Explore the vast range of titles available.

The fundamentals of theoretical methods for engineering calculations of bending vibrations of thin plates, the material of which has hereditary properties, are presented. The manifestation of the hereditary properties of the material of the plate under consideration at a given stress-strain state can be judged by the relaxation core of the material. The dependence of the creep and relaxation kernels on the time difference corresponds to the fact that the “memory” of the material about the force effect produced at a given moment is determined by the elapsed time interval. In particular, this means that if the force action on the elastic-viscous body is cyclic, then the deformation of the body will also be cyclic with some phase shift. A technique for solving forced vibrations of plates under the influence of harmonic loads is proposed. An exact solution to the problem of forced vibrations of a supported rectangular plate, whose dissipative properties are described by memory functions, is constructed.

A theoretical and experimental method is poroposed for identification of mechanical properties of the surface layers of highly elastic materials by the results of their dynamic indentation for small depths (nanoDMA). The method is based on an approximate solution of the contact problem for a rigid ball in contact with a deformable specimen, the contact being loaded by an oscillating normal force. The specimen is modeled by a linear viscoelastic half-space with the relaxation kernel presented as a sum of exponential terms. The method allows one to determine sets of parameters defining the relaxation and creep functions of a material in a time interval corresponding to the experimental range of frequencies, as well as to calculate the dynamic storage and loss moduli for each frequency. The application of the method is shown by an example of the analysis of the mechanical properties of surface layers for two types of frost-resistant rubber (butadiene-nitrile and isoprene) depending on the degree of wear of their surfaces. It is established that the wear of surfaces of the rubbers under investigation leads to an increase of the surface layers stiffness and to a decrease in their relaxation properties; these changes are more pronounced for rubber based on nitrile butadiene than for that based on isoprene.

The relations between the heredity kernels of isotropic nonlinear viscoelastic materials in combined and one-dimensional stress states are derived. The constitutive equations are presented in a form corresponding to the proportional deviator hypothesis. The nonlinearity of viscoelastic properties is described by Rabotnov’s type models. The creep strains and stress relaxation in thin-walled tubular elements subject to a combination of tension and torsion are determined and tested experimentally.

The objective of the study is development of a creep kernel recording form, which allows obtaining representations for creep curves calculation. Based on the elastic-creeping body theory a possibility of the high-rate creep movement analytical study has been shown. A creep kernel, which contains a formula to describe the aging material properties, has been built. Essential stages of the proposed creep kernel formation have been given. The correspondence of the proposed calculations to real processes has been proved by a comparison with experimental data. In the numerical implementation, decomposition of integration elements into power series has been used. A possibility of calculating functions for a long time interval has been shown. Creep kernel parameters have been determined on the basis of experimental data of early age concrete samples by minimizing the standard deviation of theoretical and empirical values.

The Laplace–Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated.

Relations between the shear and bulk creep kernels of an isotropic linear viscoelastic material in combined stress state and the longitudinal and shear creep kernels constructed from data of creep tests under uniaxial tension and pure torsion are formulated. The constitutive equations of viscoelasticity for the combined stress state are chosen in the form of a superposition of the equation for shear strains and the equation for bulk strains. The hereditary kernels are described by Rabotnov’s fractional-exponential functions. The creep strains of thin-walled pipes under a combination of tension and torsion or tension and internal pressure are calculated

The relationships between the hereditary and creep kernels are established. The hereditary kernels define the scalar properties of isotropic linear viscoelastic materials in a combined stress state. The creep kernels are obtained in uniaxial-tension and pure-torsion tests. The constitutive equations are chosen so as to meet the hypothesis of proportional deviators. The problems of analyzing the creep deformation and stress relaxation of thin-walled tubular specimens under combined tension and torsion are solved and tested experimentally

Delayed fracture of a laminated composite under tensile loads applied at infinity is studied. The composite consists of alternating elastic and aging viscoelastic layers and contains an internal penny-shaped mode I macrocrack located in parallel to the layers. A modified Leonov–Panasyuk–Dugdale crack model and the critical crack-tip opening criterion constitute a fracture model. The subcritical crack growth equations are derived using the Volterra principle and the method of operator continued fractions. The laws governing delayed fracture are studied for a specific composite material

This work proposes an effective algorithm for description of nonlinear deformation of hereditary materials based on Rabotnov’s method of isochronous creep curves. The notions have been introduced for experimental and model rheological parameters and similarity coefficients of isochronous curves. It has been shown how using them, one can find instantaneous strains at various stress levels for description of nonlinear deformation of hereditary materials at creep. Relevant equations have been determined from the nonlinear integral equation of Yu. N. Rabotnov for the application cases of Rabotnov’s fractional exponential kernel and Abel’s kernel for nonlinear deformation of hereditary materials at creep. The improved methods have been given for determination of creep parameters α, ε0, δ, β, and λ. By processing and using test results for material Nylon 6 and glass-reinforced plastic TC 8/3-250, the process has been shown for sequential implementation of the developed methods for description of linear and nonlinear deformation of these materials at creep. From the results of the experimental investigation performed by the authors of this paper, it has been determined that fine-grained, dense asphalt concrete at the temperature of 20 ± 2 °C and stresses up to 0.183 MPa at direct tension is deformed considerably in a nonlinear way. It has been shown in an illustrative way by construction of isochronous creep curves at various load durations and curves of experimental rheological parameter at various stresses. Nonlinear deformation of asphalt concrete at creep is adequately described by the proposed methods.

The problem of determining the parameters of fractional–exponential heredity kernels of nonlinear viscoelastic materials is solved. The methods for determining the parameters that are used in the cubic theory of viscoelasticity and the nonlinear theories based on the conditions of similarity of primary creep curves and isochronous creep diagrams are analyzed. The parameters of fractional–exponential heredity kernels are determined and experimentally validated for the oriented polypropylene, FM3001 and FM10001 nylon fibers, microplastics, TC 8/3-250 glass-reinforced plastic, SWAM glass-reinforced plastic, and contact molding glass-reinforced plastic.