of desired mixed materials may be employed. 
     The high energy beam preferably may be an electron beam (e-beam) or laser beam and may be applied continuously to the powder or pulsed at a predetermined frequency. In some arrangements, the use of a laser or e-beam melting process may preclude the requirement for subsequent heat treatment of the structure fabricated by the additive manufacturing process, thereby preserving the initial mechanical properties of the core or base metal when fused to the fabricated structure. The high energy beam is emitted from a beam-generating apparatus to heat the metal powder sufficiently to sinter and preferably to at least partially melt or melt the metal powder. High energy beam generation equipment for manufacturing such structures may be one of many currently available including the MCP REALIZER, the EOS M270, TRUMPF TRUMAFORM 250, the ARCAM EBM S12, and the like. The beam generation equipment may also be a custom-produced laboratory device. 
     The pore density, pore size and pore size distribution may be controlled from one location on the structure to another. It is important to note that successive powder layers may differ in porosity by varying factors used for laser scanning powder layers. Additionally, the porosity of successive layers of powder may be varied by either creating a specific type of unit cell or manipulating various dimensions of a given unit cell. In some arrangements, the porosity may be a gradient porosity throughout at least a portion of the fabricated structure. The beam generation equipment may be programmed to proceed in a random generated manner to produce an irregular porous construct but with a defined level of porosity. Pseudo-random geometries may be formed by applying a perturbation to the vertices of porous geometries when preparing model build structures corresponding to the 3D structure to be fabricated. In this manner, the porous geometries may be randomized. 
     In fabricating a structure corresponding to porous structure  200 , a first layer of metal powder may be deposited and scanned by a high energy beam to form a first section of the structure corresponding to first layer  220  of structure  200 . The first section of the structure may form a base or core of the structure, which as shown may be solid, but in alternative arrangements may be at least partially porous. 
     Successive layers of the metal powder are then deposited onto the previous layers of the metal powder and then respectively scanned with the high energy beam prior to deposition of subsequent layers of the metal powder to form a plurality of struts defining porous geometries corresponding to the plurality of struts  245  defining porous geometries  255  of model build structure  250 . In this manner, the fabricated structure is formed as a three-dimensional structure corresponding to porous structure  200  in which the struts corresponding to the plurality of struts  245  intersect at vertices corresponding to nodes  270 ,  275 , which define faces of the porous geometries corresponding to porous geometries  255 . As a result, the porous geometries of the fabricated structure corresponding to the porous geometries  255  have faces that at least partially confront the first section corresponding to first layer  220  of structure  200 . Each of the fabricated faces is connected to the first section by a single joining strut corresponding to single joining strut  240  extending to the first section from a vertex of a face partially confronting the first section and corresponding to one of the nodes  270 . 
     Due to the correspondence of the joining struts of the fabricated structure to joining struts  240  of structure  200 , the joining struts of the fabricated structure all have substantially equal lengths. This equivalency eliminates a preferential path for abrasive fluid to flow between the porous section of the fabricated structure corresponding to model build structure  250  of porous structure  200  and the first section of the fabricated structure during polishing the first section. In this manner, the fatigue strength of the fabricated structure may be increased. 
     Although the joining struts are preferably of substantially equal lengths to enhance polishing of the first section of the fabricated structure, the joining struts of the fabricated structure may correspond to any of joining struts  240 ,  340 ,  440  and thus may extend in different build directions. 
     Referring now to  FIG. 8 , a computer-generated component file is prepared at block  510 . The component file includes a porous CAD volume with a boundary having at least one predefined portion. At block  520 , a space that includes the porous CAD volume is populated, by a processor, with unit cells that overlap the predefined portion of the boundary. Such a space may be defined by sets of coordinates, such as Cartesian, polar, or spherical coordinates. At block  530 , the unit cells are populated, by a processor, with porous geometries. Within the porous geometries may be a plurality of struts. At least one end of the struts may be attached to a node. As further shown at block  530 , at least one of the struts overlaps the predefined portion of the boundary. Such a strut has a length, one node outside the porous CAD volume, and one node inside the porous CAD volume. At block  540 , any struts entirely outside the predefined portion of the boundary are removed. In some arrangements, any struts outside the entire boundary are removed. At block  550 , the space is populated, by a processor, with a second strut extending beyond the boundary from a node for connection with a mating structure. In this manner, a computer-generated model of a three-dimensional structure constructed of porous geometries is prepared. At optional block  560 , a tangible three-dimensional structure having a shape corresponding to the computer-generated model may be produced. The shape of the three-dimensional structure may be in the form of an at least partially geometric lattice structure. 
     Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention. In this regard, the present invention encompasses numerous additional features in addition to those specific features set forth in the claims below.