Numerical simulation of multilayer cellular scaffolds with 3D and 1D elements
Subject Areas : additive manufacturingHamid Reza khanaki 1 , Sadegh Rahmati 2 , Mohammad Nikkhoo 3 , Mohammad Haghpanahi 4 , Javad Akbari 5
1 - Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mechanical Engineering, Science 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
Keywords: Finite Element Modeling, Multilayer scaffold, Additive Manufacturing, numerical analysis, Open-lattice cellular scaffold,
Abstract :
In this paper, an attempt has been made to provide a numerical method for investigating the mechanical properties of multilayer scaffolding. These scaffolds can be used as implants in bone fractures. For this purpose two numerical simulation methods are introduced to predict the elastic properties of multilayer cell scaffolds. These simulations are based on two models: a 3D model with a volumetric element, and a 1D model with a linear element. To compare the results of these models, three types of two- and three-layer titanium alloy scaffolds have been simulated by the two methods. Also, Young's modulus of the scaffolds has been compared with the experimental conclusions of earlier studies. The results confirm that simulations with 1D models are more cost-effective compared to 3D ones. Additionally, because of the more reliable agreement of Young's modulus results of numerical modeling with the linear element (1.8 to 5 times) compared to the volumetric element (11 to 23 times) compared to the experimental findings, the numerical method with the linear elements can be a reliable tool for studying multilayer scaffoldings.
[1] Wang, X., Xu, S., Zhou, S., Xu, W., Leary, M., Choong, P., Qian, M., Brandt, M. and Xie, Y. M., Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review, Biomaterials, Vol. 83, No. 5, 2016, pp. 127-141.
[2] Surmeneva, M., Surmenev, R., Chudinova, E., Koptioug, A., Tkachev, M., Gorodzha, S. and Rannar, L. E., Fabrication of multiple-layered gradient cellular metal scaffold via electron beam melting for segmental bone reconstruction, Materials & Design, Vol. 133, No. 5, 2017, pp. 195–204.
[3] Laurencin, C. T., Khan, Y., Ma, P. X. and Elisseeff, J., Polymer/Calcium Phosphate Scaffolds for Bone Tissue Engineering, In: Ma, P. X., Elisseeff, J. (eds) Scaffolding in tissue engineering, 2005, pp. 253–265.
[4] Vaezi, M., Seitz, H., and Yang, S., A review on 3D micro-additive manufacturing technologies, The International Journal of Advanced Manufacturing Technology, Vol. 67, No. 5-8, 2013, pp. 1721–1754.
[5] Ahn, S., Chun, D., and Kim, C., Nanoscale hybrid manufacturing process by nano particle deposition system (NPDS) and focused ion beam (FIB), CIRP Annals-Manufacturing Technology, Vol. 60, No. 1, 2011, pp. 583–586.
[6] Petrochenko, P. E., Torgersen, J., Gruber, P., Hicks, L. A., Zheng, J., Kumar, G., Narayan, RJ., Goering, PL., Liska, R., and Stampfl, J., Laser 3D Printing with Sub-Microscale Resolution of Porous Elastomeric Scaffolds for Supporting Human Bone Stem Cells, Advanced healthcare materials, Vol. 4, No. 5, 2014, pp. 739–747.
[7] Deshpande, V. S., and Fleck, N. A., Collapse of truss core sandwich beams in 3-point bending, International Journal of Solids and Structures, Vol. 38, No. 36-37, 2001, pp. 6275–6305.
[8] Wang, J., Evans, A. G., Dharmasena, K., et al., On the performance of truss panels with Kagome cores, International Journal of Solids and Structures, Vol. 40, No. 25, 2003, pp. 6981–6988.
[9] Kooistra, G. W., Deshpande, V. S., and Wadley, H. N. G., Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium, Acta Materialia, Vol. 52, No. 14, 2004, pp. 4229–4237.
[10] Rathbun, H. J., Wei, Z., He, M. Y., et al., Measurement and simulation of the performance of a lightweight metallic sandwich structure with a tetrahedral truss core, Journal Applied Mechanics, Vol. 71, No. 3, 2004, pp. 368–374.
