Optimization of the Unit Cell of Auxetic Materials for orthopedic applications using generative design

Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Document: Report Author: González Chacón, Andreu Supervisor: Boccaccio, Antonio Degree: Master’s Degree in Industrial Engineering Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Abstract The advancement of biomaterials and engineering methodologies has revolutionized many orthopedic solutions, offering promising avenues for the development of effective orthopedic prostheses. This thesis explores the optimization of auxetic cells within orthopedic prostheses through generative design, leveraging Autodesk Fusion software. The research focuses on integrating orthopedics and metamaterials, particularly titanium alloys, to enhance biomechanical performance and biocompatibility. The study begins with a comprehensive review of porous materials for orthopedic applications, emphasizing their critical role in providing structural integrity. Titanium and its alloys are highlighted as exemplary materials for these applications due to their porosity, corrosion resistance, and mechanical strength akin to natural bone. Metamaterials, specifically auxetic materials, are introduced as innovative structures for enhancing bone prostheses. The concept of generative design using Autodesk Fusion is employed to optimize the geometry of the auxetic cells, aiming to reduce mass while maintaining or improving mechanical performance. The thesis details the workflow of generative design simulations, encompassing input parameters, geometries, constraints, and manufacturing techniques. Finite element analysis serves as a pivotal tool to evaluate the mechanical behaviour of optimized auxetic cell models. Results from FEA simulations provide insights into stress distribution, deformation characteristics, and structural response under physiological loading conditions. Comparative analyses between initial and optimized designs elucidate the efficacy of generative design in achieving superior biomechanical outcomes. In conclusion, this thesis underscores the interdisciplinary synergy of materials science, biomechanics, and computational modeling in advancing bone prostheses. By optimizing auxetic cells through generative design and integrating titanium-based prostheses, the study contributes to the evolution of orthopedic implants, offering potential benefits for patient outcomes and healthcare advancements. Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Table of contents 1 Introduction ......................................................................................................... 6 1.1 Target ...................................................................................................................... 6 1.2 Reach ...................................................................................................................... 6 1.3 Requirements .......................................................................................................... 6 1.4 Justification .............................................................................................................. 6 2 Developing Orthopedics .................................................................................... 7 2.1 Design Criteria for Orthopedic Devices Using Porous Materials ............................... 7 2.2 Porous Materials for Orthopedics ............................................................................. 8 2.2.1 Bioceramics ...................................................................................................... 8 2.2.2 Polymers .......................................................................................................... 8 2.2.3 Composites ...................................................................................................... 8 2.2.4 Metals ............................................................................................................... 9 2.3 Fabrication Techniques ............................................................................................ 9 2.3.1 Solvent Casting and Particulate Leaching ......................................................... 9 2.3.2 Electrospinning ................................................................................................. 9 2.3.3 3D Printing and Additive Manufacturing .......................................................... 10 2.3.4 Freeze-Drying ................................................................................................. 10 2.3.5 Thermally Induced Phase Separation (TIPS) .................................................. 10 3 Metamaterials and Auxetic Materials .............................................................. 10 3.1 Properties and Characteristics ............................................................................... 10 3.2 Relevance in Orthopedics ...................................................................................... 11 3.3 Existing Auxetic Cells ............................................................................................. 