K. B. Ustinov

On the Modeling of Surface and Interface Elastic Effects in Case of Eigenstrains

The constitutive equations of interface elasticity in case of eigenstrains are obtained in terms of interface (surface) values defined as integrals of the excesses of the corresponding volumetric values over the normal to the interface. The equations are consistently linearized, which corresponds to the case of both elastic strains and eigenstrains being small. It is shown that the obtained equations possess more general form then Shuttleworth equations. The obtained type of equation was confirmed by considered example: an interface formed by a thin layer of constant properties. It was also shown that the type of energetic restrictions on the surface elastic constants may depend essentially on the definition of the position of the surfaces.

Strength and Fracture Toughness of Polyurethane Elastomers Modified with Carbon Nanotubes

Very small additions of single-wall carbon nanotubes produce an anomalous change in the mechanical properties of a cross-linked polyurethane-amide-urea elastomer containing 10% of polyamide-6: its elastic modulus and ultimate stress reveal local maxima at a nanofiller content of hundredths and thousandths of a percent. Previously, the behavior of the elastic modulus was simulated reasoning from the formation of an intermediate phase layer in the elastomer at particle contact boundaries. Here, on the same basis, we simulate the behavior of its strength as a function of nanotube concentration and consider crack models accounting for the influence of nanotubes on the crack tip zone and fracture toughness.

A mechanical model of the contact interaction between the atomic force microscope measuring element and a surface under investigation

A hierarchic set of gradually complicated models is suggested. The models describe the contact condition of the mechanical interaction between the atomic force microscope (AFM) probe and the investigated surface while allowing for various factors. A variant of the AFM probe-surface mechanical interaction model is developed which takes into account the simultaneous effect of the probe geometry and the elastic deformations of the AFM cantilever that take place when there is a small or moderate curvature of surfaces under study. A variant of the model of interaction between the AFM probe and the surface of the investigated specimen is discussed, taking into consideration the simultaneous effect of the probe geometry and elastic deformations of the AFM cantilever and the probe contact with the surface under study within the framework of Derjaguin-Muller-Toropov model. Algorithms to determine the AFM probe position are created to optimize computations.

Modeling of mechanical effects related to operation of atomic force microscopes

One of the key directions of the modern development of nanotechnologies is related to the “bottom-up” technology involving the construction of multiscale structures composed of basic nano-and subnatoelements like atoms, molecules, and biocells. Such technology can be implemented and developed due to the appearance and perfection of scanning probe microscopy and, primarily, its particular type, viz. atomic force microscopy. We propose an analytic review of various working modes of atomic force microscopes (AFMs). For the dynamic mode, the relation between the description of flexural and torsional vibrations of the AFM cantilever in a simplified oscillator model and the description based on the beam model in the continuum mechanics is discussed in detail. For the static working mode of the AFM, a detailed analysis of features associated with clamping of the cantilever and its nonuniformity is carried out and inaccuracies introduced by the disregard of the resilience of clamping and poor control of the variation of thickness along the cantilever during its operation and preparation are estimated. A preliminary version of the algorithm that can be applied for numerical modelling of the contact interaction between the AFM working element and the surface being investigated in constructing a virtual AFM is described in the concluding part of the article.

Fracture Model of Anisotropic Rocks under Complex Loading

The paper proposes a deformation and fracture model for anisotropic stratified rocks and presents theoretical and experimental data on how the rock strength and fracture geometry are influenced by principal stresses and their orientation to bedding planes. Two possible mechanisms are considered for rock fracture under true triaxial load: along bedding planes of weakness and along planes in which Mohr-Coulomb stresses reach a critical combination with cohesion coefficients and internal friction angles typical of the rock. The transition of rocks to inelastic deformation is described in the context of two criteria of which one accounts for the above fracture mechanisms and the other, being a semi-empirical analogue of the Hill yield criterion, accounts for the effect of normal stress. The experimental data presented are for the strain and strength properties of rocks sampled from the Fedorovskoye and Talakanskoye oil and gas fields and tested on an original loading system for true triaxial compression with lateral pressure (similar to the Karman scheme) and for generalized shear (three unequal and nonmonotonic principal stresses). The experimental and theoretical results, including total stress-strain curves, are in good qualitative agreement and demonstrate the possibility to evaluate the parameters entered in the model from tests of particular rocks.

Deformation of Spherical Inclusion in an Elastic Body with Account for Influence of Interface Considered as Infinitesimal Layer with Abnormal Properties

The model for surface (interface) elasticity accounting for the influence of bulk and interface eigenstrains as well as the influence of not only in-plane but also out-of-plane stresses on the surface deformation, was proposed by the authors. Definition of all interface values as integrals of the excesses of the corresponding bulk values over the normal to the interface, and procedure of energy variation resulted in constitutive equations for the interface of more general type then the Shuttleworth equations (Shuttleworth, 1950). Here the model is added with the boundary conditions at the interface. The model is used to describe deformation of a spherical inclusion in elastic media.

Modeling of Deformation and Filtration Processes Near Wells with Emphasis of their Coupling and Effects Caused by Anisotropy

The approach to modeling geomechanical processes in the well vicinity including mathematical modelling of deformation, fracture and filtration as well as experimental determining the parameters involved, under conditions, corresponding to the real in situ ones is presented. The approach involves three stages: (i) choosing the mechanical model and its adopting to the considered problem; (ii) determining the model parameters by using the direct experiments; (iii) mathematical modeling of deformation, fracture and filtration processes in question.

On surface elasticity theory for plane interfaces

A closed system of surface elasticity equations was derived in terms of surface quantities defined as integrals of respective excess bulk quantities normal to the interface. The equations were consistently linearized for the case of small strains. It is shown that these equations are more general than the Shuttleworth equations. Equations of this type were also derived for the particular case of an interface formed by a thin layer with constant properties. The derived equations were used to consider bending of a plate under pressure applied to both sides.

The Mechanical Modeling of Oxygen-Containing Precipitates in Silicon Wafers on Different Stages of the Getter Formation Process

The behavior of the oxygen-containing precipitate in silicon wafer on different stages of the getter formation process is considered from the mechanical point of view. The precipitate is modeled as a spheroidal inclusion undergoing inelastic eigenstrains in an anisotropic silicon matrix. The stress-strain state in the precipitate and matrix is calculated within the framework of the model. An energetic criterion of breaking the spherical shape by the coherent precipitates is obtained and analyzed. Criteria of the formation and onset of motion of the dislocation loops in the vicinity of the precipitate are also proposed. The obtained results are compared with the available experimental data.