Mechanical Strength of Triply Periodic Minimal Surface Lattices Subjected to Three-Point Bending

Sandwich panel structures (SPSs) with lattice cores can considerably lower material consumption while simultaneously maintaining adequate mechanical properties. Compared with extruded lattice types, triply periodic minimal surface (TPMS) lattices have light weight but better controllable mechanical properties. In this study, the different types of TPMS lattices inside an SPS were analysed comprehensively. Each SPS comprised two face sheets and a core filled with 20×5×1 TPMS lattices. The types of TPMS lattices considered included the Schwarz primitive (SP), Scherk’s surface type 2 (S2), Schoen I-graph-wrapped package (I-WP), and Schoen face-centred cubic rhombic dodecahedron (F-RD). The finite element method was applied to determine the mechanical performance of different TPMS lattices at different relative densities inside the SPS under a three-point bending test, and the results were compared with the values calculated from analytical equations. The results showed a difference of less than 21% between the analytical and numerical results for the deformation. SP had the smallest deformation among the TPMS lattices, and F-RD can withstand the highest allowable load. Different failure modes were proposed to predict potential failure mechanisms. The results indicated that the mechanical performances of the TPMS lattices were mainly influenced by the lattice geometry and relative density.


Introduction
Triply periodic minimal surfaces (TPMSs) were originally discovered and described by Schwarz in 1865 [1]. However, fabricating these surfaces is still a challenge due to conventional technical limitations. The development of additive manufacturing (AM), particularly 3D printing, has made the fabrication of TPMSs possible. To increase the strength of AM products while reducing material consumption, the sandwich panel structure (SPS) was developed, which is a lattice-based cellular pattern enclosed by two face sheets. SPSs are widely applied in engineering and industry for aerospace, thermal systems, packaging and medical implants [2][3][4]. A wide range of lattice patterns can be used, such as honeycombs, tri-/quadri-grids, and TPMSs.
SPSs are commonly observed in nature, such as in human skulls, butterflies, and dragonflies [5]. SPSs provide an outstanding stiffness/strength-to-weight ratio and excellent energy absorption because of their very high moments of inertia [6]. When external load is applied on the face sheets, the force is dispersed to the lattice by decomposition. The force undertaken by the lattice causes the lattice structure to deform, and strain energy is absorbed in the lattice. SPSs also provide an efficient framework for resisting buckling and bending loads. Mahmoud and Elbestawi [7] found that SPSs can be used to develop artificial orthopaedic implants with a similar porosity to that of human bones. The porous structure allows bone to easily grow inside and strengthens the bond between the implant in three dimensions, it is defined as a TPMS [33]. TPMSs have complex shapes; therefore, generating these surfaces in the computer-aided design software is difficult. Mathematically, TPMSs can be expressed through different approaches, such as the parametric, implicit and boundary methods [34]. In this study, four types of TPMSs were considered, as shown in Figure 1: SP, S2, I-WP and F-RD. The implicit expressions are listed in Equations (1)- (4). All expressions are based on three coordinate variables each in the range of [-π, π] [21,22,35,36].

Cellular Structures and Modelling Procedure of Different TPMSs
A minimal surface is defined as the surface of the minimal area between any given boundaries. When a minimal surface repeats itself by rotating, mirroring or replicating in three dimensions, it is defined as a TPMS [33]. TPMSs have complex shapes; therefore, generating these surfaces in the computer-aided design software is difficult. Mathematically, TPMSs can be expressed through different approaches, such as the parametric, implicit and boundary methods [34]. In this study, four types of TPMSs were considered, as shown in Figure 1: SP, S2, I-WP and F-RD. The implicit expressions are listed in Equations (1)- (4). All expressions are based on three coordinate variables each in the range of [-π, π] [21,22,35,36].  (2 ) × cos(2 ) × cos (2 ) + cos(2 ) × cos(2 ) = 0 (4)

Total Deformation
Various studies have performed intensive experiments on sandwich beams with extruded lattices or foam inside the core under three-point bending loads [3,37,38]. The extruded lattice typically has a triangular, quadrilateral or honeycomb structure. The foam in the core can be polymer, metallic, ceramic or glass. Gibson and Ashby's [3] solution for the total deformation of extruded lattices and foam can be extended to this study because three-dimensional TPMSs has the same periodic and symmetric features as extruded lattices.

