On some method of the heredity kernel parameters determination of nonlinear viscoelastic materials under the complex stress state

The deformation of viscoelastic medium given by means of constitutive equations of the hereditary type. These equations establish the relationship between the components of strain tensor, the components of stress tensor and the integral time operator, and contain the set of function and coefficients that are determined from the basic experiments. А method of the heredity kernel parameters determination of nonlinear viscoelastic materials is developed. As the visco-elastic model, the constitutive equations of the hereditary type are chosen in which the relationship between the components of the strain tensor and the stress tensor is given based on the hypothesis of the deviators proportionality. The nonlinearity of the viscoelastic properties is given by the equations of Ratotnov’s type. The method is based on the relations between the creep kernels under complex stress state and the creep kernels under one-dimensional stress state. The method verified experimentally for the problems of determination of creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density.

To the problem of influence of the third invariant of stress deviator on the process of longterm deformation of nonlinear viscoelastic materials

The problem on the influence of stressed state on the process of long-term deformation of nonlinear viscoelastic materials under the simple and quasi-simple modes of loading by introduction of the function with the parameter of Lode angle into the defining equations is considered. The mentioned function is determined by analysis of base experimental data obtained from the base experiments on axial tension and pure torsion. Physical and mechanical properties of nonlinear viscoelastic solids are defined by the correspondence between the invariants of deformation tensors and tensions according to the modified nonlinear Rabotnov’s model for viscoelasticity. The heredity kernels are given by the fractional-exponential function. The constructed defining equations are verified experimentally for the problems of determination of nonlinear creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density and low pressure polyethylene. As a result of juxtaposition of experimental data and calculations it is a stated that allowing for the type of stressed state improves their agreement qualitatively and quantitatively.

Towards the solution of creep problems of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials

A new approach to the creep strains analysis of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials under combined loading with uniaxial tension and torsion has been proposed. The system of equations that is constructed according to the deviators proportionality hypothesis has been chosen as the creep constitutive equations the nonlinearity of viscoelastic properties in which is given with respect to the creep strain intensity and volumetric strain by the Rabotnov type models. The kernels of creep strain intensity and volumetric strain are given by the relations that establish the relationships between these kernels and one-dimensional creep kernels determined from a system of base experiments. One-dimensional tension with the measurement of longitudinal and transverse strains as well as one-dimensional tension and pure torsion with the measurement of longitudinal and shearing strains have been considered as base experiments. The functions of nonlinearity of viscoelastic properties are given by smoothing cubic splines. The problems of the analysis of longitudinal, transverse and shearing strains of thin-shelled tubular specimens made of “high density polyethylene PEHD” have been solved and experimentally approved.