In this paper, we extend the asymptotic analysis in (Licht et al. in J. Math. Pures Appl. 99:685–703, 2013 ) performed, in the framework of small strains, on a structure consisting of two linearly elastic bodies connected by a thin soft nonlinear Kelvin–Voigt viscoelastic adhesive layer to the case in which the total mass of the layer remains strictly positive as its thickness tends to zero. We obtain convergence results by means of a nonlinear version of Trotter’s theory of approximation of semigroups acting on variable Hilbert spaces. Differently from the limit models derived in (Licht et al. in J. Math. Pures Appl. 99:685–703, 2013 ), in the present analysis the dynamic effects on the surface to which the layer shrinks do not disappear. Thus, the limiting behavior of the remaining bodies is described not only in terms of their displacements on the contact surface, but also by an additional variable that keeps track of the dynamics in the adhesive layer.

中文翻译：

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由重薄软粘弹性层连接的两个线弹性体的动力学

在本文中，我们扩展了 (Licht et al. in J. Math. Pures Appl. 99:685–703, 2013 ) 中的渐近分析，在小应变的框架内，在由两个连接的线弹性体组成的结构上执行通过薄的软非线性 Kelvin-Voigt 粘弹性粘合剂层，在该层的总质量保持严格为正的情况下，其厚度趋于零。我们通过非线性版本的 Trotter 的半群逼近理论来获得收敛结果，该理论作用于可变 Hilbert 空间。与 (Licht et al. in J. Math. Pures Appl. 99:685–703, 2013 ) 中导出的极限模型不同，在本分析中，层收缩到的表面上的动态效应不会消失。因此，