Total Deformation
Various studies have performed intensive experiments on sandwich beams with extruded lattices or foam inside the core under three-point bending loads [3,37,38]. The extruded lattice typically has a triangular, quadrilateral or honeycomb structure. The foam in the core can be polymer, metallic, ceramic or glass. Gibson and Ashby's [3] solution for the total deformation of extruded lattices and foam can be extended to this study because three-dimensional TPMSs has the same periodic and symmetric features as extruded lattices.
Deformation occurs when the SPS is loaded and reaches equilibrium. The total deformation includes the bending component δ b and shear component δ s . Figure 2 shows a schematic of an SPS under a three-point bending load. Deformation occurs when the SPS is loaded and reaches equilibrium. The total deformation includes the bending component and shear component . Figure 2 shows a schematic of an SPS under a three-point bending load. The total deformation, δ, can be calculated as follows: Load along the vertical direction. The length of the SPS beam. ( ) Equivalent flexural rigidity, as shown Equation (6). ( ) Equivalent shear rigidity, as shown Equation (7). 1 and 2 Constants of proportionality which depend on the geometry of loading, as listed in Table 1 [3].
where * is the Young's modulus of the lattice core, Ef is the Young's modulus of the solid material making up the face sheets, and * is the shear modulus of the lattice core. Both * and * are functions of the relative density * / : where is the Young's modulus of the lattice material, * is the density of the lattice core, is the density of the solid material and 1 and 2 are constants of proportionality that depend on the loading geometry, as listed in Table 1 [3]. Table 1. Constants for the three-point bending testing [3].  Figure 3 shows a schematic of the relationship between the bounding box and lattice volume for an SPS. The porosity is the fraction of pore space in the bounding box and is obtained from (1 − * / ). The relative density is given by: The total deformation, δ, can be calculated as follows: p Load along the vertical direction. l The length of the SPS beam.
(AG) eq Equivalent shear rigidity, as shown Equation (7). B 1 and B 2 Constants of proportionality which depend on the geometry of loading, as listed in Table 1 [3].
where E * c is the Young's modulus of the lattice core, E f is the Young's modulus of the solid material making up the face sheets, and G * c is the shear modulus of the lattice core. Both E * c and G * c are functions of the relative density ρ * c /ρ s : where E s is the Young's modulus of the lattice material, ρ * c is the density of the lattice core, ρ s is the density of the solid material and C 1 and C 2 are constants of proportionality that depend on the loading geometry, as listed in Table 1 [3]. Table 1. Constants for the three-point bending testing [3].

Loading Mode
Three-point bending, loading at the centre 1 0.4 48 8 Figure 3 shows a schematic of the relationship between the bounding box and lattice volume for an SPS. The porosity is the fraction of pore space in the bounding box and is obtained from (1 − ρ * c /ρ s ). The relative density is given by: Relative density = Lattice cellular structure mass/Bounding box volume Density o f solid (10)

Weight of the SPS
The total weight of the SPS can be written as where is the standard gravity of Earth.

Failure Modes of Sandwich Beams
Previous studies [3,13,39] have shown that four different failure modes need to be considered for SPSs: face yielding, face wrinkling, core failure and bond failure. All these failure modes must be considered because any failure mode can occur when the geometry or the loading changes.

Geometry Design
In this study, Grasshopper and computer codes developed in house were used to generate single cells of TPMSs. The single cells were generated in an 8 mm × 8 mm× 8 mm cubic box and patternised to generate 20 × 5 × 1 lattices to serve as the SPS cores, as shown in Figure 4. SPSs were built with two flat layers fused to the top and bottom of each core. The overall dimensions of each SPS core were 160 mm × 40 mm × 8 mm, as given in Figure 4 and Table 2. All dimensions for the exterior geometry except the span length followed the ASTM D790 standard [40].  Figure 2 for the definitions of the geometric parameters.

Weight of the SPS
The total weight of the SPS W can be written as where g is the standard gravity of Earth.

Failure Modes of Sandwich Beams
Previous studies [3,13,39] have shown that four different failure modes need to be considered for SPSs: face yielding, face wrinkling, core failure and bond failure. All these failure modes must be considered because any failure mode can occur when the geometry or the loading changes.

