WO2023228063A1

WO2023228063A1 - Cell with octagonal structure and lattice structure comprising said cell for biomedical applications

Info

Publication number: WO2023228063A1
Application number: PCT/IB2023/055271
Authority: WO
Inventors: Gabriella EPASTO; Fabio DISTEFANO
Original assignee: Mt Ortho S.R.L.; GUGLIELMINO, Eugenio
Priority date: 2022-05-24
Filing date: 2023-05-23
Publication date: 2023-11-30

Abstract

The present invention concerns a new cell configuration with octagonal structure and a lattice structure comprising a plurality of said octagonal cells for applications in the biomedical field. More particularly, the present invention concerns the mechanical and morphological characterization of a new unit cell for applications in the biomechanical field, more specifically for the production of bone scaffolds. The proposed octagonal structure cell, advantageously realized by means of EBM techniques Electron Beam Melting- allows to make lattice structures suitable for application in the field of biomechanics and having improved mechanical characteristics. Th tree-dimensional cell structure (1) according to the present invention is made of biocompatible metallic material and comprises a plurality of struts (11) that meet at nodes (12) to define a plurality of constituent elements (10a) interconnected in elementary ring structures (10, 10', 10"). Said cell structure (1) comprises constituent elements (10a) of regular octagonal shape, and its particular structure allows to be able to vary the relative density value of the structure, defined as the ratio of the volume (Vc) occupied by the struts (11) of the unit cell to the total volume of the geometry (Vm), by varying the structural parameters of the cell so as to have a relative density between 0.05 and 0.3, more preferably between 0.1 and 0.2.

Description

CELL WITH OCTAGONAL STRUCTURE AND LATTICE STRUCTURE COMPRISING SAID CELL FOR BIOMEDICAL APPLICATIONS

FIELD OF THE INVENTION

The present invention concerns a new cell configuration with octagonal structure and a lattice structure comprising a plurality of said octagonal cells for applications in the biomedical field.

More particularly, the present invention concerns the mechanical and morphological characterization of a new unit cell for applications in the biomechanical field, more specifically for the production of bone scaffolds.

The proposed octagonal structure cell, advantageously made by means of EBM techniques - Electron Beam Melting- allows to make lattice structures suitable for application in the field of biomechanics and having improved mechanical characteristics.

BACKGROUND ART

Morphologically ordered lattice structures based on one or more repeated unit cells are known in the state of the art.

Examples of such repeated cell lattice structures are described in the earlier documents US 2018/228612 Al, US 10 695 184 B2, US 2021/228360 Al, US 2011/076316 Al and US 6206 924 Bl.

Additive Manufacturing (AM) techniques enable the manufacture of complex lattice structures, having a geometry that would otherwise be unfeasible with traditional manufacturing methods.

The unit cells made with these technologies are defined by the dimensions and by the connection methods of their constituent elements, which are connected at nodes.

Many lattice structures composed of several unit cells based on known geometries have been studied over the years. Micro-reticulated structures based on the rhombic dodecahedron (RD) or on solids such as the cubottahedron, the truncated octahedron (Kelvin cell), the rhombicubottahedron or the truncated cubottahedron have been studied through the finite element investigation (FEM) methods to estimate their mechanical properties or with experimental tests.

In other research, microlattice structures with unit cells having shapes derived from the observation of nature, for example like diamond and gyroid have been studied by performing experimental tests. These structures have also been studied for application in the biomechanical field.

In other works, the mechanical response and the process of the deformation mechanism at different stresses have been studied by means of quasi-static compression and FEM tests for lattice structures and single unit cells.

Several studies have proposed new unit cells. For example, Mahbod et al. proposed a new unit cell called double pyramid dodecahedron developed by deriving the analytical relationships to estimate the mechanical properties of the structure.

The unit cell lattice structures have been used and studied through finite element analysis (FEM) also for applications in the biomechanical field for the manufacture of devices with both porous and solid structures in the treatment of bone diseases of the hip, in the long bones and in the spine.

A biomimetic-inspired design approach is widely used in the design of cellular and lattice structures for use in the biomedical field. This approach is based on the observation of natural elements with repeated geometry, such as: honeycomb structure, microstructure of the wood, spongy bone and so on.

The solutions of known type, therefore, are not without drawbacks.

In particular, the shape and materials of the cellular and lattice structures of known type have limitations in the mechanical characteristics. In fact, on the one hand, these characteristics must be compatible with use in the biomechanical sector, in particular as regards the elasticity of the structure, on the other hand they must make it possible to replicate as much as possible the mechanical behaviour of the natural bone.

