Dr Nikolay Perepelkin

The effective elastic contact modulus and the work of adhesion are crucial material parameters needed for the application of theories of adhesive contact to various problems of modern nanotechnology. It is quite common that these parameters are identified using two different kinds of depth-sensing indentation (DSI) tests; in particular, the elastic characteristics are evaluated using indentation that involves the use of a sharp indenter, whereas the work of adhesion is estimated from a series of the DSI tests in which a spherical indenter is used. It can be argued, however, that the customary approaches have various drawbacks. In 2008, Borodich and Galanov showed that these material properties of primary interest may be identified from a single test using a new approach named the BG (Borodich-Galanov) method. The BG method is based on an inverse analysis of a stable region of the dimensionless force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. The method employs the established theories of adhesive indentation, mainly the JKR theory. The BG method was then extended in 2019 by Perepelkin and Borodich (the eBG method) by introducing new approaches to the processing experimental data and a different objective functional for data fitting. In the present work, some theoretical aspects of the BG and eBG methods are discussed. It is shown that both the BG and eBG methods are simple and robust.

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics. © Published under licence by IOP Publishing Ltd.

Concepts of non-linear normal modes (NNMs) of vibration in conservative and near-conservative systems are considered. Construction of the NNMs and some their applications in applied problems are presented. The non-linear vibro-absorption problem, the cylindrical shell non-linear dynamics, the vehicle suspension non-linear dynamics, and the rotor dynamics are considered.

© 2017, Springer Science+Business Media B.V. Rauscher method becomes the matter of interest because in combination with the method of nonlinear normal vibration modes it allows to calculate steady forced vibrations in the system with multiple degrees of freedom (DOF) via reduction in the number of DOFs. However, modern realizations of that approach have drawbacks such as iterative nature and the need to have initial approximation for the solution. The primary principle of Rauscher method is in obtaining periodic solutions of a non-autonomous system via studying some equivalent autonomous one. In the paper, a new non-iterative variant of Rauscher method is considered. In its current statement, the method can be used in analysis of forced harmonic oscillations in a nonlinear system with one degree of freedom. The primary goals of the study were to find out what kind of equivalent autonomous systems could be built for a given non-autonomous one and how they can be used for the construction of periodic solutions and/or periodic phase plane orbits of the initial system. It is shown that three different types of equivalent autonomous dynamical systems can be built for a given 1-DOF non-autonomous one. The system of 1st type is a fourth-order dynamical system. Technically it can be considered as a 2-DOF system where additional “DOF” is explicitly “responsible” for forced oscillations. The system of 2nd type is a third-order dynamical system. Its periodic orbits are exactly the same as in the initial system. Using the invariant manifold of the system of 1st type, the system of 2nd type can be reduced to the form W(x, x′) = 0 (which is called here the equivalent system of the 3rd type). It is important that the function W(x, x′) can be built a priori. Once W(x, x′) is found: (i) one can obtain different periodical orbits corresponding to forced oscillations in the initial system; (ii) one can estimate amplitudes of vibrations for these regimes; (iii) one can track bifurcations of periodical regimes of the initial system with respect to change in amplitude of external excitation f. As shown in the paper, periodical orbits of the initial non-autonomous system can be obtained via two different approaches: (i) as set of points on phase plane satisfying the condition W(x, x′) = 0 ; (ii) via the application of harmonic balance method to the equivalent system of 1st type using system’s energy level as a continuation parameter. This approach has advantage over application of harmonic balance method to initial system because the latter requires good initial guess for expansion coefficients, while the new approach does not and always starts from zero initial guess.

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius.

© 2018 Elsevier Ltd The depth-sensing indentation (DSI) is currently one of the main experimental techniques for studying elastic properties of materials of small volumes. Usually DSI tests are performed using sharp pyramidal indenters and the load-displacement curves obtained are used for estimations of elastic moduli of materials, while the curve analysis for these estimations is based on the assumptions of the Hertz contact theory of non-adhesive contact. The Borodich–Galanov (BG) method provides an alternative methodology for estimations of the elastic moduli along with estimations of the work of adhesion of the contacting pair in a single experiment using the experimental DSI data for spherical indenters. The method assumes fitting the experimental points of the load-displacement curves using a dimensionless expression of an appropriate theory of adhesive contact. Earlier numerical simulations showed that the BG method was robust. Here first the original BG method is modified and then its accuracy in the estimation of the reduced elastic modulus is directly tested by comparison with the results of conventional tensile tests. The method modification is twofold: (i) a two-stage fitting of the theoretical DSI dependency to the experimental data is used and (ii) a new objective functional is introduced which minimizes the squared norm of difference between the theoretical curve and the one used in preliminary data fitting. The direct experimental validation of accuracy and robustness of the BG method has two independent steps. First the material properties of polyvinyl siloxane (PVS) are determined from a DSI data by means of the modified BG method; and then the obtained results for the reduced elastic modulus are compared with the results of tensile tests on dumbbell specimens made of the same charge of PVS. Comparison of the results of the two experiments showed that the absolute minimum in relative difference between individual identified values of the reduced elastic modulus in the two experiments was 3.80%; the absolute maximum of the same quantity was 27.38%; the relative difference in averaged values of the reduced elastic modulus varied in the range 16.20.. 17.09% depending on particular settings used during preliminary fitting. Hence, the comparison of the results shows that the experimental values of the elastic modulus obtained by the tensile tests are in good agreement with the results of the extended BG method. Our analysis shows that unaccounted factors and phenomena tend to decrease the difference in the results of the two experiments. Thus, the robustness and accuracy of the proposed extension of the BG method has been directly validated.

