Discrete a non-linear Hamiltonian dynamics models of hyper elastic deformable media

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.