Numerical Simulation of Homogeneous, Two and Three Lattice Layers Scaffolds with Constant Density

محورهای موضوعی : Additive manufacturing processes

Hamid Khanaki ¹ (Department of Mechanical Engineering, Sciences and Research Branch, Islamic Azad University, Tehran, Iran)
Sadegh Rahmati ² (Department of Mechanical Engineering, Sciences and Research Branch, Islamic Azad University, Tehran, Iran)
Mohammad Nikkhoo ³ (Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran)
Mohammad Haghpanahi ⁴ (Biomechanics Group, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran)
Javad Akbari ⁵ (Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran)

تاریخ دریافت : 1398/12/17 تاریخ پذیرش : 1399/02/01 تاریخ انتشار : 1399/02/12

کلید واژه: numerical analysis, Implant, Bone Scaffold, Additive Manufacturing,

چکیده مقاله :

Advances in the additive manufacturing technology have led to the production of complex microstructures with unprecedented accuracy and due todesigning an effective implant is a major scientific challenge in bone tissue regeneration and bone growth. In this research, titanium alloy cylindrical scaffolds with three-dimensional architectures have been simulated and compared for curing partial bone deficiencies. The cylindrical networks in the scaffold (outer diameter 15 and length 30 millimeters) were designed in 36 different convergent, two-layer and three-layer types with 50% and 70% porosity. In all the samples, outer layers were denser than the inner layers. Mechanical characteristics of these scaffolds have been determined by simulating uniform compression load. The stress-strain curve of the samples showed that Young’s modulus and yield stress in the scaffolds with constant porosity were related to a unit-cell and the two-layer scaffolds, without changing Young’s modulus, had higher yield stress. This advantage was more significant in high-density scaffolds.

منابع و مأخذ:

[1]Wang, X.,Xu, S.,Zhou, S.,Xu, W.,Leary, M.,Choong, P.,Qian, M.,Brandt, M. andXie, Y.M. 2016.Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: a review. Biomaterials. 83: 127-141.

[2]Feng, Y. F., Wang, L., Li, X., Ma, Z. S., Zhang, Y., Zhang, Z. Y. and Lei, W. 2012.Influence of Architecture of β-tricalcium Phosphate Scaffolds on Biological Performance in Repairing Segmental Bone Defects. PLOS One. 7(11): 1-12.

[3]Das,S. A. andBotchwey,E. 2011.Evaluation of Angiogenesis and Osteogenesis. Tissue Engineering Part B: Reviews. 17(6): 403-414.

[4] Gérard,C. and Doillon, C.J. 2010.FacilitatingTissue Infiltration and Angiogenesis in a Tubular Collagen Scaffold. Journal of Biomedical Materials Research Part A. 93(2): 615-624.

[5] Tampieri, A.,Celotti, G.,Sprio, S.,Delcogliano, A. andFranzese, S.2001.Porosity-graded Hydroxyapatite Ceramics to Replace Natural Bone. Biomaterials. 22: 1365–1370.

[6]Pompe, W.,Worch, H.,Epple, M.,Friess, W.,Gelinsky, M.,Greil, P.,Hempel, U.,Scharnweber, D. and Schulte, K.2003.Functionally Graded Materials for Biomedical Applications, Materials Science and Engineering: A. 362: 40-60.

[7]Becker, B. and Bolton, J.1997.Corrosion Behaviour and Mechanical Properties of Functionally Gradient Materials Developed for Possible Hard-tissue Applications, Journal of Mater Sci-Mater M. 8: 793–797.

[8] Gibson, L.J. and Ashby, M.F. 1997.Cellular Solids: Structure and Properties, Cambridge University Press.

[9] Luxner, M.H.,Woesz, A.,Stampfl, J.,Fratzl, P. andPettermann, H.E. 2009.A Finite Element Study on the Effects of Disorder in Cellular Structures. ActaBiomaterialia. 5: 381-390.

[10] Parthasarathy, J.,Starly, B., Raman, S. and Christensen, A. 2010.Mechanical Evaluation of Porous Titanium (Ti6Al4V) Struc-tures with Electron Beam Melting (EBM). Journal of the Mecha- nical Behavior of Biomedical Materials. 3: 249-259.

[11] Hedayati, R.,Sadighi, M.,Mohammadi-Aghdam, M. andZadpoor, A.A. 2016.Mechanical Properties of Regular Porous Bio-materials Made from Truncated Cube Repeating unit Cells: Analytical Solutions and Computational Models. Materials Science and Engineering: C.60: 163-183.

[12] Babaee, S.,Jahromi, B.H.,Ajdari, A.,Nayeb-Hashemi, H. andVaziri, A. 2012.Mechanical Properties of Open-cell Rhombic Dodecahedron Cellular Structures. ActaMaterialia. 60: 2873-2885.

[13] Borleffsm, M. 2012.Finite Element Modeling to Predict Bulk Mechanical Properties of 3D Printed Metal Foams, TU Delft, Delft University of Technology.

[14]Hedayati, R.,Sadighi, M.,Mohammadi-Aghdam, M. andZadpoor, A.A. 2016. Mechanical Behavior of Additively Manufac-tured Porous Biomaterials Made from Truncated Cuboctahedron unit Cells. International Journal of Mechanical Sciences. 106: 19-38.

[15] Shulmeister, V., Van der Burg, M., Van der Giessen, E. and Marissen, R. 1988.A Numerical Study of Large Deformations of Low-density Eastomeric Open-cell Foams. Mechanics of Materials. 30: 125-140.

[16] Warren, W. andKraynik, A. 1997.Linear Elastic Behavior of a Low-density Kelvin Foam with Open Cells. Journal of Applied Mechanics. 64: 787-794.

