© H. Xue et al., Published by EDP Sciences, 2024

1 Introduction

With ageing, bone injury osteoporosis and other aspects of the disease will become more and more common, and bone grafting has become the main method of treatment of the disease [1]. As shown in Table 1, in bone grafting, the implanted metal prosthesis is prone to stress concentration and stress shielding after implantation because its elastic modulus does not match with human bone. Therefore, choosing the appropriate structure and processing method to reduce the elastic modulus of bone substitute scaffolds has become a major research focus. To solve the problems of bone loosening and revision surgery caused by the elastic modulus mismatch, porous structure bone substitutes have come into people's view. The porous structure has a larger surface area due to its internal structure, which can provide more attachment sites for the cells of bone tissue and facilitate the connection of new fibres, thus promoting the patient's recovery [2], the porous structure is more compatible with the elastic modulus of human bone and does not produce the phenomenon of stress shielding [3]. The porous structure is lighter than the solid structure [4], which makes the patient's movement easier and less burdensome.

Although porous structure has many advantages, its moulding is more difficult, and it is difficult to control the internal structure and porosity of porous structure with traditional processing methods such as investment casting, grooving, forging, mesh stamping-brazing etc. [5,6]. Since the 21st century, the development of additive manufacturing technology has brought breakthroughs to the porous structure of skeletal scaffolds for tissue engineering, and selective laser moulding (SLM) is one of the most important technologies for 3D printing. Printing can achieve the demand for personalised customisation of patient prosthetic scaffolds, solving the problem of difficult shaping by traditional processing methods, it can effectively control the structural characteristics, size, and porosity of the scaffolds to ensure the success rate of the replacement surgery [7]. Therefore, in this study, additive manufacturing (3D printing) was used to build a porous structural scaffold to replace the damaged bone so that the patient can promote recovery and carry out normal activities.

Selective laser melting technology (SLM) is a kind of additive manufacturing [8], is also way this expectation of printing, is achieved in the process of processing with a laser so that the powder is completely melted, without the need for adhesives, the mechanical properties of the moulding and the accuracy of the formation of a solid than the use of adhesives to form a solid technology of adhesive bonding of metal [9]. SLM use metal powder melting directly after one step to form a finished product with low porousness. Because it has (1) no need for moulds; (2) can quickly customise products; (3) high precision; (4) can create complex geometric shapes; (5) can use different materials for printing; (6) can achieve zero-waste production; (7) can quickly manufacture samples.

2 Porous structure design and modelling

2.1 Porous structures bracket models

The mechanical properties of three-dimensional structures formed by different forms of unitary bodies are different, according to the research results of previous research scholars, it is found that when the structures of inverted V-60°, inverted V-90°, orthotetrahedron and ortho-octahedron as shown in Figure 1 are compared, the orthotetrahedron structure is stronger in comparison with the four structures [10]; when the structures of hexahedron, diagonal, octahedron, and body-centred-cubic are compared under the same loading force environment as shown in Figure 2, the strength limit of ortho-hexahedron porous structures is the greatest. When the loading force environment is compared, the strength limit of the ortho-hexahedral porous structure is the largest [11], sufficient strength will reduce the chance of re-fracture of the patient after prosthesis implantation, in this paper, we hope to compare the two kinds of stable and not easy to be twisted structures of hexahedron and tetrahedron, and explore their deformation patterns and mechanical properties through compression simulation.

Fig. 1 Structure of inverted V-60, inverted V-90, regular tetrahedron, regular octahedron and three-round intersection cell.

Fig. 2 Hexahedral, diagonal, octahedral and core cubic unit structures.

2.1.1 Ortho-hexahedral unit structure

The ortho-hexahedral unitary structure, shown in Figure 3, is one of the more common unitary structures with good compressive strength and fatigue resistance and is used in porous scaffold bone grafting and defect repair [12–15].

Fig. 3 Positive hexahedral cell structure.