Geometry Design
In this study, Grasshopper and computer codes developed in house were used to generate single cells of TPMSs. The single cells were generated in an 8 mm × 8 mm× 8 mm cubic box and patternised to generate 20 × 5 × 1 lattices to serve as the SPS cores, as shown in Figure 4. SPSs were built with two flat layers fused to the top and bottom of each core. The overall dimensions of each SPS core were 160 mm × 40 mm × 8 mm, as given in Figure 4 and Table 2. All dimensions for the exterior geometry except the span length followed the ASTM D790 standard [40]. Thickness of a face sheet 1 mm * Refer to Figure 2 for the definitions of the geometric parameters.

Model
Many studies have demonstrated that discretising the core surface as a shell rather than a solid mesh produces superior results. This is because the thickness aspect ratio is large, and the shell model can provide more accurate results [26][27][28]. To generate the shell model, the software Rhino was used to generate TPMS geometries, which were then exported to ANSYS for finite element analysis (FEA) of the structure. The thickness of each TPMS was calculated for different relative densities, as given in Table 3. Figure 5 shows the shell models of SPSs with four different TPMS lattice cores. All numerical models are 1/2 symmetry. A vertical load of 500 N was applied to the centre of the top face sheet, and total fixed conditions are assumed at both the end supports ( Figure 2).

Model
Many studies have demonstrated that discretising the core surface as a shell rather than a solid mesh produces superior results. This is because the thickness aspect ratio is large, and the shell model can provide more accurate results [26][27][28]. To generate the shell model, the software Rhino was used to generate TPMS geometries, which were then exported to ANSYS for finite element analysis (FEA) of the structure. The thickness of each TPMS was calculated for different relative densities, as given in Table 3. Figure 5 shows the shell models of SPSs with four different TPMS lattice cores. All numerical models are 1/2 symmetry. A vertical load of 500 N was applied to the centre of the top face sheet, and total fixed conditions are assumed at both the end supports (

Materials
Acrylonitrile butadiene styrene (ABS) is a common thermoplastic polymer with nearly constant elastic modulus and other mechanical properties under the operation temperature. It has loads of advantages, such as great heat resistance, high tensile strength, and low cost. Hence, ABS was selected as the material of the SPS specimens, and Table 4 presents its mechanical properties. model, the software Rhino was used to generate TPMS geometries, which were then exported to ANSYS for finite element analysis (FEA) of the structure. The thickness of each TPMS was calculated for different relative densities, as given in Table 3. Figure 5 shows the shell models of SPSs with four different TPMS lattice cores. All numerical models are 1/2 symmetry. A vertical load of 500 N was applied to the centre of the top face sheet, and total fixed conditions are assumed at both the end supports ( Figure 2).  Acrylonitrile butadiene styrene (ABS) is a common thermoplastic polymer with nearly constant elastic modulus and other mechanical properties under the operation temperature. It has loads of advantages, such as great heat resistance, high tensile strength, and low cost. Hence, ABS was selected as the material of the SPS specimens, and Table 4 presents its mechanical properties.

Results and Discussion
In this study, the mechanical performances of SPSs with four different TPMS lattice cores were evaluated and compared. In addition, the calculation results based on the equations presented in the 'Theoretical background' section were compared with the numerical results obtained using the FEA approach.

Results and Discussion
In this study, the mechanical performances of SPSs with four different TPMS lattice cores were evaluated and compared. In addition, the calculation results based on the equations presented in the 'Theoretical background' section were compared with the numerical results obtained using the FEA approach.

Weight Difference
To compare the mechanical performance of SPS with different TPMS lattices, the total weight of each SPS must be considered first. The weight calculated from Equation (11) and the weight acquired from the FEA models are listed in Table 5. The difference was <3% for all SPSs, which indicates that the geometry of the FEA model was sufficiently accurate and that Equation (11) could precisely calculate the weight of the SPS. Furthermore, Table 5 indicates that the increase in the relative density can increase the total weight of the SPS.