The porosity of the structure represents a critical parameter that influences the mechanical behaviour and, consequently, the ability of the cell to come as close as possible to the mechanical behaviour of the bone.

In fact, a structure having a greater porosity, i.e. a ratio of density to volume, can advantageously be brought into contact with the cortical bone, and a structure having a lower porosity, i.e. a ratio of density to volume, can promote osseointegration with the spongy bone thanks to the mechanical affinity with this tissue.

SUMMARY OF THE INVENTION

In light of the above, the task of the present invention is to provide a cell in biocompatible metallic material and a lattice structure comprising one or more of said repeated unit cells for the production of bone scaffolds, which is adapted to guarantee improved morphological and mechanical characteristics with respect to solutions of known type.

The design and the production of an artificial structure that reproduces a natural structure can be achieved in various ways, for example by directly replicating the natural structure, by means of reverse-engineering operations, or with a generically bio-inspired design approach, as described in the article A. du Plessis et al., “Beautiful and Functional: A Review of Biomimetic Design in Additive Manufacturing” Addit. Manuf., vol. 27, no. March, pp. 408-427, 2019, doi: 10.1016/j.addma.2019.03.033.

Starting from this “biomimetic” approach, the cell object of the present invention has been devised and designed, which can be defined Triply Arranged Octagonal Rings (TAOR), and has been developed by applying the Gibson-Ashby model (M. F. Ashby, “The properties of foams and lattices ” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 364, no. 1838, pages 15-30, 2006, doi: 10.1098/rsta.2005.1678.) and Maxwell's criterion (V. S. Deshpande, M. F. Ashby, and N. A. Fleck, “Foam topology: Bending versus stretching dominated architectures” Acta Mater., vol. 49, no. 6, pages 1035-1040, 2001, doi: 10.1016/S1359-6454(00) 00379-7.) as well as performing tests and compression tests in the laboratory.

Through the aforementioned criteria, the mechanical and morphological characterization of the cell has been achieved for applications in biomechanical devices used in the treatment of bone diseases according to the present invention, which is preferably made of biocompatible metallic material, in particular in titanium alloy, preferably in Ti6A14V ELI and produced using the EBM technology (electron beam melting).

The cell with octagonal structure and the lattice structure comprising a plurality of said octagonal cells according to the present invention allow to optimize the mechanical and morphological characteristics of the constituent unit of the lattice, in particular, thanks to the specific structure of the new cell, it is obtained that the first and the last layer of elements are deformed before the central part since their deformation mechanism is dominated by the failure of the nodes. The yielding of the vertical struts is buckling- dominated, which causes the final collapse of the cell. This failure mode allows a programmed energy absorption system to be designed.

Furthermore, the cell with octagonal structure and the lattice structure comprising a plurality of said octagonal cells according to the present invention have higher values of elastic modulus, and crush resistance, than cells of known shape, for example the Kelvin cells, with any density level of the cell.

In particular, the elastic modulus is an important parameter for application in the biomechanical field, because values of the elasticity of the cell, and of the lattice structure obtained with a plurality of said cells, in the range of the elastic modulus of the bone from 0.5 to 20 GPa promote the osseointegration process. The mechanical properties of the microlattice structures studied increase with increasing relative density, according to the data in the literature (T. Maconachie et al., “SLM lattice structures: Properties, performance, applications and challenges’’ Mater. Des., vol. 183, p. 108137, 2019, doi: 10.1016/j.matdes.2019.108137).

Aim of the present invention is therefore to provide a cell for the realization of lattice structures for biomedical applications, in particular for the realization of bone scaffolds, as it allows to obtain a structure with mechanical characteristics that are variable according to the density of the structure. In this way, by choosing a higher density ratio the structure can be brought into contact with the cortical bone, whereas a portion of the device made with a lower density lattice structure can ensure mechanical affinity with the spongy bone, promoting osseointegration.