2.1.2 Ortho-tetrahedron unitary structure

The ortho-tetrahedral structure is shown in Figure 4 and is created by selecting the points and vectors in a spatially closed ortho-tetrahedral wireframe consisting of four congruent positive triangles using the feature body column command. All the rods are of equal length and have a unique structure that resists deformation and can resist compression and tension or bending and torsion, effectively resisting external forces and improving structural stability.

Fig. 4 Orthotetrahedral element structure.

Fig. 5 Pillar diameter d and length l.

2.2 Design of porous structure parameters

The design of porous structure parameters includes strut diameter, strut length, porosity, and external dimensions of the porous structure, which play a crucial role in the application of the designed skeletal scaffold and its mechanical properties [16]. When designing the porous structure, the following aspects should be paid attention to: firstly, the designed porous structure should have connectivity, to meet the supply of nutrients and the discharge of metabolic wastes from the human body; secondly, the designed porous structure should have good mechanical properties, especially a certain degree of strength and stiffness, which can withstand a certain degree of impact and stretching [17], and can continue to have a high mechanical property when subjected to external forces.

2.2.1 Design of column diameters and lengths

The size of the strut diameter d and length l can directly affect the size of the porous diameter and the volume of the cell and thus the size of the porosity [18], the parameter representation is shown in Figure 5, so the size of the porosity of the porous structure can be controlled by adjusting the diameter and length of the strut. To ensure that the SLM can be manufactured smoothly, the minimum strut diameter is limited to 300 µm, the upper limit is set to 600 µm, and the length size is generally in the range of 1000–2000 µm, so this study will control the strut diameter in the range of 300–600 µm, and the strut length of 1000–2000 µm.

2.2.2 Porosity

In biomedical engineering, porosity is an important parameter as it relates to aspects such as cell attachment, biocompatibility and mechanical properties of biomaterials [19]. Therefore, porosity is a very important material parameter. Higher porosity indicates more pore space in the material and less density of the material. Porosity is the ratio of the total volume of pores within a porous structure to the total apparent volume of that porous structure [20], and the desired value is achieved by controlling the diameter and length of the pillars, which is calculated as follows:

$$\text{Φ}=\frac{{\text{V}}_1}{V_2}\times 100\%=1-(\frac{{\text{V}}_3}{{\text{V}}_2})\times 100\%$$(1)

Φ is the porosity of the porous structure; V₁(mm³) is the volume of pores within the structure; V₂ (mm³) is the total volume outside the structure; V₃ (mm³) is the volume of the solid part measured by the measuring body command inside the UG.

2.2.3 Design parameters

In this paper, two variables are designed as porous structure morphology and porosity to analyse the mechanical property laws [21]. Changing the design parameters such as rod length and rod diameter will be directly related to the size of the porosity of the unit cell, and the change of porosity is an important factor in determining the mechanical properties of the porous structure. To make the study more comprehensive, six porosities are controlled by designing two different morphological structures to form 12 models to analyse the laws.

Firstly, a porous model was established by referring to the data of previous researchers, and the solid volume of this porous structure was measured using the command of UG Measurement of Volume of Body, and the size of the porosity was calculated by applying equation (1), and then the parameters were changed to get the expected value of the porosity. The specific parameter values are shown in Tables 2 and 3.

2.2.4 Materials

In this study, Ti6Al4V alloy [22] was chosen as the material for the porous structure, and its composition is shown in Table 4. Ti6Al4V is one of the commonly used skeletal implant materials in the current international medical field [23]. It has the following advantages: (1) small mass, high strength, is a lightweight and high-strength metal structure material, designed as a porous and to a certain extent to reduce the burden on the patient. (2) Good heat and corrosion resistance, can adapt to the human body's weak alkaline body fluids environment. (3) Biocompatibility is excellent, to ensure that the prosthesis will not be loosened after implantation and the human body does not appear to have the advantages of the reaction of rejection, etc. [24–27].

