We consider the transmission problem of couple stress elasticity in a fixed domain \(\Omega _{-}\) juxtaposed with a thin layer \(\Omega _{+}^{\delta }\). Our aim is to model the effect of the thin layer \(\Omega _{+}^{\delta }\) on the fixed domain \(\Omega _{-}\) by an impedance boundary condition. For that we use the techniques of asymptotic expansion to approximate the transmission problem by an impedance problem set in the fixed domain \(\Omega _{-}\), and we prove an error estimate between the solution of the transmission problem in \(\Omega _{-}\) and the solution of the approximate impedance problem.

中文翻译：

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耦合应力弹性中平面薄层的近似阻抗

我们考虑固定域\(\Omega _{-}\)与薄层\(\Omega _{+}^{\delta }\)并列的耦合应力弹性的传输问题。我们的目标是通过阻抗边界条件模拟薄层\(\Omega _{+}^{\delta }\)对固定域\(\Omega _{-}\)的影响。为此，我们使用渐近展开技术通过在固定域\(\Omega _{-}\) 中设置的阻抗问题来近似传输问题，并且我们证明了\( \Omega _{-}\)和近似阻抗问题的解。