Мария Сергеевна Черкасова (Bauman Moscow State Technical University) :
Articles:
539.36 Microstructural model anisotropic flow theory for elastic-plastic layered composites
Dimitrienko Y. I. (Bauman Moscow State Technical University), Черкасова М. С. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University)
doi: 10.18698/2309-3684-2022-3-4770
A microstructural model of layered elastic-plastic composites based on the anisotropic flow theory is proposed. The model represents the effective constitutive relations of the transversally isotropic theory of plastic flow, in which the model constants are determined not experimentally, but on the basis of approximations of the deformation curves of composites obtained by direct numerical solution of problems on the periodicity cell for basic loading trajectories, which arise in the method of asymptotic averaging. The problem of identifying the constants of this composite model is formulated; for the numerical solution of this problem, methods of optimizing the error functional are used. The results of numerical simulation by the proposed method for layered elastic-plastic composites are presented, which showed good accuracy of approximation of numerical strain diagrams.
Димитриенко Ю.И., Черкасова М.С., Димитриенко А.Ю. Микроструктурная модель анизотропной теории течения для упруго-пластических слоистых композитов. Математическое моделирование и численные методы, 2022, № 3, с. 47–70.
Dimitrienko Y. I. (Bauman Moscow State Technical University), Черкасова М. С. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-4-318
The problem statement of calculation of deformation of layered elastic-plastic composites based on generalized flow theory is proposed. As constitutive relations, it is proposed to use equations of so-called microstructural theory of plastic flow for transversely isotropic media. In this theory, constants of the model of anisotropic theory of composite flow are determined by means of direct solution of local problems of plasticity on periodicity cell, and also components of stress concentration tensors are calculated, allowing calculation of microstress in components of composite. An example of numerical solution of the problem on calculation of stresses in thin elastic-plastic layered composite pipe under pressure is given. Composite layers obey isotropic theory of plastic flow with kinematic hardening; the case is considered when periodicity cell consists of two elastic-plastic layers: steel-aluminum. Using the proposed method for solving the problem, it is shown that the level of micro-stresses in the composite significantly exceeds the values of macro-stresses in the composite structure, so their consideration is necessary to improve the accuracy of calculations of deformation and strength of composite structures.
Димитриенко Ю.И., Черкасова М.С. Моделирование деформирования слоистых упругопластических композитов на основе микроструктурной теории течения. Математическое моделирование и численные методы, 2024, № 4, с. 3–18.
539.3 Modeling the deformation of layered periodic composites based on the theory of plastic flow
Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Черкасова М. С. (Bauman Moscow State Technical University)
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.
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.