The design of the porous structure on the surface of the material promotes the growth of bone tissue and improves the mobility of body fluids, resulting in better interaction between the porous implant and the bone, thus enhancing the bonding between the bone and the implant material [28]. In addition, the low modulus of elasticity of this porous material reduces stress masking and extends the service life of the implant.

2.3 Porous modelling

According to the parameters described above, the design was made using UG NX12.0, and the established cell structure was used to obtain an orderly stacked array by applying the Geometric Array command, and then Boolean intersection operation with the columns was performed to establish the porous structure, as shown in Figure 6.

Fig. 6 Modeling process of the cell body structure.

3 Finite element simulation and discussion

3.1 Overview of finite element analysis

ANSYS finite element method is a computer-aided engineering analysis software that uses the finite element method (FEM) to simulate and analyse various engineering problems. The finite element method is a numerical analysis method that breaks down a complex structure into many small, simple elements and then calculates each element to finally obtain the behaviour of the entire structure ANSYS finite element method can be used to simulate and analyse a variety of engineering problems, including the fields of mechanics, fluids, thermodynamics, electromagnetism, acoustics, etc. It can help engineers predict the behaviour of a structure during the design and development process, as well as predict the behaviour of the structure during the design and development process. It can help engineers predict and optimise product performance during the design and development process, improve product quality and productivity, and reduce costs and risks [29]. In this paper, the uniaxial compression simulation and fluid simulation carried out by Workbench and Fluent modules in ANSYS, and the Ansys finite element static mechanical properties and internal fluid field analysis carried out by adaptive meshing are used.

3.2 Simulation process

Taking the hip joint as an example, the femur of the hip joint is the key bone to bear the upper body, and the human femur can bear 3–4 times its weight. It is assumed that the maximum pressure of the 80 kg male bone is 320 kg, which acts on the 6 cm² femoral section, with a pressure of 5.3 MPa. Now, 10 MPa downward pressure is applied to the end face of the multi-hole structure, as shown in Figure 7, to observe the mechanical property law under compression. In addition to adding Ti6AI4V material, this paper also adds a rigid body indenter that can make the upper surface of the structure evenly stressed. Its elastic modulus is three orders of magnitude higher than that of titanium alloy, and the influence of deformation on this simulation can be ignored. Table 5 shows the parameters of Ti6AI4V.

Import the porous structure created in UG NX 12.0. After the geometric structure is imported, select the previously set materials, and assign rigid to the indenter and Ti6Al4V to the porous structure. The contact surface between the indenter and the porous structure is set with friction, and the friction coefficient is 0.1. When setting the grid size, ensure each piece can be divided while saving time. The grid division is shown in Figure 8, and the grid size is 0.2 mm. Simulate the deformation and internal stress change of the model caused by applying loads of different sizes and directions. To prevent the lower-end face from sliding under pressure, fixed constraints are required, as shown in Figure 9.

Fig. 7 Clamp down.

Fig. 8 Mesh division.

Fig. 9 Fixed constraints.

3.3 Analysis workbench simulation

3.3.1 Force distribution and compression deformation trend analysis

The low porosity of 60% and the high porosity of 80% are listed for the comparison of force distribution and deformation trend. Figure 10a shows the compressive equivalent stress cloud diagram of an orthotetrahedron with 60% porosity, from which it can be seen that the three tilted pillars in the longitudinal direction are subjected to higher stresses, which are more concentrated at their intersection, and the pillars in the transverse direction are subjected to fewer stresses in comparison. The reason is that the porous structure as a whole is subjected to downward pressure, and when the orthotetrahedron is arranged as shown in the figure, the three inclined pillars intersecting in the longitudinal direction bear more stresses, while the pillars in the transverse direction share less. Figure 10b shows the compression equivalent stress cloud diagram of the orthohexahedron with 60% porosity. It can be seen from the diagram that the stresses are more concentrated in the longitudinal columns and around the connection point of the transverse and longitudinal columns, and the transverse columns are subjected to smaller stresses because the porous structure is subjected to the longitudinal direction of the force, and therefore it will be subjected to more forces.

