Antiplane Axisymmetric Creep Deformation of Incompressible Medium

Abstract

Model problems with simplified geometry and kinematics has a great value for developing theories of mechanical behavior of materials. Analytical solutions of such problems allow one to perform qualitative analysis of investigated process and to verify numerical solutions. 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. In this paper anti-plane deformation problem is solved in the context of theory of large elastoplastic deformations. This theory is based on non-equilibrium thermodynamics formalism. 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. The points of the medium are restricted to move only along lines parallel to the element of the cylinder. We suppose that medium deforms both reversibly and irreversibly. In addition, irreversible deformation accumulation is due to creeping of medium. Present work is the continuation of the research [6, 7] in which similar problem statement was used. The main distinction of works [6,7] is that irreversible deformation of medium is due to plastic flow.