Misyura E. Large deformations of piecewise-homogeneous anisotropic hyperelastic body of revolution

The object of research is the stress-strain state of rubber-technical structures and mathematical model of the heart left ventricle. The purpose of work is elaboration of the numerical solution's methodics of axisymmetric physically and geometrically nonlinear problems for the nearly incompressible piecewise-homogeneous transversely isotropic hyperelastic bodies of revolution. General method of research is the stepping algorithm of the finite element method for the solution of nonlinear problems based on the principle of possible displacements in the increments. The theoretical meaning of work is the improvement of methodics of the numerical research of large deformations of the nearly incompressible piecewise-homogeneous isotropic and transversely isotropic hyperelastic bodies of revolution based on the finite element method which realized the principle of possible displacements in the increments on the example of solution an axisymmetric (with and without the torsion) physically and geometrically nonlinear problems of such bodies deformations. A practical meaning of work is the methodics, algorithm and program which allows to obtain the numerical solution of axisymmetric physically and geometrically nonlinear problems for the nearly incompressible piecewise-homogeneous transversely isotropic hyperelastic bodies of revolution. The scientific novelty of work is: the methodics of numerical solution of the finite element method of the nonlinear problems for the nearly incompressible piecewise-homogeneous transversely isotropic hyperelastic bodies of revolution based on the principle of possible displacements in the increments was elaborated; a new kind of the potential for nearly incompressible transversely isotropic hyperelastic material was constructed and scientifically grounded; the mathematical model of the heart left ventricle as nearly incompressible piecewise-homogeneous transversely isotropic hyperelastic with the account of the nonhomogeneous transverse isotropy was for the first time constructed;the new results of the numerical investigation of the anisotropy degree's influence, the analysis of the stress-strain state and the inside cavity volume of the left ventricle's model with the account of the relatively stiff inclusions depending upon their disposition and sizes as well as, geometrical and mechanical parameters of model were obtained; the results of contact problems solution of definition of the stress-strain state of the different kinds of rubber support and new structures of shock-absorbers depending upon form and value of gap between the elastic elements and stiffer wall was for the first time obtained. The results of researches are used in educational process on the mechanical and mathematical faculty and faculty of fundamental medicine of Kharkov national university by V.N. Karazine and declarational patent on the useful model "The shock-absorbers" as well. The obtained results of researches may be used in engineering calculations of rubber-technical structures of modern technique in machinebuilding and modelling of heart's function with the biomechanics standpoint of heartily-vesseling system of human and researches of different illnesses of heart in scientific researches institutes.