Interfacial plane crack under time-harmonic loading

Vasyl Menshykov, Oleksandr Menshykov

Research output: Contribution to conferenceAbstractpeer-review


Nowadays, the wide use of high-strength materials make it possible to reduce considerably the weight of designed constructions. It is a common knowledge that all modern structural materials contain different defects (cracks, shells, etc.). Such defects appear due to the process of material manufacture, creation of elements of the construction and its further exploitation. If the stress-strain relationship was determined regardless of the possibility for cracks to occur and grow, then it might result in sudden collapse of structures under considerably low stresses. Therefore, it is extremely important to study the load capacity of structural materials with existing and incipient cracks under dynamic loading.

Moreover, the low amplitude waves are almost ideally suited for application to non-destructive testing and geophysical exploration, since they may propagate relatively large distances inside most solid materials without causing any permanent change in the material as a result of their passage. These waves are usually used in order to measure the thickness of the solid stratum, to locate flaws, to measure the size and shape of different inclusions. When an elastic wave propagating inside a solid body encounters an interface separating two different strata, then reflection and refraction accompanied by mode conversion takes place. The presence of different dislocations, in general, complicates the distribution of wave characteristics considerably, and the problem has not been solved analytically. That is why the numerical modelling of the stress-strain state near dislocations under low amplitude waves should be an indispensable stage in solving of mechanics problems for cracked solids.

The present work aimed at solving of a three-dimensional fracture dynamics problem for a stratified medium with a plane interfacial crack under time-harmonic loading. The reflection and the refraction of the wave on the interface between strata stratum were studied. In order to solve the problem numerically the method of boundary integral equations was used. The distribution of the displacement discontinuity vector on opposite faces of the crack was investigated for different materials and different wave numbers.
Original languageEnglish
Number of pages1
Publication statusPublished - Jun 2005
EventXXXIII Summer School – Conference “Advanced Problems in Mechanics” - St. Petersburg (Repino), Russian Federation
Duration: 28 Jun 20055 Jul 2005
Conference number: 33


ConferenceXXXIII Summer School – Conference “Advanced Problems in Mechanics”
Abbreviated titleAPM2005
Country/TerritoryRussian Federation
CitySt. Petersburg (Repino)
Internet address


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