A complete and consistent review is made of the results of studies into the contact interaction of crack edges by methods of fracture mechanics. Also some new results are presented.

Elastodynamic Unilateral Contact Problems with Friction for Bodies with Cracks

We introduce a new methodology to predict the topographic site‐effect amplification. Ground motions obtained from a large database of 3D earthquake simulations show that the curvature of the Earth’s surface, defined as the second spatial derivative of the elevation map, is correlated with the topographic site amplification. The highest correlation between the frequency‐dependent topographic amplification and the topographic curvature is reached when the curvature is smoothed over a characteristic length equal to the S wavelength divided by two (i.e., frequency‐scaled curvature [FSC]). This implies the amplification is caused by topographic features for which horizontal dimensions are similar to half of the S wavelength. The largest ground‐motion variabilities are found at sites located on slopes and on the largest summits, whereas intermediate variabilities occur over narrow ridges and a stable behavior in the bottom valleys. The FSC proxy allows the identification of topographic features with similar characteristic dimensions and probabilistic estimates of amplification values accounting on the variability of ground motions due to source–site interactions. Amplification estimates using the FSC proxy are robust and easily computed from digital elevation maps provided that reasonable values of S‐wave velocities are available in the area of interest.

/pdf/frequency-scaled-curvature-as-a-proxy-for-topographic-site-2nflyqfldi.pdf

Frequency-Scaled Curvature as a Proxy for Topographic Site-Effect Amplification and Ground-Motion Variability

Comprehensive studies in geophysics and seismology have dealt with scattering phenomena in unbounded elastic domains containing fractures or cavities. Other studies have been carried out to investigate scattering by discontinuities located near a free surface. In this last case, the presence of fractures and cavities significantly affects wave motion and, in some cases, large resonant peaks may appear. To study these resonant peaks and describe how they can be affected by the presence of other near-free-surface fractures or cavities we propose the use of the indirect boundary element method to simulate 2D scattering of elastic P and SV waves. The geometries considered are planar and elliptic cracks and cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in both frequency and time domains. In the planar cracks located near the free surface, we validate the method by comparing results with those of a previously published study. We develop several examples of various fractures and cavities to show resonance effects and total scattered displace- ment fields, where one can observe conspicuous peaks in the frequency domain and important wave interactions in the time domain. Finally, we show how our dimen- sionless graphs can be used to deal with materials like clay, sand, or gravel and compare the response with finite-element analysis of elastic beams.

https://msvlab.hre.ntou.edu.tw/BSSA-Rodr-2006.pdf

Multiple Scattering of Elastic Waves by Subsurface Fractures and Cavities

In this review article general results are presented concerning problems in the fracture dynamics of elastic bodies with allowance for unilateral crack edge contact interaction with friction.. A formulation has been made of the elastodynamic contact problem with unilateral restrictions for bodies with cracks under arbitrary dynamic loading . A specific case of liarmonic loading important to these applications has also been considered. The mathematical aspects of the elastodynamics problem for bodies with cracks and with unilateral restrictions in the form of inequalities on the crack edges have been considered in brief. A variational formulation of the problem has been given. Boundary variational inequalities and boundary functionals have been derived. The boundary integral equations (BIE) method in a Laplace transform domain has been used as a solution for the elastodynamic problem for bodies with cracks. Singularities of the kernels in these integral equations have been studied. Two regularization methods of the potentials with \"strongly\" singular kernels have been considered. The first is based on its transformation into integro-differentional equations. The second consists of the utilization of the BIE with hypersingular integrals, which are considered in the sense of a finite part, according to Hadamard. An algorithm for the solution of the elastodynamic unilateral contact problem for bodies with cracks has been elaborated. The algorithm is based on finding a saddle point of a sub-differentional boundary functional. It has been shown that the algorithm may be considered as a compressive operator, which acts in corresponding functional spaces. This means that the algorithm is convergent. Numerical methods have been elaborated for the solution to elastodynamic contact problems with unilateral restrictions and friction for bodies with cracks. The problem has been solved, for plane liarmonic tension-compression wave propagation in a plane with one and two colinear finite length cracks and with allowance for unilateral contact interaction of the crack edges. Dependence of the solution accuracy on the approximation of coordinates and time, and also of numbers of terms in the expansion of the stress-strain state components into Fourier series, has been investigated. Numerical results have also been presented. Quantitative and qualitative effects caused by contact interaction of the crack edges have been investigated. This review contains 170 references.

Fracture Dynamics with Allowance for Crack Edge Contact Interaction

Results of studies into dynamic processes (both stationary and nonstationary) in differently excited shell systems interacting with a liquid are generalized and systematized. Problems related to this division of mechanics are formulated and methods developed for solving them are stated. Typical numerical results are presented.

Dynamics of shell systems interacting with a liquid

Diffraction of elastic waves

The article is devoted to the study of processes of formation of the institution of pedagogical mentoring in the conditions of the modern educational space. The author pays considerable attention to the analysis of mentoring from the position of professional self-determination as one of the important factors for the success of this process at the stage of professional adaptation of a young teacher. The author considers options for reviving the institution of mentoring in Russian schools as an effective way to integrate and socialize a young teacher, to form an understanding in the pedagogical community of the functionality of a mentor, the technology for implementing mentoring, and the interaction between a mentor and a young specialist. The article actualizes the need to develop a system model and apply mentoring technology for the professional development of a young specialist, reveals the main theoretical and methodological approaches to understanding this technology. Analysis of the difficulties faced by young teachers at the stage of entry into the professional activities is presented. Empirical data obtained by the author testify to a number of problems that young specialists face at the stage of entry into pedagogical activity (lack of free time, problems in organizing personal time, difficulties in teaching the subject, communicating with students and their parents). All this, in turn, actualizes the need to revive the institution of mentoring in order to solve a binary problem: help and support for young professionals, as well as reducing the teaching load for experienced teachers with a long teaching experience and school administration, whose mentoring functions are formalized. Along with the growing interest in the quality of training of a young teacher, it gives grounds for concluding that the scientific understanding of this issue is promising. The article draws the main conclusions and proposals for introducing the institution of mentoring into the school education system as part of a pilot approach in the Khabarovsk Territory with the aim of subsequently consolidating and replicating the experience of other interested subjects of the Far-Eastern federal district.

M. A. Cherevko

Papers

Diffraction of elastic waves

Pedagogical mentoring as a factor of professional self-determination of young teachers (regional aspect)