Deformation
The total deformations of the SPSs with different TPMS lattices cores under a threepoint bending load calculated using Equation (5) were compared against the numerical predictions obtained by FEA. Table 6 lists the calculated parameters, maximum total deformation and the numerical predictions. The difference between the calculated results and numerical predictions was 1%-21% at all relative densities, which indicates good agreement. For the SP lattice core SPS, the calculated values were 1.6%-17.5% higher than the numerical prediction. F-RD lattice core SPS has the largest difference of approximately 20.7% at 10% relative density. It is because the F-RD lattice is the most complex structure compared to other types of TPMS in this study. The meshing is highly complex on the connecting mesh boundary, and the thickness of the F-RD lattice with 10% relative density is the thinnest. This is considered to be the reason behind this highest difference. Figure 6 presents the comparison between the calculated and predicted maximum deformations of SPSs with different TPMS lattice cores. The deformation decreases with increasing relative density. If the S2 lattice cell rotates from its original array direction (Figure 7a) along the vertical axis (Figure 7b), the numerical prediction of the maximum deformation at different relative densities will be altered. S2 with the rotated direction is designated as S2 90 in the followings. Table 7 and Figure 8 show that the numerical results of maximum deformations of S2 90 at relative densities of 10% and 20% were extremely large compared to the calculated results. This clearly indicates that the cell direction causes this extremely huge difference. Other TPMS lattices considered in this study (i.e., SP, I-WP and F-RD) do not demonstrate this difference because their cell rotation does not affect the array direction ( Figure 4). In addition, the maximum deformation decreased as the relative density increased.
followings. Table 7 and Figure 8 show that the numerical results of maximum defor-mations of S290 at relative densities of 10% and 20% were extremely large compared to the calculated results. This clearly indicates that the cell direction causes this extremely huge difference. Other TPMS lattices considered in this study (i.e., SP, I-WP and F-RD) do not demonstrate this difference because their cell rotation does not affect the array direction ( Figure 4). In addition, the maximum deformation decreased as the relative density increased.   mations of S290 at relative densities of 10% and 20% were extremely large compared to the calculated results. This clearly indicates that the cell direction causes this extremely huge difference. Other TPMS lattices considered in this study (i.e., SP, I-WP and F-RD) do not demonstrate this difference because their cell rotation does not affect the array direction ( Figure 4). In addition, the maximum deformation decreased as the relative density increased.    The above results show that the calculation method and parameters used for the total deformation are not only adequate for TPMS structures but also can be used to predict the structures' mechanical performance. Moreover, the cell direction appears to play an important role in the mechanical performance of the SPS with the S2 lattice core. Generally, when the thickness of wall increases, which will increase the relative density simultaneously, the weight of the SPS will correspondingly be increased and the total deformation will decrease.
The above results show that the calculation method and parameters used for the total deformation are not only adequate for TPMS structures but also can be used to predict the structures' mechanical performance. Moreover, the cell direction appears to play an important role in the mechanical performance of the SPS with the S2 lattice core. Generally, when the thickness of wall increases, which will increase the relative density simultaneously, the weight of the SPS will correspondingly be increased and the total deformation will decrease.  Figure 9 shows the deformation distribution of SPSs with different TPMS lattice cores under three-point bending. The maximum deformation was at the mid-span and possessed symmetry along the span. Therefore, the maximum deformation at the centre of the SPS beam was considered to represent the total deformation. Figure 10 shows the numerical prediction of the maximum deformations of the different TPMS lattices under three-point bending. At the same loading force and relative density, the SP lattice resulted in the smallest deformation. At the relative density of 10%, SP had the smallest deformation, followed by S2, I-WP and F-RD; at 20% relative density, SP had the smallest deformation, followed by S2, F-RD, and I-WP; as the relative density reached 30%, SP still maintained the smallest deformation, followed by F-RD, S2 and I-WP. In general, the thicker the lattice is, the stronger the SPS structure will be. The S2 lattice possesses the maximum thickness in this study. However, the S2 lattice structure has many discontinuities on its geometry boundary, and the shape is not as normalised as the SP surface. This gives rise to that the stiffness of the SPS with SP lattices core is higher than the S2 lattice, and its maximum deformation is the lowest when compared to the other types of TPMS. Moreover, the I-WP lattice provides the lowest stiffness, even when the relative density is increased from 20% to 30%. Results also indicate that the lattice geometry is a crucial factor for the mechanical performance. Furthermore, Figure 10 also demonstrates that when the relative density increases, the maximum deformation correspondingly decreases.  Figure 9 shows the deformation distribution of SPSs with different TPMS lattice cores under three-point bending. The maximum deformation was at the mid-span and possessed symmetry along the span. Therefore, the maximum deformation at the centre of the SPS beam was considered to represent the total deformation. Figure 10 shows the numerical prediction of the maximum deformations of the different TPMS lattices under three-point bending. At the same loading force and relative density, the SP lattice resulted in the smallest deformation. At the relative density of 10%, SP had the smallest deformation, followed by S2, I-WP and F-RD; at 20% relative density, SP had the smallest deformation, followed by S2, F-RD, and I-WP; as the relative density reached 30%, SP still maintained the smallest deformation, followed by F-RD, S2 and I-WP. In general, the thicker the lattice is, the stronger the SPS structure will be. The S2 lattice possesses the maximum thickness in this study. However, the S2 lattice structure has many discontinuities on its geometry boundary, and the shape is not as normalised as the SP surface. This gives rise to that the stiffness of the SPS with SP lattices core is higher than the S2 lattice, and its maximum deformation is the lowest when compared to the other types of TPMS. Moreover, the I-WP lattice provides the lowest stiffness, even when the relative density is increased from 20% to 30%. Results also indicate that the lattice geometry is a crucial factor for the mechanical performance. Furthermore, Figure 10 also demonstrates that when the relative density increases, the maximum deformation correspondingly decreases.    Because the numerical results were based on a three-point bending load, the deformation in the loading direction was also considered. Table 8 and Figure 11 compare the Z-axis deformations of the SPSs with different lattice cores. F-RD resulted in the smallest Z-axis deformation, which is because the lattice was being twisted when subjected to bending. The linear approximations of the total deformation error estimation, R 2 , of the SPSs with different TPMS lattice cores versus the relative density are presented in Table 9 and Figure 10. R 2 was close to 1 for all SPSs with the different lattice cores, which indicates that the linear approximated total deformation from Equations (12) to (15) can reliably predict the deformations of SPSs with different TPMS lattices.  Because the numerical results were based on a three-point bending load, the deformation in the loading direction was also considered. Table 8 and Figure 11 compare the Z-axis deformations of the SPSs with different lattice cores. F-RD resulted in the smallest Z-axis deformation, which is because the lattice was being twisted when subjected to bending. The linear approximations of the total deformation error estimation, R 2 , of the SPSs with different TPMS lattice cores versus the relative density are presented in Table 9 and Figure 10. R 2 was close to 1 for all SPSs with the different lattice cores, which indicates that the linear approximated total deformation from Equations (12)- (15) can reliably predict the deformations of SPSs with different TPMS lattices.    Figure 11. Z-axis deformations of SPSs with different TPMS lattice cores. Table 9. Linear approximations of the deformation.