LIST OF FIGURES

Further characteristics and advantages will become more apparent from the following exemplary but non-limiting description of a preferred embodiment of the present invention which will be given hereinbelow with the aid of the attached drawings in which:

Figure 1 shows a schematic perspective representation of a cell structure according to the present invention;

Figure 2 shows a schematic perspective representation of one of the three elementary ring structures that make up the cell structure of Figure 1,

Figure 3 shows a front view of the cell structure according to the present invention in which the constituent elements of the elementary ring structures are constituted by regular octagons made of struts that connect in nodes;

Figure 4 shows, in views a), b) and c) a lattice structure comprising a plurality of cell structures according to the present invention with variable relative densities of the lattice structures, compared in views d), e) and f) with cell structures of the Kelvin type;

Figure 5 shows a perspective view of a model of the finite elements of the cell structure according to the present invention constrained below and to which a crushing has been imposed in a vertical direction with an upper plane to which a shift has been imposed;

Figure 6 illustrates the results of the finite element analysis FEM carried out on the cell model of Figure 5;

Figure 7 illustrates two graphs showing the results of the compression tests carried out on the two different cell structures: the cell structure according to the present invention (indicated with TAOR), in graph (a), the Kelvin cell structure of known type, in graph (b);

Figure 8 shows the comparison between the results of the compression tests carried out on three tested unit cell structures, namely TAOR, Kelvin and RD;

Figure 9 illustrates the curves obtained from the interpolation of the relative elastic modulus (a) and relative strength (b) data and plotted against the relative density for the TAOR cell structures according to the present invention;

Figure 10 illustrates the curves obtained from the interpolation of the relative elastic modulus (a) and relative strength (b) data and plotted against the relative density for the Kelvin cell structures;

Figure 11 illustrates the same data as Figures 9 and 10 plotted in a Gibson-Ashby diagram for comparison with other microlattice structures wherein diagram (a) reproduces the trend of the relative elastic modulus plotted against the relative density and diagram (b) reproduces the trend of the relative strength plotted against relative density;

Figure 12 illustrates the mode of breakage of a reticulated structure sample consisting of TAOR cells in (a) compared to a reticulated structure sample consisting of Kelvin cells in (b);

Figure 13 illustrates a diagram that correlates the application of the load and the onset of the damage in compression tests carried out on specimens that have been monitored by means of an infrared camera capable of detecting the thermal response of the cells, i.e. the temperature increase detected in particular on the TAOR 0.05 specimen during the compression test.

DETAILED DESCRIPTION OF THE INVENTION

The cell structure 1 according to the present invention has a substantially octagonal structure. More specifically, with particular reference to Figure 1, the cell structure 1 according to the present invention comprises an elementary ring structure 10, visible in Figure 2, formed by eight constituent elements 10a having equal dimensions to each other and arranged side by side, and each formed by struts 11 that meet in a series of nodes 12. Advantageously, said base elements 10a are octagonal in shape and, preferably, said struts 11 consist of substantially straight sections of cylindrical shape having a diameter d and a length L connected together in nodes 12 to form octagonal structures, according to what is visible in Figure 3. Advantageously said base elements 10a have a regular structure since the struts 11 that form said base elements are characterized by the same diameter d and by the same length L.

To ensure the functionality of the structure, a symmetrical design was then imposed, so that each unit cell 1 is composed of three identical rings 10, 10’, 10” arranged perpendicularly to each other, according to the direction of the axis-triad shown in Figure 1. To better clarify the structure of the cell 1, each ring 10, 10’, 10” is in turn formed by a plurality of octagonal elements 10a that are interconnected according to what is shown in Figure 2. Each of said ring structures 10, 10’, 10” identifies a plane of symmetry passing through the axis of symmetry of the ring itself.

A first ring structure 10, shown in Figure 2, will therefore define a plane of symmetry lying in a first plane YZ, a second ring structure 10’ will define a plane of symmetry lying in a second plane XY, and a third ring structure 10” will define a plane of symmetry lying in a third plane XZ, said planes of symmetry being orthogonal to each other.

By combining the three rings 10, 10’, 10” to each other, the complexity of the structure can be obtained solely by means of additive manufacturing (AM) techniques. Making a structure with multiple rings would lead to having a structure with a number of struts and nodes that is not manageable with the current AM techniques.

Figure 3 shows the structure of the cell 1 according to the present invention in which the main geometric parameters are indicated.

The letter D indicates the diameter of the cell, while L and d respectively indicate the length and the diameter of the struts 11. A indicates the dimension of the face of the octagonal unit element 10a which must meet the morphological requirements in order to guarantee the osseointegration process.

Furthermore, the “aspect ratio” is defined as the ratio of the diameter of the struts to the length of the struts.

In accordance with the preferred embodiment illustrated here by way of example of the octagonal cell 1 according to the present invention, said cell comprises 120 struts and 48 nodes, and can be made by means of the current additive manufacturing techniques. The present invention also relates to the lattice structure 20 comprising a plurality of said cells 1 according to the present invention.

