Numerical investigation of nonlinear deformations with contact interaction

 A.I. Abdrakhmanova*, L.U. Sultanov**

Kazan Federal University, Kazan, 420008 Russia

E-mail: *A061093@mail.ru, **Lenar.Sultanov@kpfu.ru

Received February 6, 2018

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Abstract

The paper is devoted to the development of a computational algorithm for investigation of finite deformations of solids with contact interaction. The algorithm is based on the master-slave approach. The projection of the slave point onto the master surface, which is given parametrically, has been considered. All necessary kinematic relations have been constructed. To identify the contact areas, the closest point projection algorithm has been applied. The frictionless contact interaction between the contacting surfaces has been considered. The penalty method has been used for regularization of the contact conditions. The principle of virtual work in terms of the virtual velocity equation in the actual configuration has been used. The variation formulation of the solution of the problem with the contact interaction has been given. The functional of contact interaction from an unknown rate of penetration of one body into another has been constructed. The elastic deformation potential function has been used to obtain the constitutive relations. The incremental method has been applied to solve the nonlinear problem. The resolving equation has been constructed as a result of the linearization of the equation of the principle of virtual work in actual configuration. The linearized relations have been obtained. The algorithm of solving the nonlinear problem has been developed. The finite element implementation of the algorithm has been presented. The spatial discretization has been constructed on the basis of an eight-node finite element and a five-node contact element implementing solutions of the variational contact problem. The results of solving the model problems have been presented.

Keywords: finite deformations, contact interaction, penalty method, closest point projection algorithm

Acknowledgments. The study was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan as part of research project no. 18-41-160021.

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For citation: Abdrakhmanova A.I., Sultanov L.U. Numerical investigation of nonlinear deformations with contact interaction. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 3, pp. 423–434. (In Russian)

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