539.36 Modeling microstructural model of the plasticity deformation theory for transversally isotropic composites

Dimitrienko Y. I. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University), Yurin Y. V. (Bauman Moscow State Technical University)

COMPOSITES, NUMERICAL MODELING, DEFORMATION THEORY OF PLASTICITY, TRANSVERSALLY ISOTROPIC MATERIALS, MICROSTRUCTURAL MODEL, ASYMPTOTIC AVERAGING METHOD, FINITE ELEMENT METHOD, UNIDIRECTIONALLY REINFORCED COMPOSITES, METAL COMPOSITES, STRAIN DIAGRAMS, INVARIANTS


doi: 10.18698/2309-3684-2022-1-1541


Within the framework of the deformation theory of plasticity under active loading, a model of constitutive relations for elastic-plastic composites belonging to the class of transversally isotropic materials is proposed. The theory of spectral expansions of stress and strain tensors and the spectral representation of nonlinear tensor functions for transversely isotropic media are used to develop a nonlinear constitutive relations. Specific models of plasticity functions are proposed, depending on the spectral invariants of the strain tensor. To determine the model constants, a method is proposed in which these constants are calculated based on the approximation of deformation curves obtained by direct numerical solution of three-dimensional problems on the periodicity cell of elastic-plastic composites. Problems on the periodicity cell are formulated using the method of asymptotic averaging of periodic media. The numerical solution of problems on the periodicity cell is carried out using the finite element method within the framework of software developed at the Scientific and Educational Center "Supercomputer Engineering Modeling and Development of Software Systems" of Bauman Moscow State Technical University. An example of numerical calculation of the constants of a composite model using the proposed method for a unidirectionally reinforced composite based on carbon fibers and an aluminum alloy matrix is given. Examples of verification of the proposed model for different loading trajectories of the composite in a 6-dimensional stress space are given. It is shown that the proposed microstructural model and the algorithm for determining its constants provide a sufficiently high accuracy in predicting the elastic-plastic deformation of transversely isotropic composites


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Certificate no. 2019666176 Programma NonlinearEl_Disp_Manipula dlya prognozirovaniya diagramm nelinejno-uprugogo deformirovaniya dispersno-armirovannyh kompozitov pri malyh deformaciyah na osnove konechno-elementnogo resheniya 3D lokal'nyh zadach mikromekhaniki: svidetel'stvo ob ofic. registracii programmy dlya EVM [The program NonlinearEl_Disp_Manipula for predicting diagrams of nonlinear elastic deformation of dispersed-reinforced composites under small deformations based on the finite element solution of 3D local problems of micromechanics: certificate of ofic. registration of a computer program] / Yu.I. Dimitrienko, Yu.V. Yurin, S.V. Sobshchikov, I.O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665098; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2019666172 Programma StrengthCom SMCM dlya konechno-elementnogo rascheta prochnostnyh harakteristik kompozitnyh materialov so slozhnoj strukturoj s uchetom nakopleniya mikro-povrezhdenij i kinetiki mezoskopicheskih defektov: svidetel'stvo ob ofic. registracii programmy dlya EVM [The StrengthCom SMCM program for finite element calculation of strength characteristics of composite materials with a complex structure, taking into account the accumulation of micro-damage and the kinetics of mesoscopic defects]: certificate of ofic. registration of a computer program / Yu. I. Dimitrienko, E. A. Gubareva, Yu. V. Yurin, S. V. Sobshchikov, I. O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665109; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2018614767 Programma MultiScale_SMCM dlya mnogomasshtabnogo modelirovaniya napryazhenno-deformirovannogo sostoyaniya konstrukcij iz kompozicionnyh materialov, na osnove metoda mnogourovnevoj asimptoticheskoj gomogenizacii i konechno-elementnogo resheniya trekhmernyh zadach teorii uprugosti [MultiScale_SMCM program for multiscale modeling of the stress-strain state of structures made of composite materials, based on the method of multilevel asymptotic homogenization and finite element solution of three-dimensional problems of elasticity theory]: certificate of ofic. registration of computer programs/ Yu.I. Dimitrienko, S.V. Sborshchikov, Yu.V. Yurin; applicant and copyright holder: BMSTU —no. 2018677684; application 21.02.2018; registered in the register of computer programs 17.04.2018 — [1].


Димитриенко Ю.И., Сборщиков С.В., Димитриенко А.Ю., Юрин Ю.В. Микроструктурная модель деформационной теории пластичности трансверсально-изотропных композитов. Математическое моделирование и численные методы, 2022, № 1, с. 15–41.



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