The most important parameter to be determined in the morphological analysis of a lattice structure is its relative density, defined as the ratio of the volume occupied by the struts of the unit cell to the total volume of the geometry:

In the above formula, p_c and V_c represent the density and the volume of the unit cell, p_m is the density of the material, V_m is the volume of the geometry. The ratio of p_c to p_m is the relative density.

The porosity calculated as a percentage value is defined as an inverse function of the relative density: 100

(2)

The frame designs based on struts can be classified according to Maxwell's criterion as bending-dominated or stretching-dominated, applying the formula:

M = b — 3j + 6 (3) where b is the number of struts and j is the number of nodes.

If M < 0, the structure is bending dominated; if M ~ 0, the structure is stretching dominated; if M > 0, the structure is hyper-stiff

Bending-dominated structures refer to the struts that tend to bend under the compressive load, with consequent shear stress yielding, whereas the stretching-dominated structures are stiffer and yield with a layer-by-layer mechanism.

In the case of cell 1 according to the present invention, the number of struts b is equal to 120, while the number of nodes j is 48 Applying Maxwell's criterion, the calculated M value is 18, so the unit cell has a bending-dominated behaviour. The mechanical characterization of the cell can be performed by applying the Gibson-Ashby models (M. F. Ashby, “The properties of foams and lattices” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 364, no. 1838, pages 15-30, 2006, doi: 10.1098/rsta.2005.1678).

In their study, Gibson-Ashby provided a series of equations that relate the mechanical properties of a lattice structure to its relative density:

where E_c and G_C are the elastic modulus and the compressive strength of the lattice structure, E_m and o_m are the elastic modulus and the compressive strength of the material of which the cell is made.

Ci, ni, C2, are constant values that can be calculated by means of experimental tests.

The results of the experimental tests can be used to trace the Gibson-Ashby diagrams. In these graphs, the relative modulus and the relative strength are plotted as a function of the relative density on logarithmic scales. By interpolating the data obtained in the experimental tests, the constant values Ci, ni, C2, m can be calculated for a given unit cell lattice structure.

The cell for applications in the biomechanical field according to the present invention has been characterized mechanically and morphologically. In particular, a comparison has been made with other lattice structures currently known in the sector.

The unit cells selected for comparison tests are the rhombic dodecahedron (RD) and the Kelvin cell. The unit cell RD had already been analysed by some authors in a previous work (G. Epasto, G. Palomba, D. D’Andrea, E. Guglielmino, S. Di Bella, and F. Traina, “Ti-6Al-4V ELI microlattice structures manufactured by electron beam melting: Effect of unit cell dimensions and morphology on mechanical behaviour” Mater. Sci. Eng. A, vol. 753, no. November 2018, pp. 31-41), whereas the mechanical behaviour and the morphology of the cell according to the present invention, referred to as TAOR (Triply Arranged Octagonal Rings) and those of the Kelvin cell were compared by performing compression tests.

The reticulated structures were produced by EBM using Ti6A14V ELI fine powder (grade 23). The titanium alloy used contains reduced levels of oxygen, nitrogen, carbon and iron and its particle size distribution is between 45 and 100 pm.

Three different relative density levels ranging from 0.05 to 0.2 were analysed. The three configurations were obtained by varying the diameter D of the cell while keeping the diameter d of the strut constant (Fig. 3).

The MATLAB software was used to calculate the diameter D of the cell as a function of the relative density for a given diameter d of the struts.

The volume of the cell TAOR V_c and the volume of the geometry TAOR V_m were calculated for the application of equation (1) reported above for the calculation of the relative density.

Using MATLAB Curve Fitting Toolbox, the formula V_m was evaluated as to TAOR of length of the edge L:

K_m = ll² ’ £³ (6)

A diameter d of the strut of 0.2 mm was imposed and the diameter D of the cell was evaluated as a function of the relative density, applying the following equation:

The relative densities and the dimensions of the unit cells considered are based on the characteristics necessary for application in the biomechanical field. Thus, the geometric parameters of the individual unit cells adopted for the production of the lattice structures are reported in Table 1. TAOR cell Kelvin cell

Pc/pm 0.05 0.1 0.2 0.05 0.1 0.2

Porosity [%] 95 90 80 95 90 80

D [mm] 4.4 3 2.1 4.4 3 2.1 d [mm] 0.2 0.2 0.2 0.2 0.2 0.2

L [mm] 0.72 0.48 0.33 1.55 1.06 0.74

A [mm] 1.61 1.03 0.66 2.48 1.63 1.08 d/L 0.28 0.42 0.61 0.13 0.19 0.27

Table 1: Geometric design parameters of the individual unit cells

All the analysed configurations have six unit cells for each edge of the structure in order to avoid the presence of edge effects; thus, each specimen is composed of 6x6x6 unit cells as shown in Figure 4, from (a) to (f).