At the same time, compression deforms the structure to a certain extent. Figures 11a and 11b shows the deformation cloud diagrams of the two structures at a porosity of 60%, which shows that the closer the porous structure is to the side subjected to the force the greater the stress suffered by the object. When an object is subjected to an external force, the atoms inside the object are displaced and deformed, resulting in stress. At the stressed proximal end of the object, the distance between the atoms becomes shorter due to the force, which leads to an increase in the interaction force between the atoms at the proximal end, which in turn leads to an increase in the stress on that side. Whereas at the stressed distal end of the object, the distance between the atoms is relatively longer and the interaction force between the atoms is smaller, thus the stress on that side is relatively smaller. This is also accompanied by a more pronounced deformation of both structures, where the apertures are distorted, and the deformation trend is a drum that expands from the centre to the sides shape.

Figure 12a for the porosity of 80% of the orthotetrahedron compression equivalent stress cloud diagram, from the figure can be more clearly seen that the stress is distributed in the axial direction of the three columns, and the stress is concentrated in the vicinity of the intersection point, the transverse support bar stress is smaller than the range of low porosity structure is larger and more obvious, the same Figure 12b porosity of 80% of the ortho-hexahedron longitudinal columns on the stress is larger, and transverse longitudinal The stress at the junction point of the columns is also greater than that of the transverse columns, which is the same as the deformation phenomenon of the low porosity structure, and the effect is more obvious.

Fig. 10 (a) Cloud map of a tetrahedral structure with 60% porosity; (b) Cloud map of a hexahedral structure with 60% porosity.

Fig. 11 (a) Cloud of compression deformation of tetrahedral structure with porosity of 60%; (b) Cloud of equivalent compression. deformation of hexahedral structure with porosity of 60%.

Fig. 12 (a) Cloud map of the positive tetrahedral structure with 80% porosity; (b) Cloud map of the positive hexahedral structure with 80% porosity.

3.3.2 Comparison of compression data of two structures with different porosities

Figures 13 and 14 are two porous structures are compressed under the same load environment, and the cloud diagrams of “equivalent force” and “deformation” of different porosity are obtained sequentially in the workbench module, which can be used to assess the difference of their mechanical properties more intuitively, the maximum equivalent force of a hexahedron is lower than that of a tetrahedron under the same load and porosity, which indicates that a hexahedron has a better compression bearing effect. Under the same compression load and the same porosity, the maximum equivalent force of a hexahedron is lower than that of a tetrahedron, and the deformation of a hexahedron is smaller than that of a tetrahedron, which indicates that a hexahedron has a better compression-bearing effect, and the compression does not have much effect on the upper-end face, and the difference in the stress between the bone scaffold and the bone contact surface is not big after implantation, and the stress is more homogeneous. Meanwhile, it is found that the equivalent stress of two porous structures with the same load and the same morphology increases with the increase of porosity, which is because the distance between the connecting holes will be reduced with the increase of porosity in the case of the same external dimensions, and the pore wall will become thinner, which makes the change of its structural strength. Observing Figure 13, the trend of the curves, it can be concluded that with the increase of porosity, the maximum equivalent force of the hexahedron is more gentle than that of the tetrahedron, which indicates that if implanted with the growth of bone cells and tissues, there will be no drastic changes in strength due to fluctuations in porosity, and thus it shows a more stable and reliable performance.

Fig. 13 Comparison of maximum equal effect forces.

Fig. 14 Comparison of the maximum deformation amount.

3.3.3 Calculate the modulus of elasticity and compare

The maximum equivalent force of the 12 models did not exceed the compressive strength of Ti6Al4V, and the deformation did not fail, ensuring that the applied compressive force was within its linear elastic deformation.