Classical methods of material testing become extremely complicated or impossible at micro-/nanoscale. At the same time, depth-sensing indentation (DSI) can be applied without much change at various length scales. However, interpretation of the DSI data needs to be done carefully, as length-scale dependent effects, such as adhesion, should be taken into account. This review paper is focused on different DSI approaches and factors that can lead to erroneous results, if conventional DSI methods are used for micro-/nanomechanical testing, or testing soft materials. We also review our recent advances in the development of a method that intrinsically takes adhesion effects in DSI into account: the Borodich-Galanov (BG) method, and its extended variant (eBG). The BG/eBG methods can be considered a framework made of the experimental part (DSI by means of spherical indenters), and the data processing part (data fitting based on the mathematical model of the experiment), with such distinctive features as intrinsic model-based account of adhesion, the ability to simultaneously estimate elastic and adhesive properties of materials, and non-destructive nature.

The new method of the forced resonance vibrations construction in mechanical systems with internal resonance is represented. According to this approach, the generalized theory of non-linear normal vibration modes by Shaw and Pierre, the modified Rauscher method and the harmonic balance method are combined with a new iterative computation procedure. The proposed approach is used in analysis of the single-disk rotor system with the isotropic-elastic shaft and the non-linear supports of Duffing type. Gyroscopic effects, asymmetrical disposition of the disk on the shaft and internal resonance are also taken into account. The NNM approach allows reducing the 8-DOF problem of the rotor dynamics to the 2-DOF non-linear system for each non-linear normal mode. Both the model of massless supports and the model of supports with inertial effects are considered. It is shown that in last case all resonance regimes are separated into two different kinds. First kind corresponds to cyclic symmetric trajectories in a system's configuration space; the second kind corresponds to centrally symmetric ones. Regimes of the first kind can be evaluated by the use of the simplified mathematical model proposed in this work. Simplified model consists only of four generalized coordinates instead of the eight initial ones. © 2013 Elsevier Ltd.

Bioinspired materials that act like living tissues and can repair internal damage by themselves, i.e. self-healing materials, are an active field of research. Here a methodology for experimental testing of self-healing ability of soft polymer materials is described. The methodology is applied to a recently synthesized polyurethane material Smartpol (ADHTECH Smart Polymers & Adhesives S.L., Alicante, Spain). Series of tests showed that the material demonstrated self-healing ability. The tests included the following steps: each Smartpol specimen was cut in halves, then it was put together under compression, and after specified amount of time, it was pulled apart while monitoring the force in contact. The test conditions were intentionally chosen to be non-ideal. These non-idealities simultaneously included: (1) separation time was rather long (minutes and dozens of minutes), (2) there was misalignment of specimen parts when they were put together, (3) contacting surfaces were non-flat, and (4) repeated testing of the same specimens was performed and, therefore, repeated damage was simulated. Despite the above, the recovery of structural integrity (self-healing) of the material was observed which demonstrated the remarkable features of Smartpol. Analysis of the experimental results showed clear correlation between adhesion forces (observed through the values of maximum pull-off force) and the time in contact which is a clear indicator of self-healing ability of material. It is argued that the factors contributing to self-healing of the tested material at macro-scale were high adhesion and strong viscoelasticity. The results of fitting the force relaxation data by means of mathematical model containing multiple exponential terms suggested that the material behaviour may be adequately described by the generalized Maxwell model.

An investigation of transient is important in engineering, in particular, in problem of absorption. Over the past years different new devices have been used for the vibration absorption and for the reduction of the transient response of structures [1–4]. It seems interesting to study nonlinear passive absorbers for this reduction.In presented paper the transient in a system containing a linear oscillator, linearly coupled to an essentially nonlinear attachment with a comparatively small mass, is considered. A damping is taken into account. It is assumed that some initial excitation implies vibrations of the linear oscillator.

The classic Johnson–Kendall–Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres. The advantage of the classical JKR formalism is the use of the principle of superposition of solutions to non-adhesive axisymmetric contact problems. In the recent years, the JKR formalism has been extended to other cases, including problems of contact between an arbitrary-shaped blunt axisymmetric indenter and a linear elastic half-space obeying rotational symmetry of its elastic properties. Here the most general form of the JKR formalism using the minimal number of conditions is studied. The corresponding condition of energy balance is developed. For the axisymmetric case and a convex indenter, the condition is reduced to a set of expressions allowing explicit transformation of force–displacement curves from non-adhesive to corresponding adhesive cases. The implementation of the developed theory is demonstrated by presentation of a two-term asymptotic adhesive solution of the contact between a thin elastic layer and a rigid punch of arbitrary axisymmetric shape. Some aspects of numerical implementation of the theory by means of Finite-Element Method are also discussed. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

To describe properly interactions between contacting solids at micro/nanometre scales, one needs to know both adhesive and mechanical properties of the solids. Borodich and Galanov have introduced an effective method (the BG method) for identifying both characteristics from a single experiment on depth-sensing indentation by a spherical indenter using optimal fitting of the experimental data. Unlike traditional indentation techniques involving sharp indenters, the Borodich-Galanov methodology intrinsically takes adhesion into account. It is essentially a non-destructive approach. These features extend the scope of the method to important applications beyond the capabilities of conventional indentation. The scope of the original BG method was limited to the classic JKR and DMT theories. Recently, this restriction has been overcome by introducing the extended BG (eBG) method, where a new objective functional based on the concept of orthogonal distance curve fitting has been introduced. In the present work, questions related to theoretical development of the eBG method are discussed. Using the data for elastic bulk samples, it is shown that the eBG method is at least as good as the original BG method. It is shown that the eBG can be applied to adhesive indentation of coated, multilayered, functionally graded media.