An upper and a lower plate of 1 mm in thickness were used for the application of the loads during the experimental tests. It has been experimentally verified that the presence of plates does not affect the rupture mechanisms and the compression response of the lattice structure specimens. The geometric characteristics of the specimens are summarized in Table 2 shown below, where 0.05, 0.1 and 0.2 represent the relative densities of the lattice structures.

TAOR TAOR TAOR Kelvin Kelvin Kelvin 0.05 0.1 0.2 0.05 0.1 0.2

Length _{25 4 n 1 1 6 25 4 17 n 6}

[mm]

Wiidutuhi _{25 4 17 1 1 6 25 4 17 1 1 6}

[mm]

Table 2: Geometric properties of the samples

Finite element models (FEMs) of the individual unit cells were developed to evaluate by numerical simulation the compression behaviour and the modes of breakage of the structures, and to compare the results with those obtained from the application of the theoretical models and from the experimental tests.

The material considered for the FE analysis is the titanium alloy Ti6A14V ELI having the mechanical characteristics summarized below in Table 3, the two different cell types, TAOR and Kelvin, were analysed, each with relative density from 0.05 to 0.2.

^T1^*_t ^4V 115 0.34 905 1006 9.4 17.3 10’³

Table 3: Mechanical properties of the alloy Ti6A14V ELI

Wherein E and v represent the Young's modulus and the Poisson ’s ratio, o_m and e_m are the engineering breaking stress and the engineering stress strain at break, Sb is the elongation at break and so is the strain rate.

By making cells with a different number of struts and nodes as in Table 4, the boundary conditions were applied to replicate the compression tests.

TAOR_ TAOR_ TAOR_ Kelvin_ Kelvin_ Kelvin_

0.05 0.1 0.2 0.05 0.1 0.2

Elements 30720 16656 9304 20696 10184 5824

Nodes 36962 20490 11514 23618 12114 7074

Table 4: Elements of the unit cells and number of nodes

A speed of 1 mm/min along the Y axis was applied to the upper plate and the lower plate was constrained in all degrees of freedom by interlocking as shown in Figure 5. In addition, an additional constraint was applied to the upper plate to prevent translation in the X and Z directions, and the rotation in all directions.

The compression tests were performed on a Zwick-Roell Z250 test machine equipped with a 250 kN load cell, at a constant speed of 1 mm/min. A preload of 5 N was applied during the tests. Two repetitions were performed for each configuration of the specimen.

To evaluate the damage mechanism of the lattice structure due to the compressive load, the evolution of the temperature during the mechanical tests was recorded by an infrared thermal camera with 1280x1024 pixel InSb-cooled detector (FLIR Systems x8400sc). A 28 mm HD lens was used. The integration time was 0.3121 ms and an API post-processing algorithm was applied.

The observation at the scanning electron microscope (SEM) was performed before the experimental tests were carried out, to evaluate the correspondence of the geometric parameters between the designed structure and the real one. The visual tests and the observation at the SEM were performed to analyse the modes of breakage induced by the compression tests.

Coming to the results of the experimental tests and of the simulations carried out to the finished elements, Figure 6 reports the results of the finite element analysis FEM.

For a comparison of the compression behaviour and of the modes of breakage of different cell types and dimensions, the figure shows different levels of shifts considered as a percentage value of the diameters of the cells.

The finite element model was developed considering the real parameters of the alloy Ti6A14V ELI, so the real value of the breaking stress considered for the representation of the Von Mises stresses is 1107 MPa.

The deformation modes shown with the finite element model of the two types of unit cells were consistent with the results obtained experimentally. Thus, the reliability of the numerical model was confirmed, and can be applied to the entire lattice structure to predict the macroscopic mechanical properties of structures with different unit cell configurations.

For all the finite element analyses performed, the simulations showed that the breakage occurs at the nodes of the structure, where the intensification of the stresses occurs.

With particular reference to Figure 6, it can be noted that for TAOR cells it can be observed that the first and last layer deform before the central part since their deformation mechanism is dominated by the yielding of the nodes. The yielding of the vertical struts is instead buckling-dominated, which causes the final collapse of the cell.