11 4 Optimization with Generative Design.............................................................. 12 4.1 Application in Orthopedics ..................................................................................... 12 4.1.1 Explore Complex Design Spaces .................................................................... 12 4.1.2 Optimize Performance .................................................................................... 12 4.1.3 Incorporate Biological Considerations ............................................................. 13 4.1.4 Enable Customization and Personalization ..................................................... 13 4.2 Benefits of Generative Design in Orthopedics ........................................................ 13 5 The Models of Unit Cells Built ......................................................................... 13 5.1 Basic Cells and Parameters ................................................................................... 13 5.2 Cell Modeling with Solidworks................................................................................ 15 5.3 Generating Optimal Cells with Autodesk Fusion .................................................... 16 5.4 Finite Element Analyses with Abaqus..................................................................... 18 6 Results of the Finite Element Analyses .......................................................... 19 6.1 Structure Formation from Auxetic Unit Cells........................................................... 19 6.2 Load and Boundary Conditions in Abaqus ............................................................. 20 6.3 Von Misses Stress Analyses .................................................................................. 21 6.4 Evaluation of Results ............................................................................................. 22 6.4.1 Histograms for Cell 1 ...................................................................................... 22 6.4.2 Histograms for Cell 2 ...................................................................................... 24 6.4.3 Histograms for Cell 3 ...................................................................................... 26 6.5 Selection of the Best Auxetic Cell .......................................................................... 29 7 References ........................................................................................................ 30 Table of figures Figure 1. Re-entrant Auxetic Cell (Taken from link [6] of References) ....................... 11 Figure 2. Chiral Auxetic Cell (Taken from link [6] of References) ............................... 11 Figure 3. Complementary Auxetic Cell (Taken from link [7] of References) ............... 12 Figure 4. Hip Prosthesis Using Auxetic Materials (Taken from link [3] of References) .................................................................................................................................. 14 Figure 5. Critical Section of the Hip Bone Prosthesis ................................................ 14 Figure 6. Auxetic Cells 1, 2 and 3 in Solidworks ........................................................ 16 Figure 7. The Three Spaces in Autodesk Fusion for Cell 1 ....................................... 16 Figure 8. The Three Spaces in Autodesk Fusion for Cell 2 ....................................... 17 Figure 9. The Three Spaces in Autodesk Fusion for Cell 3 ....................................... 17 Figure 10. Generative Objectives Configuration ........................................................ 17 Figure 11. Optimized Auxetic Cells 1, 2 and 3 ........................................................... 18 Figure 12. Substructure in Abaqus Made of Initial Auxetic Cells 2 ............................. 18 Figure 13. Structure Formation From Initial Auxetic Cells 1, 2 and 3 ......................... 19 Figure 14. Structure Formation From Optimized Auxetic Cells 1, 2 and 3 ................. 20 Figure 15. Load and Boundary Conditions ................................................................ 20 Figure 16. Von Misses Stress Analyses for Auxetic Cell 1 ......................................... 21 Figure 17. Von Misses Stress Analyses for Auxetic Cell 2 ......................................... 21 Figure 18. Von Misses Stress Analyses for Auxetic Cell 3 ......................................... 22 Figure 19. Histograms of Last Convergent Time Increment of Simulation (Cell 1) .... 23 Figure 20. Histogram for the 350 MPa Situation to the Optimized Geometry (Cell 1) 24 Figure 21. Histograms of Last Convergent Time Increment of Simulation (Cell 2) .... 25 Figure 22. Histograms for the 350 MPa Situation (Cell 2) ......................................... 26 Figure 23. Histograms of Last Convergent Time Increment of Simulation (Cell 3) .... 27 Figure 24. Histograms for the 350 MPa Situation (Cell 3) ......................................... 