Задача часткового відшарування пружного міжфазного тонкого включення в умовах поздовжнього зсуву біматеріалу: Fìz.-mat. model. ìnf. tehnol. 2021, 31:60-66

• Datum: 2021
• 1. Verfasser: Piskozub, Yosyf
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Schlagworte: поздовжній зсув; відшарування; тонке включення; біматеріал; функції стрибка
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/190
• Назва журналу: Physico-mathematical modeling and informational technologies

The problem of longitudinal displacement of a bi -material with a thin inclusion of arbitrary physical and mechanical nature at the interface of the matrix materials is considered. The bulk is loaded by normal compression and various force factors in the longitudinal direction. The possibility of partial delamination of a part of the boundary between the inclusion and the matrix, where dry friction slip occurs, is assumed. A complete system of equations for the formulated problem is constructed. It is proposed to construct the solution using the structural modular method of jump functions, a description of which is given. A condition for the appearance of a slip zone on the inclusion-matrix boundary is founded. A convergent iterative algorithm for numerically analytical determination of the size of this zone is developed. References Sulym, H. T. (2007). Osnovy matematychnoi teorii termopruzhnoi rivnovahy deformivnykh tverdykh til z tonkymy vkliuchenniamy. Monohrafiia. Lviv: Doslidno-vydavnychyi tsentr NTSh. Sulym, H. T., Piskozub, Y. Z. (2004). Umovy kontaktnoi vzaiemodii (ohliad). Mat. metody i fiz.-mekh. polia, 47(3), 110–125. Panasyuk, V. V., Savruk, M .P., Datsishin, A. P. (1976). Raspredelenie napryazheniy okolo treschin v plastinah i obolochkah. K.: Naukova dumka. Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc.Soc. Lond. A: Math. Phys. Eng. Sci., 241(1226), 376–396. Aleksandrov, V. M., Smetanin, B. I., Sobol, B. V. (1993). Tonkie kontsentratoryi napryazheniy v uprugih telah. Moskva: Fizmatlit. Panasyuk, V. V., Stadnik, M. M., Silovanyuk, V. P. (1986). Kontsentratsiya napryazheniy v trehmernyih telah s tonkimi vklyucheniyami. KiYiv: Nauk. dumka. Piskozub, J. Z., Sulim, G. T. (2008). Thermoelastic equilibrium of piecewise homogeneous solids with thin inclusions. Journal of Engineering Mathematics. Special Issue Thermomechanics, 61, 315–337. DOI doi.org/10.1007/s10665-008-9225-3 Ilina, I. I., Silvestrov, V. V. (2005). Zadacha o tonkom zhestkom mezhfaznom vklyuchenii, otsloivshemsya vdol odnoy storonyi ot sredyi. Mehanika tverdogo tela, 3, 153-166. Ilina, I. I., Silvestrov, V. V. (2007). Chastichnoo otsloivsheesya tonkoe zhestkoe vklyuchenie mezhdu raznyimi uprugimi materialami pri nalichii treniya v zone kontakta. Vestnik SamGU. Estestvennonauchnaya seriya, 4(54), 124-139. Popov, G. Ya. (1982). Kontsentratsiya uprugih napryazheniy vozle shtampov, razrezov, tonkih vklyucheniy i podkrepleniy. Moskva: Nauka. Pasternak, Ya. M., Sulym, H. T., Pasternak, R. M. (2012). Pozdovzhnii zsuv tila z tonkymy strichkovymy nakladkamy ta pruzhnymy vkliuchenniamy zminnoi zhorstkosti pry yikhnomu. Mekhanika i fizyka ruinuvannia budivelnykh konstruktsii: zbirnyk naukovykh prats, 9, 98-113. Peleh, B. L., Maksimuk, A. V., Korovaychuk, I. M. (1988). Kontaktnyie zadachi dlya sloistyih elementov konstruktsiy i tel s pokryitiyami. K.: Nauk. dumka. Pasternak, Ya. M., Sulim, G. T., Piskozub, L. G. (2010). Modeli tonkogo vklyucheniya v usloviyah ego idealnogo i neidealnogo kontaktnogo vzaimodeystviya s okruzhayuschim materialom. Trudyi VI Mezhdunar. simp. po tribofatike MSTF 2010 (Minsk, 25 okt. – 1 noyab. 2010 g.) V2 ch. Ch. 2.– Minsk; BGU. Martyniak, R. M., Serednytska, Kh. I. (2017). Kontaktni zadachi termopruzhnosti dlia mizhfaznykh trishchyn v bimaterialnykh tilakh. Lviv: Rastr-7. Sulym, H. T., Piskozub, I. Z. (2018). Nonlinear deformation of a thin interface inclusion. Materials Science, 53, 5, 600-608. DOI doi.org/10.1007/s11003-018-0114-2 Piskozub, L. H. (2014). Pozdovzhnii zsuv zoseredzhenoiu syloiu bimaterialu z mizhfaznoiu trishchynoiu z urakhuvanniam tertia. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii, 20, 160-172. Sulym,H., Piskozub, L., Piskozub, Y. (2015). Iaroslav Pasternak Antiplane Deformation of a Bimaterial Containing an Interfacial Crack with the Account of Friction. 2. Repeating and Cyclic Loading. ACTA Mechanica et Automatica, 9(3), 178-185. DOI doi.org/10.1515/ama-2015-0030 Pasternak, Ia., Sulym, H. T. (2010). Thin inclusions theory integral equations numerical solution using the boundary element method procedure. Proc. Int. Conf. «Integral Equations — 2010», 25-27 August 2010 (Lviv). Lviv: PAIS. Pasternak, Ya. M., Sulym, H. T. (2011). Modeli tonkykh neodnoridnostei z urakhuvanniam mozhlyvosti yikhnoho neidealnoho kontaktu z seredovyshchem. Visnyk Dnipropetrovskoho universytetu. Seriia «Mekhanika», 15(5), 200-210. Pasternak, Ya. M., Sulym, H. T., Pasternak, R. M. (2012). Pozdovzhnii zsuv tila z tonkymy strichkovymy nakladkamy ta pruzhnymy vkliuchenniamy zminnoi zhorstkosti pry yikhnomu idealnomu ta neidealnomu kontaktakh. Mekhanika i fizyka ruinuvannia budivelnykh konstruktsii: zbirnyk naukovykh prats, 9, 98-113.