Comparison of Maximum Allowable Load of Different TPMS Lattice Cores in the SPS
The SPSs were made from ABS, and its maximum yield strength is about 45 MPa. Thus, the maximum allowable load at different relative densities can be calculated by numerical analysis. Figure 12 shows the results for SPSs with different TPMS lattice cores. At relative densities of 10% and 20%, SP had the highest maximum allowable loads of 584 and 702 N, respectively. However, at a relative density of 30%, F-RD had the highest maximum allowable load of 790 N, followed by I-WP, SP and S2. The maximum allowable load increased with the relative density. These results are in good agreement with those of Kladovasilakis et al. [21]. The cell direction of the S2 lattice core was again found to have a significant influence. For the S2 lattice, the maximum allowable load consistently increased with the relative density. In contrast, the maximum allowable load for the S2 90 lattice did not increase when the relative density was increased from 20% to 30% but instead declined. In addition, the maximum allowable load was generally lower for S2 90 than for S2. These results demonstrate that the geometry and relative density of the lattice core are significant to the structural performance. The maximum allowable load increased with the relative density. The array direction of the lattice had a significant effect on the performance of S2, which was the only TPMS in this research with different cell direction because of its two openings in the geometry.

Comparison of Maximum Allowable Load of Different TPMS Lattice Cores in the SPS
The SPSs were made from ABS, and its maximum yield strength is about 45 MPa. Thus, the maximum allowable load at different relative densities can be calculated by numerical analysis. Figure 12 shows the results for SPSs with different TPMS lattice cores. At relative densities of 10% and 20%, SP had the highest maximum allowable loads of 584 and 702 N, respectively. However, at a relative density of 30%, F-RD had the highest maximum allowable load of 790 N, followed by I-WP, SP and S2. The maximum allowable load increased with the relative density. These results are in good agreement with those of Kladovasilakis et al. [21]. The cell direction of the S2 lattice core was again found to have a significant influence. For the S2 lattice, the maximum allowable load consistently increased with the relative density. In contrast, the maximum allowable load for the S290 lattice did not increase when the relative density was increased from 20% to 30% but instead declined. In addition, the maximum allowable load was generally lower for S290 than for S2. These results demonstrate that the geometry and relative density of the lattice core are significant to the structural performance. The maximum allowable load increased with the relative density. The array direction of the lattice had a significant effect on the performance of S2, which was the only TPMS in this research with different cell direction because of its two openings in the geometry.   Table 10 lists the von Mises stresses of the four TPMSs. Figure 13 shows the stress distribution of the SP lattice core inside the SPS. The maximum stress was at the interface between the lattice and face sheets. The maximum yield strength of the SPSs was about 45 MPa. Thus, the von Mises stress exceeded the yield strength for some of the TPMSs, and plastic deformation occurred. Increasing the relative density decreased the von Mises stress and improved the stiffness of the SPS.