This modes of breakage of the cell allows to design lattice structures with programmed absorption of energy.

In particular, again with reference to Figure 6, it can be noted how the cell TAOR_0.05 shows a different behaviour compared to the other configurations at a 25% deformation, since the upper part deforms before the lower end; moreover, the rotation along the z-axis and the instability due to the lower aspect ratio can be observed. When the deformation is 50%, a symmetrical deformation can be observed for all configurations. At a 75% deformation, the central part of the unit cells collapses and the cell TAOR_0.2 shows lower stress values than the other configurations.

Taking the Kelvin cell as a reference with relative densities 0.05 and 0.2, a symmetrical behaviour is noted for a 25% deformation, while at a 50% deformation the lower part collapses before the upper end because of the fracture of the nodes in contact with the lower plate, at which the interlocking constraint is applied.

Kelvin_0.1 shows a different behaviour since the upper part collapses before the lower end for a 25% deformation, while at a 50% deformation there is a symmetrical deformation of the structure. For a 75% deformation the deformation behaviour is symmetrical for all configurations with stress intensifications at the nodes of the structures.

Coming to the morphological analysis, the results of which are reported hereinbelow in Table 5, a comparison was made between the structures actually produced and those designed, to evaluate the correspondence of the geometric parameters between the designed structure and the one actually obtained with the production by additive manufacturing techniques. The electron microscopic observation of the microstructure was performed before carrying out the experimental tests. The correspondence between the real diameter of the cells and the design value was evaluated. Table 5 reports the comparison results for all TAOR and Kelvin cell configurations.

TAOR_ TAOR_ TAOR_ Kelvin_ Kelvin_ Kelvin_

0.05 0.1 0.2 0.05 0.1 0.2

Ddesigned [mm] 4.4 3 2.1 4.4 3 2.1

D_mi |min| 4.2 2.8 1.9 4.5 2.9 2.0

Variation [%] -4.5 -6.7 -9.5 2.3 -3.3 -4.8

Table 5 Percentage variation in the diameter of the cell between the real and design values

The study carried out made it possible to highlight how the discrepancies between the diameters of the real cells obtained and those designed increase as the relative density of the cell increases. Higher percentage variations were observed in the TAOR cell compared to the Kelvin cell for each relative density value. The design values are higher than the real values for each configuration except for Kelvin_0.05. The dimension of the face of the unit cell to meet the morphological requirements for the osseointegration process was evaluated in the real structures and compared with the design values, as reported in Table 6 hereinbelow.

TAOR TAOR TAOR Kelvin Kelvin Kelvin

0.05 0.1 0.2 0.05 0.1 0.2

Adesigned [mm] 1.61 1.03 0.66 2.48 1.63 1.08

Areal [mm] 1.24 0.78 0.45 1.8 1.2 0.75

Variation [%] -23.0 -24.3 -31.8 -27.4 -26.4 -30.6

Table 6: Percentage variation in the dimensions of the face between the real and design values

The design values were greater than the real values for all configurations. However, the dimension of the face is greater than the minimum value of 600 pm required to meet the osseointegration process for all specimens, except for the cell TAOR_0.2.

Figure 7 shows the results of the compression tests carried out on the two different TAOR and Kelvin cell structures.

The results of the compression tests are reported in Figure 7 in terms of stress-strain curves. Stress was obtained as the ratio of the axial load to the cross-section of the upper plate of the specimens, whereas the deformation was evaluated by the shift of the crosspiece (R. Gumriik and R. A. W. Mines, “Compressive behaviour of stainless steel micro-lattice structures” Int. J. Meeh. Sci., vol. 68, pages 125-139, 2013, doi: 10.1016/j.ijmecsci.2013.01.006).

The stress-strain curves resulting from the compression tests show a first stage representing the initial linear elastic region, followed by a slight slope variation up to a maximum stress value, which was evaluated as the compressive strength o_c of the lattice structure.

In the second stage, because of the yielding of some unit cells within the lattice, a sudden drop of the load appears, followed by a plateau region, with significant stress fluctuations. In the third stage, the densification of the lattice caused by the contact of completely collapsed cells leads to an increase of the stress.

Table 7 hereinbelow shows the parameters obtained from the compression tests: Young's modulus E, compressive strength o_c, crush resistance G_CS, specific energy absorption (SEA). The crush resistance was evaluated as the average stress in the plateau region. SEA was calculated as the ratio of the total absorbed energy (TEA) to the density of the lattice structure. TEA was evaluated as the area under the load-shift curve obtained during the compression tests. In order to guarantee the comparability of the results, TEA was calculated, for all samples, up to a deformation equal to 12%.

