Geodesic
Estimation of the effective Young’s modulus for open cell porous titanium based on $3D$ Gibson - Ashby cell array
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 75-82.

Voir la notice de l'article provenant de la source Math-Net.Ru

The objective of study is to determine the effective Young’s modulus of open cell porous titanium based on the Gibson – Ashby model. Two novel models are proposed in the form of $3D$ Gibson – Ashby cell arrays with two variants for connecting vertical and horizontal beams – hinged support and rigid clamping. Calculations made on the basis of the developed models are compared with results of known models and literature data. It is proved the assumption that at high porosity, the deformation of samples occurs to a greater extent due to the deflection of horizontal beams, and with a decrease in porosity, the compressive deformation of vertical beams is playing an important role.
Keywords: Gibson – Ashby model; porous titanium; open pores; effective Young’s modulus. 
@article{BGUMI_2022_1_a7,
     author = {A. V. Nikitin and G. I. Mikhasev},
     title = {Estimation of the effective {Young{\textquoteright}s} modulus for open cell porous titanium based on $3D$ {Gibson} - {Ashby} cell array},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {75--82},
     publisher = {mathdoc},
     volume = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a7/}
}
TY  - JOUR
AU  - A. V. Nikitin
AU  - G. I. Mikhasev
TI  - Estimation of the effective Young’s modulus for open cell porous titanium based on $3D$ Gibson - Ashby cell array
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2022
SP  - 75
EP  - 82
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a7/
LA  - ru
ID  - BGUMI_2022_1_a7
ER  - 
%0 Journal Article
%A A. V. Nikitin
%A G. I. Mikhasev
%T Estimation of the effective Young’s modulus for open cell porous titanium based on $3D$ Gibson - Ashby cell array
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2022
%P 75-82
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a7/
%G ru
%F BGUMI_2022_1_a7
A. V. Nikitin; G. I. Mikhasev. Estimation of the effective Young’s modulus for open cell porous titanium based on $3D$ Gibson - Ashby cell array. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 75-82. http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a7/

[1] A. V. Nikitsin, “Estimation of the mechanical properties for bone – titanium biocomposite based on computed tomography data and finite element modeling”, Journal of the Belarusian State University. Mathematics and Informatics, 2 (2020), 79–85 | DOI

[2] L. J. Gibson, M. F. Ashby, Cellular solids: Structure and properties, Cambridge University Press, Cambridge, 1997, XVIII+510 pp. | DOI

[3] L. J. Gibson, “Mechanical behavior of metallic foams”, Annual Review of Material Science, 30 (2000), 191–227 | DOI

[4] T. Uhlirova, W. Pabst, “Conductivity and Young’s modulus of porous metamaterials based on Gibson – Ashby cells”, Scripta Materialia, 159 (2019), 1–4 | DOI

[5] R. Singh, P. D. Lee, T. C. Lindley, C. Kohlhauser, C. Hellmich, M. Bram, “Characterization of the deformation behavior of intermediate porosity interconnected Ti foams using micro-computed tomography and direct finite element modeling”, Acta Biomaterialia, 6:6 (2010), 2342–2351 | DOI

[6] A. A. Umanskii, Handbook of the designer of industrial, residential and public buildings and structures. Calculation-theoretical, Gosudarstvennoe izdatel’stvo literatury po stroitel’stvu, arkhitekture i stroitel’nym materialam, Moscow, 1960, 1046 pp.

[7] A. V. Nikitsin, “Biomechanical assessment of the bone ingrowth effect during cementless endoprosthesis osteointegration”, Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 13:4-1 (2013), 90–96 | DOI

[8] A. Schuh, J. Luyten, R. Vidael, W. Honle, T. Schmickal, “Porous titanium implant materials and their potential in orthopedic surgery”, Materials Science and Engineering Technology, 38:12 (2007), 1015–1018 | DOI

[9] C. E. Wen, M. Mabuchi, Y. Yamada, K. Shimojima, Y. Chino, T. Asahina, “Processing of biocompatible porous Ti and Mg”, Scripta Materialia, 45:10 (2001), 1147–1153 | DOI

[10] C. E. Wen, Y. Yamada, A. Nouri, P. D. Hodgson, “Porous titanium with porosity gradients for biomedical applications”, Material Science Forum, 539–543 (2007), 720–725 | DOI

[11] S. Thelen, F. Barthelat, L. C. Brinson, “Mechanics considerations for microporous titanium as an orthopedic implant material”, Journal of Biomedical Materials Research, 69A:4 (2004), 601–610 | DOI

[12] N. G. Davis, J. Teisen, C. Schuh, D. C. Dunand, “Solid-state foaming of titanium by superplastic expansion of argon-filled pores”, Journal of Materials Research, 16:5 (2001), 1508–1519 | DOI