Том 19, № 3 (2016)

The paper analyzes Poynting’s effect for chiral cylindrically anisotropic nano/microtubes of cubic, tetragonal and orthorhombic crystals. It is shown based on the solution of a problem on longitudinal tension and torsion of such tubes that there is a linear direct Poynting’s effect of tension of a tube in torsion and a linear reverse Poynting’s effect of torsion of a tube in tension. Vor nano/microtubes of cubic six-constant tetragonal and orthorhombic crystals both these effects disappear at a zero chiral angle and their dependence on the chiral angle is odd. Vor nano/microtubes of seven-constant tetragonal crystals both the effects are present at a zero chiral angle but disappear at certain nonzero values of the chiral angle.

The goal of this study is to construct simple electromechanical models of nanoresonators as mass detectors. A major obstacle in the achievement of sufficient measurement accuracy for the resonant frequency associated with the adsorption of additional mass onto the graphene layer is a low quality factor of the oscillatory system containing the graphene layer. A graphene resonator can be considered as an elastic system with distributed parameters. The application of the Galerkin method to study nearly resonant vibrational modes reduces the problem to considering an oscillatory system with a few degrees of freedom with pronounced nonlinear properties. These properties are, first of all, due to the nonlinear dependence of the forces produced by the electric field on the graphene deflection and, second, due to the nonlinear dependence of the graphene layer tension on its deflection. Taking into account the nonlinear properties leads to the appearance of characteristic drops in the resonance curve which allow for a more accurate resonant frequency measurement. Resonance curves with such characteristic drops can be obtained using a demonstration experimental macromodel of the resonator. Two absolutely new layouts are proposed, such as a differential resonator and resonator with parametric excitation. The oscillations excited in the differential resonator that contains two graphene layers resemble beats. In this case, small changes in the mass of the main layer correspond to significant changes in the frequency of the envelope. This effect is illustrated by oscillograms obtained for an experimental macromodel of the differential resonator. The parametric resonator has one graphene layer between two conducting surfaces. Parametric excitation of steady-state high amplitude oscillations is possible in this resonator only in a narrow frequency band close to the eigenfrequency. The band width reduces with a decrease in the quality factor of the oscillatory system. The latter fact can be useful for the improvement of eigenfrequency measurement accuracy at a low quality factor of the oscillatory system.

The paper discusses nonlocal elasticity theories among which are models of media with defect fields, gradient elasticity theories, and hybrid nonlocal elasticity theories. Gradient theories are analyzed, and their correctness properties are examined. Applied theories that satisfy the correctness conditions are developed, and known applied gradient theories are verified for the correctness properties. A new nonlocal generalized theory has been developed for which the operator of balance equations is represented as the product of the equilibrium operator of classical elasticity theory and the Helmholtz operator. It is shown that this theory is one-parameter and is the only representative of hybrid models constructed by a complete system of equations for forces and moments. Unlike classical elasticity that is free from scale parameters characterizing the internal material structure, nonlocal elasticity theories naturally incorporate these parameters. That is why they are suitable for the modeling of scale effects and find application in the solution of numerous applied problems for heterogeneous structures with developed phase interfaces where the degree of influence of scale effects depends on the density of phase boundaries. Nonlocal continuum models are especially attractive for modeling the properties of various micro/nanostructures, elastic properties of composites and structured materials with submicron- and nanosized internal structures in which effective properties are to a great extent defined by the scale effects (short-range interaction effects of cohesion and adhesion). Generalized elasticity theories even for isotropic materials contain many additional physical constants that are difficult or impossible to determine experimentally. Applied models with a small number of additional physical parameters are therefore of great interest. However, the reduction of nonlocal theories aimed at reducing the number of additional parameters is a nontrivial task and may lead to incorrect theories. The goal of this paper is to study the symmetry properties in gradient theories, to analyze the correctness of gradient theories, and to develop applied one-parameter elasticity theories.

A model of contact fatigue damage of a coated body in high-cycle friction performed using a periodic system of indenters has been proposed. The influence of wear of non-fatigue origin on damage accumulation in the coating and substrate is studied. It is shown that the rate of damage accumulation in the coating decreases but remains unchanged or increases at the coating-substrate interface. Comparison of results for a constant and stochastically time-varying pressure distribution shows that variable loading increases the number of detachments of finite-thickness layers and inhibits contact fatigue damage accumulation at the interface.

The paper considers scaling regularities in the deformation and failure of condensed matter (solids and liquids) as effects of a special type of critical phenomena—structural scaling transitions in mesodefect ensembles— and associated structural relaxation mechanisms. The scaling regularities in nonequilibrium processes of plasticity, failure, and turbulence are analyzed with the use of self-similar intermediate asymptotic solutions describing the collective behavior of mesodefects. The predicted role of defect modes in the self-similar response of condensed media is confirmed by original experiments on dynamic, fatigue, and shock loading over a wide range of load intensities.

The well-known round-tip V-notched Brazilian disk specimen is utilized for conducting mixed mode I/II fracture tests on PMMA under negative mode I conditions for different notch angles and various notch radii with the aim to measure experimentally the fracture load and the fracture initiation angle. It is shown by the finite element analysis that although the notch is under negative mode I loading, one side of the notch border still experiences tensile tangential stresses suggesting that fracture would take place from the same side of notch border. Experimental observations also indicated that fracture occurs from the tensile side of the notch border confirming the finite element results. The experimental results are then theoretically estimated by means of two stress-based brittle fracture criteria, namely the round-tip V-notch maximum tangential stress and the mean-stress criteria. It is shown that both criteria provide very good predictions to the experimental results obtained under negative mode I conditions.