28 Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design 1 Introduction 1.1 Target The primary target of this project is to optimize the design of auxetic cells used in prostheses to enhance their mechanical performance, biocompatibility, and overall effectiveness in supporting bone regeneration. The optimization will be conducted using Autodesk Fusion's generative design tools, focusing on reducing mass while maintaining or improving structural integrity and functionality. 1.2 Reach The reach of this project extends to multiple stakeholders in the field of orthopedic and biomedical engineering, including patients, aiming to improve the quality of life for individuals requiring prostheses by offering more effective and reliable implants. To healthcare providers, offering advanced prosthetic solutions that enhance patient outcomes and reduce recovery times. Additionally, to medical device manufacturers by enhancing product offerings with optimized and innovative designs that meet the latest standards in biocompatibility and mechanical performance. Finally, to the research community by contributing to the body of knowledge in orthopedics and metamaterials, potentially influencing future research and development efforts. 1.3 Requirements To achieve the project target, the following requirements must be met: • Material Selection: Identify and use appropriate materials that are biocompatible, durable, and suitable for generative design and manufacturing processes. This includes bioceramics, polymers, composites, and metals like titanium. • Design Parameters: Define the design parameters for the auxetic cells, including geometry, porosity, and mechanical properties such as stiffness and strength. • Generative Design Process: Utilize Autodesk Fusion's generative design tools to explore a wide range of design options, optimize the auxetic cell structures, and reduce the mass of the prosthesis. • Finite Element Analysis: Conduct thorough FEA to evaluate the mechanical performance of the optimized designs under various loading conditions, ensuring they meet the required standards for strength and durability. • Manufacturing Feasibility: Ensure that the optimized designs can be manufactured using existing technologies, such as 3D printing or other additive manufacturing techniques. 1.4 Justification The optimization of auxetic cells in orthopedic prostheses is justified by the potential to significantly improve patient outcomes. Optimized prostheses can lead to better integration with natural bone, reduced risk of implant failure, and enhanced overall patient mobility and quality of life. Additionally, this optimization contributes to advancements in materials science by developing and enhancing the unique properties of auxetic materials and optimizing existing technologies. In terms of generative design, we can improve efficiency in both design and manufacturing. This approach allows for the exploration and creation of innovative, efficient structures that minimize material use, reduce manufacturing costs, and maintain high performance. Finally, a crucial aspect is addressing actual clinical needs. There is a continuous demand for improved orthopedic implants that better mimic the properties of natural bone and support the body's healing processes, making this research highly relevant and impactful. 2 Developing Orthopedics Porous materials play a crucial role in orthopedics by providing a 3D framework that supports cell attachment, proliferation, differentiation, and the formation of new extracellular matrix (ECM). Below is a detailed discussion on porous materials for orthopedics, covering their design criteria, materials, fabrication techniques, and recent advancements. 2.1 Design Criteria for Orthopedic Devices Using Porous Materials The design of orthopedic devices with porous materials must meet several key criteria to be effective. That’s because these criteria ensure that the orthopedic devices can adequately support the biological processes necessary for bone regeneration and provide the mechanical stability needed during the healing process. Biocompatibility: It ensures that the orthopedic devices does not provoke an immune response when implanted into the body. If it is not biocompatible, it can cause inflammation, rejection, or other adverse reactions, which can impede healing and potentially cause further damage to the surrounding tissues. A biocompatible material supports cellular activities such as adhesion, proliferation, and differentiation, which are critical for effective bone regeneration. Mechanical Properties: Orthopedic devices must possess mechanical properties that are similar to the natural bone they are replacing or supporting. This includes adequate compressive strength, tensile strength, and elastic modulus to withstand physiological loads. Proper mechanical properties are essential to ensure that it can support normal physical activities and maintain structural integrity. Mismatched mechanical properties can lead to failure or insufficient support for normal activities. Porosity and Interconnectivity: High porosity and interconnected pores are essential for facilitating cell infiltration, vascularization, nutrient and oxygen diffusion, and waste removal. These characteristics promote the integration of the prosthesis with the host tissue and support the survival and function of the cells surrounding it. Surface Properties: The surface properties of the orthopedic devices, including texture and chemical composition, play a critical role in promoting cell attachment. Surface modifications or coatings with bioactive molecules can enhance the prosthesis ability to support cellular functions. A surface that mimics the natural extracellular matrix (ECM) can significantly improve the prosthesis performance by encouraging cells to adhere to it. After considering all these criteria, we can ensure that if the design of the orthopedic devices meets them, it will be effective from both a medical and mechanical perspective. Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design 2.2 Porous Materials for Orthopedics Various materials are used for orthopedic prosthesis, each with its advantages and limitations. These materials can be broadly classified into bioceramics, polymers, composites and metals. 2.2.1 Bioceramics Bioceramics are a class of ceramic materials specifically designed for medical and dental applications. They are used to repair and reconstruct damaged or diseased parts of the body, particularly bones and teeth. Advantages: • Biocompatibility: Bioceramics integrate well with orthopedics without causing adverse immune reactions. • Osteoconductivity: They support new bone growth by providing a surface for bone cells to attach and proliferate. • Mechanical Strength: Bioceramics often have mechanical properties similar to natural bone, providing structural support. Limitations: • Brittleness: Bioceramics are prone to fracture under high stress or impact. • Slow Degradation Rate: Some bioceramics degrade slowly, which may not be ideal for applications requiring faster resorption. 2.2.2 Polymers Polymers are large and complex molecules made up of long chains of repeating subunits called monomers. These monomers are covalently bonded to form a polymer, which can have a wide range of properties and applications. Advantages: • Versatility: Easily processed into various shapes and structures, including porous prosthesis. • Tunable Properties: Mechanical and degradation properties can be adjusted by modifying their chemical structure or blending with other materials. Limitations: • Mechanical Weakness: Some natural polymers may not have sufficient mechanical strength for load-bearing applications. • Potential Toxicity: Degradation products of certain synthetic polymers can be acidic, potentially causing local tissue inflammation or toxicity. 2.2.3 Composites Composites are materials made from two or more materials with significantly different physical or chemical properties. When combined, these materials produce a composite with characteristics different from the individual components. The constituent materials typically consist of a matrix and a reinforcement phase. Advantages: • Combining Strengths: Combine favorable properties of different materials, such as strength of bioceramics and flexibility of polymers. • Enhanced Mechanical Properties: Achieve mechanical properties closer to those of natural bone. • Bioactivity: Can be tailored to include bioactive components promoting bone regeneration. Limitations: • Complex Fabrication: Creating composites can be more complex and costly. • Incompatibility Issues: Challenges in achieving good interfacial bonding between different materials, critical for structural integrity and performance. 2.2.4 Metals Metals are a class of materials characterized by their high electrical and thermal conductivity, malleability, ductility and they usually have a high density. Metals play a crucial role in a wide range of applications due to their diverse properties. Advantages: • High Mechanical Strength: Metals like titanium have excellent mechanical properties, providing robust structural support, particularly in load-bearing applications. • Biocompatibility: Titanium is highly biocompatible and widely used in orthopedic and dental implants. • Corrosion Resistance: Titanium is resistant to corrosion in the physiological environment, ensuring long-term stability. • Osteointegration: Titanium can form a direct bond with bone, known as osteointegration, which is crucial for the stability of implants. Limitations: • Non-Degradability: Titanium does not degrade over time, meaning it remains in the body permanently unless surgically removed. This can be a disadvantage in situations where temporary scaffolds are needed. This is not our case because the prosthesis will replace the bone. • Density: Titanium is denser and heavier than other materials like polymers and some ceramics, which can be a drawback for certain applications. • Manufacturing Complexity: Fabricating titanium prosthesis with the necessary porosity and complex structures can be technically challenging and expensive. 