Table 7: results of the compression tests

The TAOR cell has values of elastic modulus, compressive strength, crush resistance and SEA greater than those of the Kelvin cell for each level of relative density considered.

From the comparison with the RD cell it can also be seen that the elastic modulus and the compressive strength of the TAOR cell are greater as to the density of 0.1 and 0.2 while they are lower as to the density 0.05.

On the other hand, the TAOR cell has compressive strength values higher than those of the RD cell for all the relative densities considered.

The TAOR cell also has SEA values higher than those of the RD cell as to the relative density 0.2, while it is lower as to the relative densities 0.05 and 0.1.

The elastic modulus is, in particular, a very important parameter for the application in the biomechanical field as values in the range of the elastic modulus of the bone from 0.5 to 20 GPa favour the osseointegration process, as recalled above (see again R. Gumriik and R. A. W. Mines, “Compressive behaviour of stainless steel micro-lattice structures” Int. J. Meeh. Sci., vol. 68, pages 125-139, 2013, doi: 10.1016/j.ijmecsci.2013.01.006).

The mechanical properties of the investigated lattice structures increase with increasing relative density according to what is known from the literature (T. Maconachie et al., “SLM lattice structures: Properties, performance, applications and challenges,” Mater. Des., vol. 183, p. 108137, 2019, doi: 10.1016/j.matdes.2019.108137) and with the prediction of the Gibson-Ashby model (M. F. Ashby, “The properties of foams and lattices,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 364, no. 1838, pages 15-30, 2006, doi: 10.1098/rsta.2005.1678).

TEA and SEA both increase in the TAOR and Kelvin cells as the relative density increases, while in RD cell they have their maximum values in the structure with relative density 0.1.

Figure 8 reports a comparison of the results of the compression tests for the three unit cells tested, namely TAOR, Kelvin and RD.

The Gibson and Ashby model was applied for the mechanical characterization of the tested unit cells. The relative modulus and the relative strength evaluated by means of the compression tests are reported in Table 8.

Table 8: Elastic modulus and relative strength

The elastic modulus and the compressive strength of the alloy Ti6A14V ELI have been evaluated by some authors, and are therefore known in the literature.

The real relative density of the specimens, calculated as the ratio of weight to volume, was considered and the results are reported in Table 9.

Table 9 Real relative density

The curves obtained by interpolating the data of relative elastic modulus and relative strength plotted against the relative density are shown in Figures 9 and 10.

The data obtained were also plotted on a Gibson-Ashby diagram for comparison with other microlattice structures as reported in Figure 11. The points indicated with the arrows in Figure 11 represent the data obtained for the TAOR cell object of the present invention. It can be noted how the points are in the expected range for the structures with behaviour dominated by bending of the structures, in accordance with what is evaluated by means of the Maxwell criterion.

Finally, the modes of breakage of specimens made with the microlattice structures under examination were investigated. Each specimen has a macroscopic yielding according to an inclined cutting plane with an angle of about 45°, as shown in Figure 12. This behaviour is consistent with the data reported in the literature for similar microlattice structures.

Figure 12 shows the mode of breakage of the entire unit cell structure. For both cases the fractures were observed near the nodes, which are critical points because of the intensification of the stresses.

The different cells highlighted different modes of breakage. In particular, in the TAOR cell according to the present invention the fracture occurs by sliding, while in the Kelvin cell a fragile fracture has been observed, with the presence of a carving effect.

The compression tests carried out were also monitored by means of a thermal camera to evaluate the thermal response of the cells in order to detect the correlation between the application of the load and the onset of the damage. The temperature increase detected on the surface of the specimen TAOR_0.05 during the compression test is reported in Figure 13. The same considerations reported here can be made for all the configurations of the specimens analysed.

The thermographic observation made it possible to clearly identify the breaking mechanism: the peaks of the curve refer to the instants in which the unit cells of the lattice collapse. A temperature increase was recorded along an inclined plane at about 45° where the macroscopic yielding appears as detected in the visual test shown in Figure 12.

Following all the experimental tests made and computer simulations carried out, it can be concluded that the new unit cell named TAOR according to the present invention, having the structure described herein and made with an additive manufacturing EBM technique, meets the characteristics required for the applications in the biomechanical field, with a mechanical behaviour that is improved with respect to the structures of unit cells of known type.

