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<p>The paper investigates a&#xa0;boundary value problem describing an elastic body with a&#xa0;crack having an antiplane shear behaviour in the frame of gradient elasticity theory. On the crack faces, boundary conditions have the form of inequalities. Due to the Neumann type conditions at the external boundary, the problem under consideration belongs to the class of non-coercive ones with unknown contact set. Necessary and sufficient conditions for the external forces providing an existence of solutions are found. An inverse problem for finding the displacement field and a&#xa0;strain gradient coefficient is analyzed assuming that the displacement is known at a&#xa0;given point.</p>

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Nonlinear boundary problem in strain gradient elasticity for a body with a crack

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • A. M. Khludnev

摘要

The paper investigates a boundary value problem describing an elastic body with a crack having an antiplane shear behaviour in the frame of gradient elasticity theory. On the crack faces, boundary conditions have the form of inequalities. Due to the Neumann type conditions at the external boundary, the problem under consideration belongs to the class of non-coercive ones with unknown contact set. Necessary and sufficient conditions for the external forces providing an existence of solutions are found. An inverse problem for finding the displacement field and a strain gradient coefficient is analyzed assuming that the displacement is known at a given point.