Mathematics & Physics 2015, 8(4), 406–415 УДК 539.374 Antiplane Axisymmetric Creep Deformation of Incompressible Medium Sergey N. Firsov ∗ Aleksandr N. Prokudin† Institute of Machinery and Metallurgy FEB RAS Metallurgov, 1, Komsomolsk-on-Amur, 681005 Russia Received 10.05.2015, received in revised form 24.06.2015, accepted 11.09.2015 Flow of incompressible medium under varying gradient of pressure is considered. <...> It is assumed that medium exhibits nonlinear elastic and creep behavior. <...> The theory of large strains based on transport equations for the tensors of reversible and irreversible deformations is used for problem formulation. <...> DOI: 10.17516/1997-1397-2015-8-4-406-415 Introduction Model problems with simplified geometry and kinematics has a great value for developing theories of mechanical behavior of materials. <...> Anti-plane deformation problem is one of the simplest model problems. <...> This problem was solved for linear elastic medium, nonlinear elastic medium and elastoplastic medium. <...> One should mention the set of papers [1–5] published by V. D. Bondar in which anti-plane deformation problem is solved in the frameworks of finite strain elasticity and elastoplasticity. <...> It assumes that irreversible and reversible deformations are defined by differential transport equations. <...> We consider flow of incompressible medium within cylindrical tube due to pressure gradient. <...> No-slip boundary condition is set on the walls of the tube. <...> In addition, irreversible deformation accumulation is due to creeping of medium. <...> The main distinction of works [6,7] is that irreversible deformation of medium is due to plastic flow. ∗firsov.s.new@yandex.ru †prokudin@imim.ru ⃝ Siberian Federal University. <...> All rights reserved c – 406 – Sergey N. Firsov, Aleksandr N. Prokudin Antiplane axisymmetric creep deformation of incompressible . 1. <...> We use the Almansi finite strain tensor: dij = 1 2 (ui,j +uj,i −uk,iuk,j) . (1) Here ui are the components of displacement vector. <...> Let us consider reversible and irreversible strains along with temperature and entropy as state variables. <...> In accordance with [8, 9] differential transport equations are written as Deij Dt = εij −γij − where Dnij Dt = dnij dt −riknkj +nikrkj, dnij dt = ∂nij ∂t +nij <...>