Abstract:
Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination.
Citation:
T. S. Popova, “Problems on thin inclusions in a two-dimensional viscoelastic body”, Sib. Zh. Ind. Mat., 21:2 (2018), 66–78; J. Appl. Industr. Math., 12:2 (2018), 313–324
This publication is cited in the following 8 articles:
Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal, “Well-posedness of the governing equations for a quasi-linear viscoelastic model with pressure-dependent moduli in which both stress and strain appear linearly”, Z. Angew. Math. Phys., 75:1 (2024)
N. A. Nikolaeva, “Zadacha o ravnovesii uprugogo tela s treschinoi i tonkimi vklyucheniyami, kotorye sopryazheny mezhdu soboi”, Dalnevost. matem. zhurn., 24:1 (2024), 73–95
N. A. Nikolaeva, “Plastina Kirkhgofa — Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46
T. S. Popova, “On Numerical Solving of Junction Problem for the Thin Rigid and Elastic Inclusions in Elastic Body”, Lobachevskii J Math, 44:10 (2023), 4143
Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal, “A generalization of the Kelvin–Voigt model with pressure‐dependent moduli in which both stress and strain appear linearly”, Math Methods in App Sciences, 46:14 (2023), 15641
Natalia Nikolaeva, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020030
T. S. Popova, “on Equilibrium of a Two-Dimensional Viscoelastic Body With a Thin Timoshenko Inclusion”, Sib. Electron. Math. Rep., 17 (2020), 1463–1477
Tatiana S. Popova, “On numerical solving of junction problem for semirigid and Timoshenko inclusions in elastic body”, Procedia Structural Integrity, 30 (2020), 113