Ragulina V. Identification of kernel’s heredity of isotropic nonlinear viscoelastic materials under complex stress

The Thesis is devoted to the development of a three-dimensional nonlinear theory of viscoelasticity of hereditary type by building constitutive equations based on the conditions of directing tensor deviators proportionality. The nonlinearity of visco-elastic properties is given by equations of Rabotnov’s type. Two methods of the determining of heredity kernels parameters based on relations between kernels under the complex stress state and kernels under one-dimensional stresses have been developed and tested. The fractional exponential functions as the heredity kernels have been justified. The discrete values of kernels at small times using weight functions are calculated. Some problems of creep strains and stress relaxation calculation of thin-walled tube elements under combined loading by tension with torsion have been solved and experimentally approved.