[11] Queheillalt, D. T., and Wadley, H. N. G., Cellular meterial lattices with hollow trusses, Acta Materialia, Vol. 53, No. 2, 2005, pp. 303–313.
[12] Queheillalt, D. T., and Wadley, H. N. G., Pyramidal lattice truss structures with hollow trusses, Materials Science Engineering: A, Vol. 397, No. 1-2, 2005, pp. 132–137.
[13] Gibson, L. J., and Ashby, M. F., Cellular solids: structure and properties. Cambridge university press, 1997.
[14] Luxner, M. H., Woesz, A., Stampfl, J., Fratzl, P., and Pettermann, H. E., A finite element study on the effects of disorder in cellular structures, Acta biomaterialia, Vol. 5, No. 1, 2009, pp. 381–390.
[15] Parthasarathy, J., Starly, B., Raman, S., and Christensen, A., Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM), Journal of the mechanical behavior of biomedical materials, Vol. 3, No. 3, 2010, pp. 249–259.
[16] Hedayati, R., Sadighi, M., Mohammadi-Aghdam, M., and Zadpoor, A. A., Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: analytical solutions and computational models, Materials Science and Engineering: C, Vol. 60, 2016, pp. 163–183.
[17] Campoli, G., Borleffs, M., Yavari, S. A., Wauthle, R., Weinans, H., and Zadpoor, A. A., Mechanical properties of open-cell metallic biomaterials manufactured using additive manufacturing. Materials and Design, Vol. 49, 2013, pp. 957–965.
[18] Babaee, S., Jahromi, B. H., Ajdari, A., Nayeb-Hashemi, H., and Vaziri, A., Mechanical properties of open-cell rhombic dodecahedron cellular structures, Acta Materialia, Vol. 60, No. 6, 2012, pp. 2873-2885.
[19] Borleffs, M., Finite element modeling to predict bulk mechanical properties of 3D printed metal foams, TU Delft, Delft University of Technology, 2012.
[20] Shulmeister, V., Van der Burg, M., Van der Giessen, E., and Marissen, R., A numerical study of large deformations of low-density elastomeric open-cell foams, Mechanics of materials, Vol. 30, No. 2, 1998, pp. 125–140.
[21] Hedayati, R., Hosseini-Toudeshky, H., Sadighi, M., Mohammadi-Aghdam, M., Zadpoor, A. A., Computational prediction of the fatigue behavior of additively manufactured porous metallic biomaterials, International Journal of Fatigue, Vol. 84, 2016, pp. 67–79.
[22] Hedayati, R., Sadighi, M., Mohammadi-Aghdam, M., and Zadpoor, A. A., Mechanical behavior of additively manufactured porous biomaterials made from truncated cuboctahedron unit cells. International Journal of Mechanical Sciences, Vol. 106, 2016, pp. 19–38.
[23] Warren, W., Kraynik, A., Linear elastic behavior of a low-density Kelvin foam with open cells, Journal of Applied Mechanics, Vol. 64, 1997, pp. 787–794.
[24] Zheng, X., Lee, H., Weisgraber, T. H., Shusteff, M., DeOtte, J., Duoss, E. B., Kuntz, J. D., Biener, M. M., Ge, Q., Jackson, J. A., Ultralight, ultrastiff mechanical metamaterials, Science, Vol. 344, 2014, pp. 1373–1377.
[25] Hedayati, R., Sadighi, M., Mohammadi-Aghdam, M., Zadpoor, A. A., Mechanics ofadditively manufactured porous biomaterials based on the rhombicuboctahedron unit cell, Journal of the Mechanical Behavior of Biomedical Materials, Vol. 53, 2016, pp. 272–294.
[26] Ptochos, E., Labeas, G., Elastic modulus and Poisson’s ratio determination of microlattice cellular structures by analytical, numerical and homogenisation methods, Journal of San- dwich Structures and Materials, Vol. 14, 2012, pp. 597–626.
[27] Ptochos, E., Labeas, G., Shear modulus determination of cuboid metallic open-lattice cellular structures by analytical, numerical and homogenisation methods, Journal of Strain, Vol. 48, 2012, pp. 415–429.
