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Information × Registration Number 0225U005212, (0125U001293) , R & D reports Title Research on the critical state of cracks and their propagation trajectories, as well as wave propagation within nonlinear approaches of modern computational and analytical mechanics popup.stage_title Теоретичний та комп’ютерний аналіз тріщин в рамках нелінійних підходів сучасної механіки матеріалів Head Kipnis Oleksandr L., Кандидат фізико-математичних наук Registration Date 28-12-2025 Organization S.P. Tymoshenka Institute of Mechanics of the National Academy of Sciences of Ukraine popup.description1 • Development of an analytical-numerical approach to the study of the compres-sion of inhomogeneous non-linear elastic bodies with a thin coating along interface defects; • Development of methods for modeling non-stationary deformation of three-layer cylindrical shells of elliptical cross-section with discrete ribbed filler; • Development of methods for modeling the non-stationary deformation of three-layered elliptical cylindrical shells with discrete ribbed fillers; • Formulation of scenarios for the propagation of a single Friedländer wave in structural materials and soils; • Study the peculiarities of the wave field of a fluid in a cylindrical cavity caused by harmonic vibrations of a spherical segment. popup.description2 A universal semi-analytical approach within the framework of the three-dimensional linearized theory of stability has been developed to determine the critical buckling parameters of nonlinearly elastic (hyperelastic) bilayer systems under compression, which are associated with the initial stage of failure. The focus of Section I is on semi-infinite piecewise-homogeneous bodies (substrate/thin-film coating systems) with various types of interfacial contact. Using general representations of the solutions to the linearized equilibrium equations, the initial plane strain boundary value problems are reduced to transcendental equations (for defect-free bodies) or to Fredholm integral equations of the first kind (or systems thereof) for bodies with defects. This allows for the consideration of an arbitrary structure of elastic potentials for hyperelastic compressible or incompressible bilayer materials. Numerical modeling of the initial angular branching (kinking) of an edge slanted crack under plane strain conditions has been performed. The subject of Section II is the critical state of the body and the crack propagation path under mixed-mode loading. Particular attention is paid to a comparative analysis of predictions from classical linear elastic fracture mechanics and the cohesive zone model. A variational approach based on the finite element method is applied. The physical crack is supplemented by a short fictitious cohesive extension, the orientation of which is determined by minimizing the critical load or local energy. The interface behavior is described by a potential-based traction-separation law, which ensures thermodynamic consistency and symmetry of the tangent operator. The developed model accounts for full mode interaction via a coupling parameter and the disparity in fracture energies for opening and shear modes. Product Description popup.authors Lysenko Anna V. Юрчук Василь Миколайович Ostos Oleksandr Kh. Selivanov Danylo M. popup.nrat_date 2025-12-28 Close