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<p>This paper addresses the problem of a&#xa0;laminated structure consisting of an adhesive layer and two adherents within the framework of simplified strain gradient elasticity (also known as one-parameter gradient elasticity) under antiplane shear. The deformations of both the adhesive layer and the adherents are described by this theory. The shear modulus, scale parameter, and width of the adhesive layer depend on a&#xa0;small parameter&#xa0;<i>δ</i>: the width is proportional to&#xa0;<i>δ</i>, the shear modulus is proportional to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta^{-1}\)</EquationSource> </InlineEquation>, and the scale parameter scales as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\delta^p\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p = 0, 1, 2\)</EquationSource> </InlineEquation>. This scaling implies that the adhesive layer behaves as a&#xa0;thin elastic inclusion. By passing to the limit as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta\to0\)</EquationSource> </InlineEquation>, we derive three new types of limit models featuring imperfect interface conditions that effectively behave as rod-type elastic inclusions, depending on the value of the exponent&#xa0;<i>p</i>.</p>

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Thin elastic inclusion-type imperfect interface conditions in simplified strain gradient elasticity under anti-plane shear

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Evgeny Rudoy,
  • Sergey Sazhenkov

摘要

This paper addresses the problem of a laminated structure consisting of an adhesive layer and two adherents within the framework of simplified strain gradient elasticity (also known as one-parameter gradient elasticity) under antiplane shear. The deformations of both the adhesive layer and the adherents are described by this theory. The shear modulus, scale parameter, and width of the adhesive layer depend on a small parameter δ: the width is proportional to δ, the shear modulus is proportional to \(\delta^{-1}\) , and the scale parameter scales as \(\delta^p\) with \(p = 0, 1, 2\) . This scaling implies that the adhesive layer behaves as a thin elastic inclusion. By passing to the limit as \(\delta\to0\) , we derive three new types of limit models featuring imperfect interface conditions that effectively behave as rod-type elastic inclusions, depending on the value of the exponent p.