From Figure 15, it can be seen that the same porosity under the hexahedral modulus of elasticity is higher than tetrahedral, and with the increase of porosity, the two structures of the modulus of elasticity are showing a decreasing trend, 80% of the stiffness is the smallest, characterising the elastic deformation of the material with the increase in porosity and more likely to occur. It is reflected in the fact that the stress required for deformation per unit area is smaller, or applying the same size of stress it has a greater degree of elastic deformation.

To better match the implanted prosthesis to the human bone and to speed up the recovery, it is necessary to ensure that the modulus of elasticity is close to the necessary considerations. Modulus of elasticity of human bone at different locations Cortical bone: 17–20 Gpa Cancellous bone: 3.2–7.8 Gpa.

Cortical bone is denser, harder has a higher compressive strength and is mostly distributed in the limbs, constituting a tubular structure in the middle of the long bones. According to the calculated data, the modulus of elasticity consistent with cortical bone is 50% for the tetrahedral structure and 65% for the hexahedral structure. From the above analysis, the 65% porous structure of the hexahedron is preferred, taking into account that a structure with better mechanical properties and a larger porosity is better able to meet the required nutrient transport and osteoblast attachment.

Fig. 15 Comparison of the elastic modulus.

3.4 Fluent simulation analysis

Fluid simulation can be simulated on a computer, saving time and cost, helping engineers and designers to better understand and analyse the behaviour and properties of fluids under different conditions such as flow rate, pressure, temperature, etc., to understand the law of motion of fluids better, and to evaluate their performance and quality. The designed porous scaffold with its internal structure, and space volume, should be able to ensure smooth blood flow and bone tissue cells can grow attached, so the numerical analysis of the fluid field is necessary. The fluid simulation process will be solid parameters are set to Ti6Al4V, density of 4500 kg/m³; fluid parameters are set to human blood, inflow from above, the blood density is set to 1050 kg/m³, viscosity is 3.5×10⁶kg (m·s); the velocity size of 0.14 m/s, the Guaranteed accuracy is iterated 1000 times to start the calculation. The fluid model is shown in Figure 16. To compare the fluid flow under different structures with the same porosity, the pressure and velocity fields of fluid flow in tetrahedral and hexahedral structures with 65% porosity are compared in this section.

Fig. 16 The fluid model.

3.4.1 Porous structure fluid analysis

After the two porous structure scaffolds are implanted into the human body, to ensure that they can function normally in the body, the pressure distribution on the scaffolds after fluid inflow should be understood. If the pressure is too large, the force acting on the scaffold when the cells flow will be large, and the corresponding friction and collision with the scaffold will also increase, which may lead to the cells not being able to attach well or destroying the tissues, etc., and the implanted scaffold can not play the proper effect at this time; if the pressure is too small when the porous structure is still a little bit complicated, some cells may not get enough power to bring nutrients for each site, which makes the recovery slowed down. Therefore, it is necessary to simulate the fluid pressure field for the post-implantation effect.

Figures 17a and 17b shows the pressure cloud of a 65% porosity hexahedral porous structure, to see the pressure situation inside the hole more intuitively, a YZ section was made in the centre of the body, it can be seen that initially, the fluid inflow is at a higher pressure, with a maximum of 298 Pa. As the fluid inflow fills up the internal space, the pressure slowly decreases and the overall circulation is smooth. Then explore the change of pressure on the stent under the same conditions when the structure is different, Figures 17c and 17d shows the pressure cloud diagram of a 65% porosity tetrahedral porous structure, it can be seen that the maximum pressure it can withstand is 634 Pa, in the centre of the body made XY section, the fluid inflow from above is mainly in the triangular shaped holes outflow, the pressure is getting smaller and smaller because the tetrahedral structure is more complex than the hexahedron. Because the structure of a tetrahedron is more complex than a hexahedron, there are more staggered pillars, the structure is different at each height, the pressure is different, the pressure and resistance change obviously, and the impact and friction are bigger when the fluid is left quickly, so it bears more pressure. The structure of the hexahedron is more uniform, the fluid is easier to circulate, and the pressure change is not big, a relatively stable trend, the pressure is smaller.

