Geodesic
Axisymmetric growth of a~hollow hyperelastic cylinder
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 209-227

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The finite deformations of the growing cylinder fabricated of an incompressible elastic material of Mooney–Rivlin type are under consideration. We assume that the deformations are axisymmetric and constant along the cylinder axis. The discrete and continuous types of growing are studied. The analytical solutions of the corresponding boundary-value problems are derived. The computational examples show the convergence of solutions obtained for the discrete growth to corresponding solutions for continuous growth under the following conditions: the number of discrete plies increases while their thickness decreases such that the final volume of growing solid is fixed. 
@article{ISU_2014_14_2_a9,
     author = {S. A. Lychev and A. V. Mark},
     title = {Axisymmetric growth of a~hollow hyperelastic cylinder},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {209--227},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a9/}
}
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S. A. Lychev; A. V. Mark. Axisymmetric growth of a~hollow hyperelastic cylinder. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 209-227. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a9/