Geodesic
Discrete a~non-linear Hamiltonian dynamics models of hyper elastic deformable media
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 237-246

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A method of mathematical modeling of the dynamics of three-dimensional nonlinear deformable hyperelastic media is developed in this paper. The method is based on the Hamiltonian description of discrete classical mechanics and on symplectic integration method for the solution at each instant of time. Comparative results of the solution of a model problem are presented. The results of solution of the topical problem of dynamic behavior of an artificial aortic artery are also presented.
Keywords: deformable media, finite deformation, Hamiltonian description, symplectic integrator, point approximation, mathematical simulation. 
@article{JSFU_2013_6_2_a10,
     author = {Vladimir A. Petushkov},
     title = {Discrete a~non-linear {Hamiltonian} dynamics models of hyper elastic deformable media},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {237--246},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a10/}
}
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Vladimir A. Petushkov. Discrete a~non-linear Hamiltonian dynamics models of hyper elastic deformable media. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 237-246. http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a10/