Geodesic
Computer modeling deformation of porous elastoplastic materials and identification their characteristics using the principle of three-dimensional similarity
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 746-755.

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It is proposed to numerically model large deformations of porous specimens, using the 3D-similarity principle in structural elements, which makes it possible to account for the inhomogeneity of the stress-strain state due to the presence of pores and allows one to vary the number of representative volumes without changing porosity values and dimensions of the specimens. A methodology for determining true deformation diagrams of materials, using the results of compression tests, has been developed. The efficiency of using the 3D-similarity principle is demonstrated by comparing the numerical and experimental results for the example analyzing compression of porous specimens of an aluminum alloy with free lateral surfaces and fixed in a rigid cartridge.
Keywords: porous metal, diagramm of deformation, deformation, 3D-similarity principle, structural element. 
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Valentin G. Bazhenov; Maxim N. Zhestkov. Computer modeling deformation of porous elastoplastic materials and identification their characteristics using the principle of three-dimensional similarity. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 746-755. http://geodesic.mathdoc.fr/item/JSFU_2021_14_6_a7/

[1] P.G.Cheremskoy, Metody issledovaniya poristosty tverdyh tel, Energoatomizdat, M., 1985, 112 pp. (Russian)

[2] A.A.Vityaz, V.M.Kaptsevich, A.G.Kostornov, Formirovanie struktury i svoistv poristyh poroshkovyh materialov, Metallurgiya, M., 1993, 240 pp. (Russian)

[3] A.Ya.Krasovskiy, “Nekotorye zakonomernosti deformirovaniya i razrusheniya poristyh metallokeramicheskih materialov na osnove zheleza. Soobshchenie 1”, Poroshkovaya metallurgiya, 4 (1964), 3–7 (Russian)

[4] A.Ya.Krasovskiy, “Nekotorye zakonomernosti deformirovaniya i razrusheniya poristyh metallokeramicheskih materialov na osnove zheleza. Soobshchenie 2”, Poroshkovaya metallurgiya, 5 (1964), 9–15 (Russian)

[5] V.V.Skorokhod, L.M.Tuchinskiy, “Uslovie plastichnosti poristyh tel”, Poroshkovaya metallurgiya, 11 (1978), 83–87 (Russian)

[6] L.J.Gibson, M.F.Ashby, Cellular Solids structure and properties, Pergamon Press, Oxford, 1988, 503 pp. | Zbl

[7] E.Andrews, W.Sanders, L.J.Gibson, “Compressive and tensile behavior of aluminum foams”, Materials Science and Engineering, A270 (1999), 113–124 | DOI

[8] V.V.Polyakov, A.V.Golovin, “Moduli uprugosti poristyh materialov”, FMM, RAN, 79:2 (1995), 57–60 (Russian)

[9] V.V.Polyakov, A.V.Golovin, “Vliyanie poristosti nd uprugie harakteristiki metalla”, Metally, 4 (1995), 81–85 (Russian)

[10] K.S.Chernyavskiy, Stereologiya v metallovedenii, Metallurgia, M., 1977, 280 pp. (Russian)

[11] R.Bradford, T.M.Dofine, H.Preston-Thomas, Pribory i methody fizicheskogo metallovedeniya, Mir, M., 1973, 786 pp. (Russian)

[12] J.Banhart, J.Baumeister, “Deformation characteristics of metal foams”, Journal of mat. Science, 33 (1998), 1431–1440 | DOI

[13] H.Bart-Smith, A.F.Bastawros, A.G.Evans and other, “Compressive deformation and yielding mechanisms in cellular Al alloys determined using X-ray tomografy and surface strain mapping”, Acta mat., 46:10 (1998), 3583–3592 | DOI

[14] M.Dorozhko, A.Seweryn, “Finite Element Modeling of Anisotropic Deformation Behavior of the Porous Materials Based on Microtomographic Images”, AIP Conference Proceedings, 1780 (2016), 060001 | DOI

[15] M.Dorozhko,A.Seweryn, “Pore-scale numerical modelling of large deformation behaviour of sintered porous metals under compression using computed microtomography”, Mechanics of Materials, 2019, 1–18

[16] V.L.Kirpichyov, “O podobii pri uprugih yavloniyah”, Zhurnal Russkogo fiziko-himicheskogo obshchestva, 6:9 (1874), 90–120 (in Russian)

[17] V.G.Bazhenov, M.N.Zhestkov, “Issledovanie primenimosti printsipa podobiya v zadachah uprugoplasticheskogo izgiba i ustoychivosti pri osevom szhatii gusto perforirovannyh plastin i obolochek”, Materialy XII Mezhdunarodnoy konferentsii po prikladnoy matematike I mehanike v aerokosmicheskoy otrasli, NPNJ'2018, 2018, 326–328 (in Russian)

[18] V.G.Bazhenov, M.N.Zhestkov, “About the applicability limits of the tymoshenko model and the principle of two-dimensional similarities in problems of elastic plastic bending and stability of densely perforated plates and shells”, Journal of physics: conference series, 1158 (2019), 022022 | DOI

[19] V.G.Bazhenov, S.L.Osetrov, D.L.Osetrov, A.A.Artemyeva, “Influence of the type of stress-strain state on the true stress-strain curve for the elastoplastic materials”, Materials physics and mechanics, 28:1–2 (2016), 53–56

[20] V.G.Bazhenov, V.K.Lomunov, S.L.Osetrov, E.V.Pavlenkova, “Eksperimentalno-raschetniy metod issledovaniya bolshyh uprugoplasticheskih deformatsiy tsilindricheskih obolochek pri rastyazhenii do razryva i postroenie diagram deformirovaniya pri neodnorodnom napryazhenno-deformirovannom sostoyanii”, Prikladnaya mehanika i tehnicheskaya fizika, 2013, no. 1, 116–124 (in Russian) | Zbl

[21] Abaqus Analysis User's Guide. Abaqus Theory Guide, Simulia Abaqus, 2016