In particular, it has been verified that samples of TAOR cells according to the invention with relative density 0.1 and 0.2 have elastic moduli respectively of 0.743 and 10.56 GPa, i.e. within the range 0.5 - 20 GPa considered optimal for the mechanical behaviour required for the biomechanical applications.

The values of the real dimensions of the faces are less than the CAD design values for all the analysed configurations. However, the TAOR cell with relative density 0.05 and 0.1 meets the morphological requirements for the osseointegration process since the real values present are 1.24 and 0.78 mm respectively, which are higher than the required value of 0.6 mm.

Yet, considering the compressive strength and the specific energy absorption (SEA) of specimens made with a lattice structure comprising a plurality of TAOR-type unit cells according to the present invention, both values are greater than the Kelvin cell of known type for all the relative densities considered.

From the comparison with the unit cell RD, the TAOR cell also shows a greater compressive strength as to the relative densities 0.1 and 0.2, while it is lower as to the relative density 0.05. The compressive strength of the TAOR cell is higher for all the relative densities.

Both TEA and SEA are higher for TAOR structures with relative density 0.2, while they are lower for the relative densities 0.05 and 0.1. The mode of breakage of the cell appears at the nodes of the strut and has an inclined cutting plane with an angle of 45°.

From the application of the Gibson-Ashby theoretical model and of the Maxwell's criterion, a bending-dominated behaviour was evaluated for the TAOR cell, this result was confirmed by both compression tests and by the finite element analysis.

From what is shown here it follows that the cell according to the present invention represents an optimal design choice for the application in the biomechanical field, in particular for the production of bone scaffolds, considering that a structure can be obtained whose mechanical behaviour can be modulated based on the needs, varying the mechanical characterization of the cell as the density parameters of the cell itself vary. Indeed, by way of example, a part of a bone scaffold having a greater density ratio may be brought into contact with the cortical bone, and a part of the same scaffold having lower density could be brought into contact with the spongy bone in order to promote osseointegration, ensuring mechanical affinity with the spongy bone.

It has thus been shown that the unit cell according to the present invention and the lattice structure comprising a plurality of said unit cells achieve the task and the intended purposes.

The cell and the lattice structure according to the present invention are susceptible to modifications and variants, all falling within the scope of the invention as defined by the appended claims.

Claims

1. Three-dimensional cell structure (1) for biomedical application, in particular for the realization of bone scaffolds, made of biocompatible metallic material comprising a plurality of struts (11) that meet at nodes (12) to define a plurality of constituent elements (10a) interconnected in elementary ring structures (10, 10', 10"), characterized in that said struts (11) comprise substantially straight sections of cylindrical shape, connected together in nodes (12) to form constituent elements (10a) in the shape of a regular octagon having a regular octagonal shape, wherein said cell structure (1) comprises a plurality of elementary ring structures (10, 10', 10") each formed by a plurality of said constituent elements (10a) having a regular octagonal shape.

2. Cell structure (1) according to claim 1, characterized in that said struts (11) comprise substantially straight sections of cylindrical shape, having the same diameter (d) and equal length (L) connected together in nodes (12) to form constituent elements (10a) in the shape of a regular octagon.

3. A cell structure (1) according to the preceding claim, characterized by comprising three elementary ring structures (10, 10', 10"), each of which is symmetrical with respect to a plane of symmetry, and by the fact that a first (10) of said elementary ring structures therefore defines a plane of symmetry lying in a first plane (YZ), a second ring structure (10') will define a plane of symmetry lying in a second plane (XY), and a third ring structure (10") will define a plane of symmetry lying in a third plane (XZ), said first (YZ), second (XY) and third planes (XZ) being orthogonal to each other.

4. A cell structure (1) according to one or more of the preceding claims, characterized by having a relative density value, defined as the ratio of the volume (V_c) occupied by the struts (11) of the unit cell to the total volume of the geometry (V_m), between 0.05 and 0.3, more preferably between 0.1 and 0.2.

5. Cell structure (1) according to one or more of the preceding claims, characterized by being made by additive manufacturing techniques, preferably by Electron Beam Melting (EBM) techniques.

6. Cell structure (1) according to one or more of the preceding claims, characterized by being made of titanium alloy Ti6A14V ELI.

7. Lattice structure (20) for biomedical applications characterized in that it comprises a plurality of unit cell structures (1) according to one or more of the preceding claims arranged to form a regular lattice structure.

8. Bone scaffold for use in biomedical applications characterized in that it comprises a lattice structure (20) according to claim 9.