Fig. 17 (a) Overall pressure cloud map of hexahedral structure; (b) longitudinal pressure cloud map of hexahedral structure; (c) Overall pressure cloud map of tetrahedral structure; (d) Horizontal pressure cloud map of tetrahedral structure.

3.4.2 Porous structure fluid velocity field analysis

After implantation of the porous structure into the body, the flow rate of the fluid flowing inside is also crucial for the attachment and growth of bone cells and tissues in the later stages. Too large a flow rate is detrimental to the fusion of the extracellular matrix with the material and the attachment of new fibres to the bone tissue; too slow a flow rate is not suitable to fill the internal space or slow metabolic nutrient transport and slower recovery. Simulation is used to compare the vector direction and velocity magnitude of two structured fluid particles with the same porosity after inflow, providing a prediction of fluid flow after implantation of porous structured scaffolds into the human body.

As shown in Figures 18a and 18b for the porosity 65% hexahedral porous structure of the velocity cloud, also in the body of the central YZ section, can be seen that the fluid just began to flow into the interior of the porous structure, by the hole around the strut wall obstruction of the fluid to the hole in the middle of the convergence, and the closer the hole centre of the flow velocity is faster, up to 0.8 m/s, close to the wall of the hole side of the flow velocity is small, the slowest flow velocity in the horizontal position, which is due to the This is because the frictional resistance between the fluid and the hole wall is greater while the central fluid is not restricted, resulting in the fluid velocity in the hole is greater the closer to the centre, while the flow velocity near the bracket wall is slow. Figures 18c and 18d shows the velocity cloud of tetrahedral porous structure with 65% porosity, XY section was made in the upper middle and lower part of the body, it can be seen from the figure, the fluid flow rate is slower in the hole of the tetrahedral structure, but the velocity of the flow through the tip of the tetrahedron becomes faster, this is because, when the tetrahedral structure is formed, the forming angle of connecting the support rod is small, and the fluid convergence in the tip of the tip is greater than the other parts of the impact force This is because, when the tetrahedral structure is formed, the forming angle of the connecting strut is smaller, and the impact force of the fluid pooling at the tip is larger than that at other parts, so the maximum flow velocity is faster than that of the hexahedral structure, so the resistance at the tip is larger, and the speed of blood flow in the arteries of the lower limb is generally in the range of 0.3–0.8 m/s, and the maximum flow velocity is not in the range of the human body.

The design of the porous stent its internal structure, and space volume, should be able to ensure smooth blood circulation, bone tissue cells can adhere to the growth of this section of the hexahedron due to the structure of the rules of uniformity, smooth fluid circulation and by the fluid pressure is small, and the distance from the centre of the hole flow rate is the fastest, the stent wall near the flow rate is slow; tetrahedral structure due to the internal structure of the complexity of the formation of the top connecting the strut shaping angle is small, so the resistance of fluid flow through the resistance, Impact force is larger, the maximum speed at the top is larger, which is not in line with the maximum flow rate that the human body can withstand.

Fig. 18 (a) Cloud map of overall velocity of hexahedral structure; (b) Cloud map of longitudinal velocity of hexahedral structure; (c) Cloud map of overall velocity of tetrahedral structure; (d) Cloud diagram of longitudinal velocity of tetrahedral structure.

4 Conclusion

• Design and modelling of porous structure. UG was used to design 2 different unitary structures, namely orthotetrahedron and orthohexahedron, and 6 different porosities were obtained by controlling the rod length and rod diameter to form 12 porous models by orderly stacking in 3D space, to prepare for the subsequent finite element simulation to analyse their mechanical property laws.

• Ansys finite element analysis software observes the equivalent stress and deformation cloud diagrams and finds that the distribution of the two structures is slightly different but overall similar: the tetrahedral structure is axially three inclined columns and their intersections near the pressure, the hexahedral structure is the longitudinal columns and transverse and longitudinal columns at the intersection of the pressure is large, but the two overall is the longitudinal columns are more compressed than the transverse columns. In addition, the compression deformation trend of both structures is in the form of a bulge expanding from the centre to the sides, and the closer to the applied side, the greater the stress and the greater the deformation.

