An axisymmetric problem for a penny-shaped crack under the influence of the Steigmann–Ogden surface energy

A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integro-differential equations. The numerical solution to this system can be obtained by expanding the unknown functions into the Fourier–Bessel series. Then the approximations of the unknown functions can be obtained by solving a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. Parametric studies of the dependence of the solutions on the mechanical and the geometric parameters of the system are undertaken. It is shown that the surface parameters have a significant influence on the behaviour of the material system. In particular, the presence of surface energy leads to the size-dependency of the solutions and smoother behaviour of the solutions near the tip of the crack.

Granular impacts: how far the Boussinesq model can go?

A key problem on granular impacts deals with the determination of the mechanical response of the grains due to the impact of the intruder. This topic has been poorly addressed in the literature so far, a gap to which this study aims to contribute by measuring the pressure distribution at the bottom of a loose and dry sandy bed, impacted by a heavy sphere of fixed diameter. Exploring different bed thicknesses and intruder’s dropping height, we have found that the structure of this distribution is very similar to the Boussinesq model, initially proposed for a static point-force acting over an isotropic-elastic medium. This surprising result opens up many challenging questions that could help validate or refute this model in other scenarios.

To the study of the natural seismic tension of geological massifs

Методом блочного элемента проведено исследование блочной структуры, моделирующей геологический массив. Состояние геологической среды описывается уравнениями движениями для однородной, изотропной упругой среды в форме Ляме. Выписаны функциональные и псевдодифференциальные уравнения, получены интегральные представления блочного элемента. Установлены основные тенденции изменения контактных напряжений в зависимости от значений механических характеристик материала блоков и геометрических параметров структуры. The block structure method is used to study the block structure modeling a geological massif. The state of the geological medium is described by equations of motion for a homogeneous, isotropic elastic medium in the form of a Lame. Functional and pseudo-differential equations are written out, and integral representations of the block element are obtained. The main tendencies of contact stress variation are established depending on the values of the mechanical characteristics of the material of the blocks and the geometric parameters of the structure.

Analysis and Assessment of Seismic Hazard for the Azov-Black Sea Recreation Area

One of the geological structures accountable for the implementation of seismic potential of the region is the largest vertical faults in the Earth’s interior, where earthquake foci are usually located. This article is aimed at developing a better method for calculation of stresses and strains that occur in such seismogenic areas. According to the results of the analysis of data collected during the expeditionary work, the geophysical medium is modeled by a block structure in the form of a half-space with a cut rectangular parallelepiped, which is divided into five block elements. The state of material in the geological medium is described in each block by motion equations for a homogeneous, isotropic elastic medium in the Lamé form. Following the block element method, the algorithm of the differential factorization method is implemented in each block. Based on the numerical analysis results, the main trends in contact stresses and dynamics of displacement amplitudes were determined depending on the mechanical property values of the block material and the geometric parameters of the structure.

The effect of two-temperature on thermoelastic medium with diffusion due to three phase-lag model

This paper is concerned on the distribution of a homogeneous isotropic elastic medium with diffusion under the effect of Three-phase-lag model. Normal mode analysis is used to express the exact expressions for temperature, displacements and stresses functions. Comparisons are made in the absence and presence of diffusion with some theories like Three-phase-lag and GNIII.

Eigenvalue Approach in a Generalized Thermal Shock Problem for a Transversely Isotropic Half-Space

In the present work, the investigating of the disturbances in a homogeneous, transversely isotropic elastic medium with generalized thermoelastic theory has been concerned. The formulation is applied to generalized thermoelasticity based on three different theories. Laplace and Fourier transforms are used to solve the problem analytically. The essential equations have been written as a vector-matrix differential equation in the Laplace transform domain, then solved by an eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The result is used to solve a specific two-dimensional problem. The technique is illustrated by means of several numerical experiments performed. The results were verified numerically and are plotted.