Igor Guz

MIXED PLANE PROBLEMS IN LINEARIZED SOLID MECHANICS: EXACT SOLUTIONS

The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann–Hilbert methods and Keldysh–Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin

Comparing the Evolution Characteristics of Waves in Nonlinearly Elastic Micro- and Nanocomposites with Carbon Fillers

A method is proposed for studying the evolution of plane waves in micro- and nanocomposite materials. This method permits comparing the evolutions of harmonic waves and produces results that are in agreement with data obtained earlier and with the metaphysical reasoning on the nanomechanics of composite materials

Predicting the properties of micro- and nanocomposites: from the microwhiskers to the bristled nano-centipedes

The paper draws on the similarities between the well-known process of whiskerization of microfibres and the recent idea of bristled nanowires. The new method for evaluation of the effective elastic properties of such materials is suggested based on the model of four-component composition. This model assumes the transverse isotropy of continuum and predicts five elastic moduli and density as independent effective constants. An example of calculation of the constants for the particular materials is given. It shows the significant increase in the shear strength of composites with whiskerized or bristled fibres.

Boundary integral equations in elastodynamics of interface cracks

The paper concerns the validation of a method for solving elastodynamics problems for cracked solids. The proposed method is based on the application of boundary integral equations. The problem of an interface penny-shaped crack between two dissimilar elastic half-spaces under harmonic loading is considered as an example.

Boundary integral equations for an interface linear crack under harmonic loading

The present study is devoted to application of boundary integral equations to the problem of a linear crack located on the bimaterial interface under time-harmonic loading. Using the Somigliana dynamic identity the system of boundary integral equations for displacements and tractions at the interface is derived. For the numerical solution the collocation method with piecewise constant approximation on each linear continuous boundary elements is used. The distributions of the displacements are computed for different values of the frequency of the incident tension-compression wave. Results are compared with static ones.

ON PUBLICATIONS ON THE BRITTLE FRACTURE MECHANICS OF PRESTRESSED MATERIALS

The paper analyzes new publications on the brittle fracture mechanics of prestressed materials. It is found out that new scientific results published in the International Journal of Solids and Structures in 2002 are a particular case of the results obtained at the Institute of Mechanics 20 years ago

Use of a Functionally Graded Interlayer to Improve Bonding in Coated Plates

Coatings play an important role in a variety of engineering applications, protecting metallic or ceramic substrates against oxidation, heat penetration, wear and corrosion. Conventional coatings, which usually consist of one or two homogeneous layers deposited on a substrate, are susceptible to cracking and debonding due to the mismatch of thermomechanical properties between the coating and the substrate. To increase resistance of coatings to functional failure, the concept of a functionally graded material is being actively explored in coating design. One of the possible ways to eliminate the mismatch of material parameters between the coating and the substrate is to introduce a functionally graded interlayer between the substrate and the top coat. This paper investigates elastic deformation of coated plates with and without a functionally graded interlayer in the context of three-dimensional elasticity, assuming the Youngs modulus of the interlayer varies exponentially through the thickness. It is shown that the use of the functionally graded interlayer in plates subjected to transverse loading eliminates discontinuity of the in-plane normal stress across interfaces without increasing the stress magnitude at the top surface of the coating.

Vibration analysis of thin-wall structures containing piezoactive layers

A coupled dynamic problem of electro-mechanics for a layered beam is formulated based on the Kirchhoff-Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the single frequency approximation and the concept of complex moduli. As an example, the problem of forced vibration of a three-layer sandwich beam (aluminium alloy core covered with piezoelectric layers) with hinged ends is solved in order to investigate the accuracy and applicability of the approximate monoharmonic approach. Different aspects of the beam response to the mechanical and electric excitation are studied.

Influence of the Crack Widening on the Transverse Cracking in Lamellar Metal-Ceramic Composites

Stress field in the ceramic layer containing multiple transverse cracks is determined using a modified 2-D shear lag approach and a finite element method.

Internal instability as a possible failure mechanism for layered composites

This paper revisits a three-dimensional analytical approach to study internal instability in layered composites, when the behaviour of each component of the material is described by the three-dimensional equations of solid mechanics. It shows the development of a unified computational procedure for numerical realization of the three-dimensional analytical method as applied to various constitutive equations of the layers and fibres, and different loading schemes (uniaxial or biaxial loading). The paper also contains many examples of calculation of critical controlled parameters for particular composites as well as analysis of different buckling modes. The results of this method can be used as a benchmark for simplified models. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.