• Hexahedron due to the rules of uniform structure, smooth fluid flow and fluid pressure is small, and the fastest flow rate from the centre of the hole, the slow flow rate near the wall of the support; tetrahedron structure due to the complex internal structure, the top of the top connecting rod shaping Angle of the formation of a small, so the fluid flow through the resistance, impact, the top of the maximum speed is larger, does not comply with the maximum flow rate of the human body can withstand.

• Under the same porosity, the hexahedral structure has better pressure-bearing performance; the same structure, with the increase of porosity, its equivalent force are in an upward trend, the reduction of the pore wall makes the structural strength lower, and the hexahedron increases the potential of the slower, the structure is stable. The larger the porosity, the lower the value of elastic modulus, due to the reduction of the pore spacing the structure stiffness is not enough, and elastic deformation transactions occur. Finally, the structure with better adaptability to the human bone was identified.

Funding

This study was supported by Key R&D Program of Shandong Province (2022TSGC2108, 2022TSGC2402, 2023TSGC085, 2023TSGC0119, 2023TSGC0759, 2023TSGC0961).

Conflicts of interest

We declare that we do not have any commercial or associative interests that represent a conflict of interest in connection with the work submitted.

Data availability statement

Data will be made available on request.

Author contribution statement

Hui Xue: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing − Original Draft, Writing − Review and editing, Visualization. Xiujuan Song: Methodology, Software, Writing − Review and editing, Visualization. Guoliang Zhang: Validation, Formal analysis, Visualization. Shubo Xu: Resources, Supervision, Project administration, Funding acquisition, Writing − Review & Editing. Weihai Zhang: Investigation, Data curation. Siyu Sun: Methodology. Yuefei Pan: Conceptualization, Visualization. Guocheng Ren: Data curation.

References

All Tables

All Figures

	Fig. 1 Structure of inverted V-60, inverted V-90, regular tetrahedron, regular octahedron and three-round intersection cell.
In the text

	Fig. 2 Hexahedral, diagonal, octahedral and core cubic unit structures.
In the text

	Fig. 3 Positive hexahedral cell structure.
In the text

	Fig. 4 Orthotetrahedral element structure.
In the text

	Fig. 5 Pillar diameter d and length l.
In the text

	Fig. 6 Modeling process of the cell body structure.
In the text

	Fig. 7 Clamp down.
In the text

	Fig. 8 Mesh division.
In the text

	Fig. 9 Fixed constraints.
In the text

	Fig. 10 (a) Cloud map of a tetrahedral structure with 60% porosity; (b) Cloud map of a hexahedral structure with 60% porosity.
In the text

	Fig. 11 (a) Cloud of compression deformation of tetrahedral structure with porosity of 60%; (b) Cloud of equivalent compression. deformation of hexahedral structure with porosity of 60%.
In the text

	Fig. 12 (a) Cloud map of the positive tetrahedral structure with 80% porosity; (b) Cloud map of the positive hexahedral structure with 80% porosity.
In the text

	Fig. 13 Comparison of maximum equal effect forces.
In the text

	Fig. 14 Comparison of the maximum deformation amount.
In the text

	Fig. 15 Comparison of the elastic modulus.
In the text

	Fig. 16 The fluid model.
In the text

	Fig. 17 (a) Overall pressure cloud map of hexahedral structure; (b) longitudinal pressure cloud map of hexahedral structure; (c) Overall pressure cloud map of tetrahedral structure; (d) Horizontal pressure cloud map of tetrahedral structure.
In the text

	Fig. 18 (a) Cloud map of overall velocity of hexahedral structure; (b) Cloud map of longitudinal velocity of hexahedral structure; (c) Cloud map of overall velocity of tetrahedral structure; (d) Cloud diagram of longitudinal velocity of tetrahedral structure.
In the text