2.3 Fabrication Techniques The fabrication of orthopedic devices involves creating a structure with the desired shape, porosity, and mechanical properties. Various techniques are used to fabricate them, including: 2.3.1 Solvent Casting and Particulate Leaching A polymer solution is cast into a mold with a porogen (e.g., salt particles). After the solvent evaporates, the porogen is leached out, leaving a porous structure. 2.3.2 Electrospinning Electrospinning creates fibrous prosthesis by applying a high voltage to a polymer solution, which forms fine fibers collected on a target. This technique is suitable for creating structures that mimic the ECM's fibrous nature. Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design to cover the remaining volume surrounding the cell. This third solid was designed to be used as the obstacle geometry in Fusion software, ensuring that the generative result closely adhered to the auxetic geometry. Figure 6. Auxetic Cells 1, 2 and 3 in Solidworks In the image above (Figure 6), we can see the three designed cells with their respective coverings for the obstacle geometry. We will refer to them as Cell 1, Cell 2, and Cell 3, respectively. It should be noted that Cell 1 is the most commonly used auxetic cell and is known as the re-entrant cell. 5.3 Generating Optimal Cells with Autodesk Fusion The modeled cells were then imported into Autodesk Fusion, and a Generative Design analysis was selected. First, the three different parts of the cell were matched with the various considerations for generating the design, (Figures 7-9). Figure 7. The Three Spaces in Autodesk Fusion for Cell 1 Figure 8. The Three Spaces in Autodesk Fusion for Cell 2 Figure 9. The Three Spaces in Autodesk Fusion for Cell 3 For the three Auxetic Cells, we can see the three different geometries: in red is the obstacle geometry, in yellow is the initial geometry where the program can add material, and in green is the conservation geometry that cannot be altered by the algorithm. In all the images, we can observe the pressure applied to the cell, with a value of 600 MPa. We can also see the movement restrictions applied to the piece, indicating the levels of movement freedom required to ensure the piece functions as an auxetic cell. Titanium 6Al-4V was then selected as the material for study because it is used in the reference document for hip prostheses with auxetic geometries [3]. This material can be fabricated using advanced additive manufacturing techniques. Additionally, as noted earlier, this material possesses many properties suitable for both orthopedic applications and Auxetic Materials. Figure 10. Generative Objectives Configuration Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Next, for the Generative Design algorithm, we selected mass reduction as the objective with a safety factor of 2.00 for the strength of the result. This configuration ensures that the result will achieve the lowest possible mass for the applied pressure and the given geometry. Figure 11. Optimized Auxetic Cells 1, 2 and 3 We then started the generative process, during which the program sought to achieve the optimal result based on the given objectives and constraints. After several iterations, this process produced the three results for the auxetic cells, (Figure 11). 5.4 Finite Element Analyses with Abaqus Based on the results obtained from Autodesk Fusion, we proceeded to test whether the cells were reacting as expected. We also compared the optimized geometries with the initial geometries to determine if it is worthwhile to produce the new cells or if the basic geometry is sufficient. For these simulations, a group of identical auxetic cells was assembled to create a larger structure with two layers (Figure 12), allowing us to observe how the entire structure reacts to stress. Given the applied tensile stress we evaluated the structural response of the auxetic cells. For the correct analysis, we applied the constraints to the lower bases and the tensile stress on the upper bases. With this analysis we are going to determine the Von Misses stress on every single cell while applying the load and the boundary conditions to the overall structure. Figure 12. Substructure in Abaqus Made of Initial Auxetic Cells 2 To illustrate the configuration, here is the substructure of auxetic cells for the initial geometry of Cell 2. The same procedure was followed for all the other cells, resulting in a total of 6 analyses. 6 Results of the Finite Element Analyses The results of the finite element analyses provided insights into the mechanical behaviour and optimization potential of the auxetic prostheses. 6.1 Structure Formation from Auxetic Unit Cells To perform the Finite Element Analyses with Abaqus, we replicated the same auxetic unit cell to create a larger structure and observe how the entire group reacts. First, we began with the three auxetic cells in their basic geometry, which had not been optimized with generative design. The resulting structures from the three auxetic cells are shown in the following figure, (Figure 13). Figure 13. Structure Formation From Initial Auxetic Cells 1, 2 and 3 In this figure, we can observe the larger structure created by replicating the initial auxetic cells 1, 2, and 3. Von Mises stress analyses will be computed for these three structures. Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Next, we constructed the three larger structures using the optimized auxetic cells in the same manner as for the initial geometries. The results are shown in the following figure, (Figure 14). Figure 14. Structure Formation From Optimized Auxetic Cells 1, 2 and 3 6.2 Load and Boundary Conditions in Abaqus The next step was to apply the boundary and loading conditions to the overall structures to ensure they were properly defined for our analyses. The pressure applied, as previously mentioned, was 600 MPa on each cell's central beam, and the boundary condition involved embedding the bottom central beams. These details are shown in the following figure, (Figure 15). Figure 15. Load and Boundary Conditions 6.3 Von Misses Stress Analyses Once we had all the larger testing structures ready for analysis, the simulations were conducted, and the results are shown in the following figures. These figures provide a comparison between each initial auxetic cell and its optimized counterpart. The first cell we will compare is Cell 1, in both its initial and optimized forms. Figure 16. Von Misses Stress Analyses for Auxetic Cell 1 We observe that the initial cell cannot withstand the applied pressure, while the optimized cell performs well in the simulation. This indicates that the optimized Cell 1 is suitable for the stress analysis. Now we continue with the Cell 2: Figure 17. Von Misses Stress Analyses for Auxetic Cell 2 Auxetic Cell 2 performed similarly, with the initial cell unable to withstand the applied pressure, while the optimized cell successfully resisted all the analyses. Compared to Auxetic Cell 1, this Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design initial cell can endure more load, both in its initial and optimized geometries, making it slightly stiffer. Finally, we proceed with the last case, the Cell 3: Figure 18. Von Misses Stress Analyses for Auxetic Cell 3 We can observe that for Cell 3, the simulation is successful for both the optimized and nonoptimized geometries. However, the optimized geometry exhibits a stress distribution with fewer critical sections in terms of stress. As noted, a total of six Finite Element Analyses were conducted to evaluate the mechanical response of the structure. The goal was to ensure that the cells have a uniform stress distribution across the entire volume to prevent localized failures and to confirm that the overall substructure retains the recognized flexibility of auxetic materials. 6.4 Evaluation of Results The procedure for evaluating the results involves comparing the average values of the Von Mises stress analysis and the width of the histograms. This comparison allows us to determine that cells with a narrower histogram exhibit more consistent behaviour across all study cases. Using this method, we will assess whether the optimized geometries are truly a better choice by comparing the histograms of the non-optimized and optimized cells individually. Two different scenarios will be evaluated: the histograms at the final convergent time increment of each simulation, and the histograms for an applied pressure of 350 MPa. 6.4.1 Histograms for Cell 1 For the Auxetic Cell 1, we have seen that in the case of the initial geometry the simulation failed at the 58,44% of the applied stress. We must take this into account because for the histograms, the Von Mises stress for the initial geometry gives the results for an applied pressure of 350 MPa, which is the value before failure, (Figure 19). Figure 19. Histograms of Last Convergent Time Increment of Simulation (Cell 1) For the case with an applied pressure of 350 MPa, we have the case where both cells, the initial geometry and the optimized one have the same applied stress. A similar result is obtained, leading to the same conclusion: the optimized geometry for Cell 1 is significantly better in terms of stability than the initial one. This is because the Von Misses range for the initial geometry goes up to 2.700 MPa and for the optimized one it goes up to 375 MPa, (Figure 20). Optimization of the Unit Cell of Auxetic Materials for Orthopedic Applications Using Generative Design Figure 20. Histogram for the 350 MPa Situation of the Optimized Geometry (Cell 1) 6.4.2 Histograms for Cell 2 For the Auxetic Cell 2, we have seen that in the case of the initial geometry the simulation failed at the 81,41% of the applied stress. As in the last case, the Von Mises stress for the initial geometry gives the results for an applied pressure of 488 MPa, which is the value before failure, (Figure 21). Figure 21. Histograms of Last Convergent Time Increment of Simulation (Cell 2) To compare the histograms of the different cells with the same condition, we also applied a pressure of 350 MPa to both cells, the initial geometry and the optimized one. The Von Misses range for the initial geometry goes up to 2.900 MPa and for the optimized one it goes up to 400 MPa. We observe that for the same applied pressure than in the case of the Cell 1, the Von Misses range is very similar for both optimized geometries, (Figure 22).