Failure Mode
An SPS beam may fail according to several failure modes. All failure modes must be considered to determine which is dominant. With regard to face yielding, plastic deformation occurred once the stress on the face sheet was greater than the yield strength of the face material. The face normal stress σ f was calculated from Equation (16) to be about 62.5 MPa. This value is greater than the yield strength of the material, which means that face yielding would occur regardless of the TPMS lattice core inside the SPS.  Table 10 lists the von Mises stresses of the four TPMSs. Figure 13 shows the stress distribution of the SP lattice core inside the SPS. The maximum stress was at the interface between the lattice and face sheets. The maximum yield strength of the SPSs was about 45 MPa. Thus, the von Mises stress exceeded the yield strength for some of the TPMSs, and plastic deformation occurred. Increasing the relative density decreased the von Mises stress and improved the stiffness of the SPS.

Failure Mode
An SPS beam may fail according to several failure modes. All failure modes must be considered to determine which is dominant. With regard to face yielding, plastic deformation occurred once the stress on the face sheet was greater than the yield strength of the face material. The face normal stress was calculated from Equation (16) to be about 62.5 MPa. This value is greater than the yield strength of the material, which means that face yielding would occur regardless of the TPMS lattice core inside the SPS.
The shear stress has the largest effect on the core tearing during the three-point bending test [11,29,30]. The shear strength of ABS is taken as half of the yielding stress. Table  11 presents the shear stress at the SPS core predicted by FEA. For all TPMS lattice cores, yielding occurred at a relative density of 10%. When the relative density was increased to 20%, only the F-RD lattice core yielded. Face wrinkling was only observed for the SPS with an S2 lattice core at a relative density of 10% relative density from Table 11. The bond stress was calculated from Equation (17), and the results are presented in Table 12. The shear stress has the largest effect on the core tearing during the three-point bending test [11,29,30]. The shear strength of ABS is taken as half of the yielding stress. Table 11 presents the shear stress τ at the SPS core predicted by FEA. For all TPMS lattice cores, yielding occurred at a relative density of 10%. When the relative density was increased to 20%, only the F-RD lattice core yielded. Face wrinkling was only observed for the SPS with an S2 lattice core at a relative density of 10% relative density from Table 11. The bond stress σ b was calculated from Equation (17), and the results are presented in Table 12. Bond failure was highly likely for all SPSs considered in this study, because the bond stresses exceeded the yield strength.
In conclusion, the normal failure modes of the SPSs were face yielding and bond failure because of the thinness of the face sheets. Between these two failure modes, face yielding was the most severe because the stress greatly surpassed the yield strength of the material. Other failure modes, such as face wrinkling and core failure, can be prevented by increasing the relative density. These results agree with those of other studies [26,37] showing that increasing the thickness of the face sheets or using a tougher material can decrease the face normal stress and bond stress, which can prevent both failure modes. Face stress: Bond stress: Strain energy release rate: Moment:

Conclusions
In this study, the mechanical performances of SPSs with four types of TPMS lattice cores at different relative densities were evaluated thoroughly. FEA results for the deformation under the three-point bending test showed good agreement with the calculated values, with a difference of less than 21%. The lattice geometry and relative density were the primary factors affecting the mechanical performance. For a fixed relative density, the SPS with the SP lattice core had the smallest deformation, and the F-RD lattice core had the maximum allowable load before yielding. The cell direction had a significant effect on the mechanical performance of the SPS with the S2 lattice core. The most dominant failure mode was face yielding because the stress greatly surpassed the yield strength of the material used in this study. Other failure modes such as face wrinkling and core failure can be prevented by increasing the relative density. Increasing the total amount of the lattice core or using different materials for the face sheets can improve the mechanical performance of SPSs, and the SPS can be optimised to meet the requirements for various engineering applications. Informed Consent Statement: Not applicable for studies not involving humans.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.