[17] Zheng, X., Lee, H.,Weisgraber, T.H.,Shusteff, M.,DeOtte, J.,Duoss, E.B., Kuntz, J.D.,Biener, M.M.,Ge, Q. and Jackson, J.A. 2014.Ultralight, Ultrastiff Mechanical Metamaterials, Science. 344: 1373-1377.

[18] Hedayati, R.,Sadighi, M.,Mohammadi-Aghdam, M. andZadpoor, A.A. 2016. Mechanics of Additively Manufactured Porous Biomaterials Based on the Rhombicuboctahedron Unit Cell. Journal of the Mechanical Behavior of Biomedical Materials. 53: 272-294.

[19] Ptochos, E. andLabeas, G. 2012. Elastic Modulus and Poisson’s Ratio Determination of Microlattice Cellular Structures by An-alytical, Numerical and Homogenisation Methods. Journal of San- dwich Structures and Materials. 14: 597-626.

[20] Ptochos, E. andLabeas, G. 2012. Shear modulus Determination of Cuboid Metallic Open-Lattice Cellular Structures by Analyt-ical, Numerical and Homogenisation Methods. Journal of Strain. 48: 415-429.

[21] Ahmadi, S.,Campoli, G., AminYavari, S.,Sajadi, B.,Wauthl´e, R.,Schrooten, J.,Weinans, H. andZadpoor, A.A. 2014. Me-chanical Behavior of Regular Open-cell Porous Biomaterials Made of Diamond Lattice Unit Cells. Journal of the Me-chanical Behavior of Biomedical Materials. 34: 106-115.

[22] Hedayati, R.,Sadighi, M.,Mohammadi-Aghdam, M. andZadpoor, A.A. 2016. Effect of Massmultiple Counting on the Elastic Properties of Open-cell Regular Porous Biomaterials. Materials and Design. 89: 9-20.

[23]Bitsche, R.,Daxner, T. andBohm, H.J. 2005. Space-Filling Polyhedra as Mechanical Models for Solidified Dry Foams, TechnischeUniversit at Wien.

[24] Buffel, B.,Desplentere, F.,Bracke, K. andVerpoest, I. 2014. Modelling Open Cell-foams based on the Weaire-Phelan Unit Cell with AMinimal Surface Energy Approach. International Journal of Solids and Structures. 51: 3461-3470.

[25] Kraynik, A.M. andReinelt, D.A. 1996.Linear Elastic Behavior of Dry Soap Foams. Journal of Colloid and interface Science. 181: 511-520.

[26] Surmeneva, M.,Surmenev, R.,Chudinova, E.,Koptioug, A.,Tkachev, M.,Gorodzha, S. andRannar, L.E. 2017.Fabrication of Multiple-layered Gradient Cellular Metal Scaffold via Electron Beam Melting for Segmental Bone Reconstruction. Materials & Design. 133: 195-204.

[27] Daxner, T. 2010.Finite Element Modeling of Cellular Materials. Cellular and Porous Materials in Structures and Processes. Springer: 47-106.

[28] Heinl,P.,Müller, L.,Körner, C.,Singer, R.F. and Müller, F.A. 2008.Cellular Ti-6Al-4V Structures with Interconnected Macro Porosity for Bone Implants Fabricated by Selective Electron Beam Melting.ActaBiomaterialia. 4(5):1536-1544.

[29] Bandyopadhyay, A.F.,Balla, V.K.,Bose, S.,Ohgami, Y. and Davies, N.M.2010. Influence of Porosity on Mechanical Properties and in Vivo Response of Ti6Al4V Implants. ActaBiomaterialia. 6: 1640-1648.

[30] Heimann, R.B.,Hemachandra, K. and Itiravivong, P. 1999.Materials Engineering Approaches Towards Advanced Bioceramic Coatings on Ti6Al4V Implants. Journal of Metals, Materials and Minerals. 8(2): 25-40.

[31] Yavari, S.A.,Wauthlé, R.,Van der Stok, J.,Riemslag, A.C.,Janssen, M.,Mulier, M.,Kruth, J.P.,Schrooten, J.,Weinans, H. andZadpoor, A.A. 2013.Fatigue Behavior of Porous Biomaterials Manufactured using Selective Laser Melting. Materials Science and Engineering: C. 33: 4849-4858.

[32] Tan, X.P.,Tan, Y.J.,Chow, C.S.L.,Tor, S.B. and Yeong, W.Y. 2017.Metallic Powder-bed based 3D Printing of Cellular Scaffolds for Orthopaedic Implants: A Stateofthe Art Review on Manufacturing, Topological Design, Mechanical Properties and Biocompatibility. Materials Science and Engineering C. 76: 1328-1343.

[33] Choi, K.,Kuhn, J.L.,Ciarelli, M.J. and Goldstein, S.A. 1990.The Elastic Moduli of Human Subchondral, Trabecular, and Cortical Bone Tissue and the Size-dependency of Cortical Bone Modulus.Journal of Biomechanics. 23: 1103-1113.

[34] Rho, J.Y.,Kuhn-Spearing, L. and Zioupos, P. 1998.Mechanical Properties and the Hierarchical Structure of Bone.Medical Engineering & Physics. 20: 92-102.

[35]Rho, J.Y.,Ashman, R.B. and Turner, C.H. 1993.Young's Modulus of Trabecular and Cortical Bone Material: Ultrasonic and Microtensile Measurements. Journal of Biomechanics.26: 111-119.

[36] Bayraktar, H.H.,Morgan, E.F.,Niebur, G.L.,Morris, G.E.,Wong, E.K. and Keaveny, T.M. 2004.Comparison of the Elastic and Yield Properties of Human Femoral Trabecular and Cortical Bone Tissue.Journal of Biomechanics. 37: 27-35.