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

Subject Areas :

Hamid Khanaki ¹ , Sadegh Rahmati ² , Mohammad Nikkhoo ³ , Mohammad Haghpanahi ⁴ , Javad Akbari ⁵

1 - Department of Mechanical Engineering, Sciences and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mechanical Engineering, Sciences and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Biomechanics Group, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
5 - Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Received: 2020-03-07 Accepted : 2020-04-20 Published : 2020-05-01

Keywords:

References:

[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.