Geodesic
Numerical investigation of hyperelastic solids with contact interaction
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 4, pp. 644-656

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The paper is devoted to the construction of a computational algorithm for the investigation of hyperelastic solids with the contact interaction. In the framework of the previously developed algorithm for the investigation of large deformations of three-dimensional solids, the solutions of contact problems based on the equation of the principle of virtual work in velocity term have been considered. Contact interaction has been modeled on the basis of the “master-slave” approach. The closest point projection procedure has been used to find the contact area. A contact functional has been built on the basis of the principle of virtual work in velocity term within the penalty method. The linearization of the kinematic relations and contact functional are based on the capacity on the possible velocities of penetration. The solution of the nonlinear system of equations has been obtained using the method of step loading. The numerical implementation is based on the finite element method.
Keywords: finite deformations, contact interaction, penalty method. 
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     author = {A. I. Abdrakhmanova and L. U. Sultanov},
     title = {Numerical investigation of hyperelastic solids with contact interaction},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {644--656},
     publisher = {mathdoc},
     volume = {160},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_4_a3/}
}
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A. I. Abdrakhmanova; L. U. Sultanov. Numerical investigation of hyperelastic solids with contact interaction. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 4, pp. 644-656. http://geodesic.mathdoc.fr/item/UZKU_2018_160_4_a3/