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Abstract <p>A moving edge dislocation in an infinite elastic medium is considered, simulating a stationary shear rupture in the Earth’s crust at a depth of seismic activity, which increases as quickly as transverse waves travel. Based on the expansion of the vector displacement field into the sum of the potential and solenoidal fields, an exact singular solution to the problem in a plane formulation is constructed in the form of convergent series. An approximate solution in the form of series segments is analyzed in the Matlab computer system using numerical differentiation and integration procedures. It is shown that the invariant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10808_2025_1530_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(J\)</EquationSource> <!--JAMT2501013Sadovskii-m1--> </InlineEquation>-integral, whose value is equal to the driving force of the dislocation (the energy spent on the movement of the dislocation by a unit distance), is independent on its velocity.</p>

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Problem of a Moving Edge Dislocation

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • V. M. Sadovskii,
  • O. V. Sadovskaya

摘要

Abstract

A moving edge dislocation in an infinite elastic medium is considered, simulating a stationary shear rupture in the Earth’s crust at a depth of seismic activity, which increases as quickly as transverse waves travel. Based on the expansion of the vector displacement field into the sum of the potential and solenoidal fields, an exact singular solution to the problem in a plane formulation is constructed in the form of convergent series. An approximate solution in the form of series segments is analyzed in the Matlab computer system using numerical differentiation and integration procedures. It is shown that the invariant \(J\) -integral, whose value is equal to the driving force of the dislocation (the energy spent on the movement of the dislocation by a unit distance), is independent on its velocity.