Physically nonlinear deformation of a thin interphase inclusion under antiplane problem conditions: Fìz.-mat. model. ìnf. tehnol. 2020, 28:42-54 - Piskozub, Yosyf; Sulym, Heorgiy; Piskozub, Liubov (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2020)
The longitudinal shear problem of the bimaterial with thin physically nonlinear inclusion at the interface matrix materials is considered. The solution of the formulated problem is constructed by the method of the conjugation of limit values of analytical functions with the use of the jump function method. A model of thin inclusion with arbitrary nonlinear strain characteristics is constructed. The solution of the problem is reduced to a system of singular integral equations with variable coefficients. A convergent iteration method for solving such a system for different types of physically nonlinear deformation is proposed. An incremental calculation method for calculating stress-strain state under multistep (including cyclic) quasi-static loading is developed. Numerical calculations of the body stress-strain state for various values of the parameters of the nonlinearity of the inclusion material are carried out. Their influence on the mode of deformation of the matrix under loading by a balanced system of concentrated forces is investigated. References Sulym, H. T. (2007). Osnovy matematychnoi teorii termopruzhnoi rivnovahy deformivnykh tverdykh til z tonkymy vkliuchenniamy. Lviv: Doslidno-vydavnychyi tsentr. Sulym, H. T., Piskozub, Y. Z. (2004). Umovy kontaktnoi vzaiemodii (ohliad). Mat. metody i fiz.-mekh. polia, 47(3), 110-125. Panasiuk, V. V., Savruk, M. P., Datsyshyn, A. P. (1976). Raspredelenye napriazhenyi okolo treshchyn v plastynakh y obolochkakh. K.: Naukova dumka. Arkhypenko, K. M., Kryvyi, O. F. (2008). Mizhfazna balka pry riznykh typakh kontaktnoi vzaiemodii z neodnoridnoiu anizotropnoiu ploshchynoiu. Mashynoznavstvo, 3(129), 16-21. Peleh, B. L., Maksimuk, A. V., Korovajchuk, I. M. (1988). Kontaktnye zadachi dlya sloistyh elementov konstrukcij i tel s pokrytiyami. K.: Nauk. dumka. Pasternak, Ya. M., Sulim, G. T., Piskozub, L. G. (2010). Modeli tonkogo vklyucheniya v usloviyah ego idealnogo i neidealnogo kontaktnogo vzaimodejstviya s okruzhayushim materialom. Trudy VI Mezhdunar. simp. po tribofatike MSTF 2010 (Minsk, 25 okt. — 1 noyab. 2010 g.), 2(2), 399-404. Chernyh, K. F. (1999). Nelinejnaya singulyarnaya uprugost. Ch.1. Teoriya. SPb.: Izd-vo SPb un-ta. Kojic, M., Bathe, K. J. (2005). Inelastic Analysis of Solids and Structures. Berlin Heidelberg, Springer-Verlag. , L. H. (2014). Pozdovzhnii zsuv zoseredzhenoiu syloiu bimaterialu z mizhfaznoiu trishchynoiu z urakhuvanniam tertia. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii, 20, 160-172. 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. Sulym, H., Piskozub, L., Piskozub, Y., Pasternak, Ia. (2015). Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. Acta Mechanica et Automatica, 9(2), 115-121. DOI https://doi.org/10.1515/ama-2015-0020 Sulym, H., Piskozub, L., Piskozub, Y., Pasternak, Ia. (2015). Antiplane deformation of a biomaterial containing an interfacial crack with the account of friction. 2.RepeatingandCyclicloading. Acta Mechanica et Automatica, 9(3), 178-184. DOI https://doi.org/10.1515/ama-2015-0030 Sulym, H., Piskozub, L., Piskozub, Y., Pasternak, Ia. (2015). Longitudinal shear of a bimaterial with frictional sliding contact in the interfacial crack. Journal of Theoretical and Applied Mechanics, 54(2), 529-539. DOI https://doi.org/10.15632/jtam-pl.54.2.529 Piskozub, L. H., Sulym, H. T., Pasternak, Ya. M. (2014). Vplyv tertia na histerezys pry tsyklichnomu navantazhenni pozdovzhnim zsuvom masyvu z mizhfaznoiu trishchynoiu. Prykl. problemy mekh. i mat., 12, 184-191. Goryacheva, I. G. Contact Mechanics in Tribology. Springer. Atlas of Stress Strain Curves. (2002). (second edition.). ASM International. Gurtin, M. E., Murdoch, A. I. (1975). A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal., 57(4), 291-323. DOI https://doi.org/10.1007/bf00261375 Piskozub, Y. Z., Sulym, H. T. (2017). Neliniine deformuvannia tonkoho mizhfaznoho vkliuchennia. Fiz.- khim. mekhanika materialiv, 53(5), 24-30.