[28] Hedayati, R., Sadighi, M., Mohammadi-Aghdam, M., Zadpoor, A. A., Mechanics ofadditively manufactured porous biomaterials based on the rhombicuboctahedron unit cell, Journal of the Mechanical Behavior of Biomedical Materials, Vol. 53, 2016, pp. 272–294.
[29] Ptochos, E., Labeas, G., Elastic modulus and Poisson’s ratio determination of microlattice cellular structures by analytical, numerical and homogenisation methods, Journal of San- dwich Structures and Materials, Vol. 14, 2012, pp. 597–626.
[30] Ptochos, E., Labeas, G., Shear modulus determination of cuboid metallic open-lattice cellular structures by analytical, numerical and homogenisation methods, Journal of Strain, Vol. 48, 2012, pp. 415–429.
[31] Ahmadi, S., Campoli, G., Amin Yavari, S., Sajadi, B., Wauthl´e, R., Schrooten, J., Weinans, H., Zadpoor, A. A., Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells, Journal of the Mechanical Behavior of Biomedical Materials, Vol. 34, 2014, pp. 106–115.
[32] Hedayati, R., Sadighi, M., Mohammadi-Aghdam, M., Zadpoor, A. A., Effect of massmultiple counting on the elastic properties of opencell regular porous biomaterials, Materials and Design, Vol. 89, 2016, pp. 9–20.
[33] Bitsche, R., Daxner, T., B¨ohm, H. J., Space-Filling Polyhedra as Mechanical Models for Solidified Dry Foams. Technische Universit¨at Wien, 2005.
[34] Buffel, B., Desplentere, F., Bracke, K., Verpoest, I., Modelling open cell-foams based on the Weaire-Phelan unit cell with a minimal surface energy approach, International Journal of Solids and Structures, Vol. 51, 2014, pp. 3461-3470.
[35] Kraynik, A. M., Reinelt, D. A., Linear elastic behavior of dry soap foams, Journal of Colloid and interface Science, Vol. 181, 1996, pp. 511-520.
[36] Feng, Y. F., Wang, L., Li, X., Ma, Z. S., Zhang, Y., Zhang, Z. Y., and Lei, W., Influence of architecture of β-tricalcium phosphate scaffolds on biological performance in repairing segmental bone defects, PLoS One, Vol. 7, No. 11, 2012, e49955.
[37] Das, A., and Botchwey, E., Evaluation of angiogenesis and osteogenesis, Tissue Engineering Part B: Reviews, Vol. 17, No. 6, 2011, pp. 403-414.
[38] Gérard, C., and Doillon, C. J., Facilitating tissue infiltration and angiogenesis in a tubular collagen scaffold, Journal of biomedical materials research Part A, Vol. 93, No. 2, 2010, pp. 615-624.
[39] Surmeneva, M., Surmenev, R., Chudinova, E., Koptioug, A., Tkachev, M., Gorodzha, S., Rannar, L. E., Fabrication of multiple-layered gradient cellular metal scaffold via electron beam melting for segmental bone reconstruction, Materials & Design, 2017; DOI: 10.1016/ j.matdes. 2017.07.059.
[40] Khanaki, H. R., Rahmati, S., Nikkhoo, M., Haghpanahi, M., and Akbari, J., Numerical and analytical simulation of multilayer cellular scaffolds, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42, No. 268, 2020, pp. 1-13.
[41] Fundamental FEA Concepts and Applications (no data) (https://www.cae.tntech.edu/~chriswilson/FEA/ANSYS/ANSYSguide_fea-concepts.pdf)
[42] Bandyopadhyay, A., Espana, F., Balla, V. K., Bose, S., Ohgami, Y., and Davies, N. M., Influence of porosity on mechanical properties and in vivo response of Ti6Al4V implants, Acta Biomaterialia, Vol. 6, 2010, pp. 1640-1648
[43] Khanaki, H. R., Rahmati, S., Nikkhoo, M., Haghpanahi, M., and Akbari, J., Numerical Simulation of Homogeneous, Two and Three Lattice Layers Scaffolds with Constant Density, Journal of Modern Processes in Manufacturing and Production, Vol. 9, No. 2, 2020, pp. 5-22.