doi: 10.18698/2309-3684-2021-2-1537
The aim of this work is to find the constitutive relations for a layered elastoplastic composite according to the flow theory using the method of asymptotic averaging. This goal is achieved by developing an algorithm for solving the problem of the theory of plastic flow for a layered composite material, taking into account various characteristics and properties of these layers of the material, followed by visualizing the result in the form of effective plasticity diagrams connecting the components of averaged stress tensors and components of averaged strain tensors.
Dvorak G.J. Inelastic deformation of composite materials. New York, Springer–Verlag Publ., 1991, 779 p.
Kovtunov A.I., Myamin S.V., Semistenova T.V. Sloistye kompozicionnye materialy: elektronnoe uchebnoe posobie [Layered composite materials: electronic textbook]. Togliatti, TSU Publ., 2017, 75 p.
Nikitin V.S., Polovinkin V.N. State of the art and prospects of composites in foreign submarine shipbuilding. Transactions of the Krylov State Research Centre, 2017, no.4 (382), pp.57–74.
Rawal S. Metal–matrix composites for space applications. JOM, 2001, vol.53, iss. 4, pp.14–17.
Katsiropoulos Ch.V., Pantelakis Sp.G., Meyer B.C. Mechanical behavior of non-crimp fabric PEEK/C thermoplastic composites. Theoretical and Applied Fracture Mechanics, 2009, vol.52, iss.2, pp.122–129.
Adams D.F. Uprugoplasticheskoe povedenie kompozitov. Kompozitsionnye materialy. T. 2: Mekhanika kompozitsionnykh materialov [Elastic-plastic behavior of composites. Composite materials. Vol.2: Mechanics of composite materials]. Moscow, Mir Publ., 1978, pp.196–241.
Bilim A.V., Saraev L.A., Sahabiev V.A.The persicularities of two–component composite materials elastic–plastic deformation. Vestnik of Samara University, 1998, no.4, pp.113–119.
Vildeman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of inelastic deformation and destruction of composite materials]. Moscow, Nauka Publ., 1997, 288 p.
Nguyen B.N., Bapanapalli S.K., Kunc V., Phelps J.H., Tucker C.L. Prediction of the elastic–plastic stress/strain response for injection–molded long–fiber thermoplastics. Journal of Composite Materials, 2009, vol.43, no.3, pp.217–246.
Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov [Averaging processes in periodic media. Mathematical problems of the composite material mechanics]. Moscow, Nauka Publ., 1984, 352 p.
Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov Moscow State University Publ., 1984, 324 p.
Sanches–Palensiya E. Neodnorodnye sredy i teoriya kolebaniy [Nonhomogeneous media and vibration theory]. Moscow, Mir Publ., 1984, 472 p.
Bensoussan A., Lions J.L., Papanicolaou G. Asymptotic analysis for periodic structures. North-Holland, 1978, 721 p.
Églit M.E. An averaged description of processes in periodic elasticoplastic media. Mechanics of Composite Materials, 1985, vol.20, iss.5, pp.568 –574.
Khdir Y.K., Kanit T., Zaïri F., Naït–Abdelaziz M. Computational homogenization of elastic-plastic composites. International Journal of Solids and Structures, 2013, vol.50, no.18, pp.2829–2835.
Dimitrienko Yu.I., Kashkarov A.I., Makashov A.A. Finite element calculation of effective elastic-plastic characteristics of composites based on the method of asymptotic averaging. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2007, no.1, pp.102–116.
Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V., Bazyleva O.A., Lutsenko A.N., Oreshko E.I. Modeling the elastic–plastic characteristics of monocrystalline intermetallic alloys based on microstructural numerical analysis. Маthematical Modeling and Coтputational Methods, 2015, no.2, pp.3–22.
Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V. Multiscale modeling of elastic–plastic composites with an allowance for fault probability. Маthematical Modeling and Coтputational Methods, 2016, № 2, pp.3–23.
Dimitrienko Y.I., Sborschikov S.V, Yurin Y.V. Modeling of effective elastic–plastic properties of composites under cyclic loading. Маthematical Modeling and Coтputational Methods, 2020, № 4, pp.3–26.
Hill R. Matematicheskaya teoriya plastichnosti [Mathematical theory of plasticity]. Moscow, Gostekhizdat Publ., 1956, 407 p.
Ishlinskiy A.Yu. Prikladnye zadachi mekhaniki. Kniga 1. Mekhanika vyazkoplasticheskih i ne vpolne uprugih tel [Applied problems of mechanics. Book 1. Mechanics of viscoplastic and not completely elastic bodies]. Moscow, URSS, 2021, 358 p.
Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tverdogo tela [Continuum Mechanics. Vol.4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
Dimitrienko Yu.I. Mekhanika sploshnoj sredy. T. 1. Tenzornyj analiz [Continuum Mechanics. Vol.1. Tensor analysis]. Moscow, BMSTU Publ., 2011, 367 p.
Димитриенко Ю.И., Губарева Е.А., Черкасова М.С. Моделирование деформирования слоистых периодических композитов на основе теории пластического течения. Математическое моделирование и численные методы, 2021, № 2, с. 15–37.
Количество скачиваний: 366