We study the highly complex wave transmission at the interface between a two-dimensional (2D) hexagonally structured granular medium and a linearly elastic thin plate; we refer to this system as the “granular-solid interface”. By applying an impulsive excitation at the free end of the granular medium we study the nonlinear acoustics at the interface. A computational model is developed, where the thin plate under the plane-stress assumption is discretized by finite-elements (FEs), whereas the granular medium by discrete-elements (DEs). Apart from the highly discontinuous Hertzian granule-to-granule and granule-to-plate interactions, we also take into account rotational and frictional effects in the granules; these effects render the acoustics of the granular-solid interface strongly nonlinear and highly discontinuous. The interaction forces coupling the granular medium to the plate are computed by means of an algorithm of interrelated iterations and interpolations at successive time steps. Since frictional effects may yield numerical instabilities, our approach incorporates the continuous “Coulomb–tanh” friction model, whose efficacy is verified through convergence studies. By formulating appropriate theoretically predicted convergence criteria, we show that the stability of the algorithm depends on the time step, the mesh size of the FE model, and the frictional model parameters. Accordingly, convergence is ensured by introducing a self-adaptive time step scheme, which is informed by theoretical convergence criteria. An application of the algorithm for a specific granular-solid interface demonstrates its validity, accuracy and robustness. Wave transmission through the discrete–continuum interface is drastically delayed by the granular medium, which, inflicts significant “softening” to the nonlinear acoustics. Moreover, there is strong nonlinear wave dispersion and energy localization in the granular medium, resulting in highly reduced wave transmission to the plate. Moreover, these nonlinear acoustical features are tunable with the applied shock (or input energy). The model and results presented in this work apply to a broad class of nonlinear discrete–continuum interfaces, with broad applications, e.g., shock/blast mitigation, granular containers with flexible boundaries and acoustic non-reciprocity.

我们研究了二维（2D）六边形结构的粒状介质和线性弹性薄板之间的界面处的高度复杂的波传输；我们将此系统称为“颗粒-固体界面”。通过在粒状介质的自由端施加脉冲激励，我们研究了界面处的非线性声学。建立了计算模型，其中在平面应力假设下的薄板通过有限元（FE）离散化，而颗粒介质通过离散元（DEs）离散化。除了高度不连续的Hertzian颗粒与颗粒之间以及颗粒与板之间的相互作用外，我们还考虑了颗粒中的旋转和摩擦效应。这些效果使颗粒-固体界面的声学特性强烈非线性且高度不连续。通过将相关的迭代和插值算法在连续的时间步长进行计算，将颗粒状介质耦合到板上的相互作用力得以计算。由于摩擦效应可能会产生数值不稳定性，因此我们的方法采用了连续的“库仑-tanh”摩擦模型，该模型的有效性已通过收敛研究得到了验证。通过制定适当的理论上预测的收敛准则，我们表明算法的稳定性取决于时间步长，有限元模型的网格大小以及摩擦模型参数。因此，通过引入自适应时间步长方案可以确保收敛，该时间步长方案以理论上的收敛标准为依据。该算法在特定的颗粒-固体界面上的应用证明了其有效性，准确性和鲁棒性。通过离散-连续谱接口的波传输被颗粒状介质极大地延迟了，这对非线性声学造成了很大的“软化”。此外，在粒状介质中存在很强的非线性波分散和能量局限性，从而大大降低了波向板的传输。此外，这些非线性声学特征可通过施加的冲击（或输入能量）进行调整。这项工作中提出的模型和结果适用于一类广泛的非线性离散连续体接口，具有广泛的应用，例如，减震/爆炸，具有灵活边界的粒状容器和声学互不干扰。在粒状介质中存在强烈的非线性波散射和能量局限性，从而大大降低了波向板的传输。此外，这些非线性声学特征可通过施加的冲击（或输入能量）进行调整。本工作中介绍的模型和结果适用于一类广泛的非线性离散连续体接口，具有广泛的应用，例如，减震/爆炸，具有灵活边界的粒状容器和声学互不干扰。在粒状介质中存在强烈的非线性波散射和能量局限性，从而大大降低了波向板的传输。此外，这些非线性声学特征可通过施加的冲击（或输入能量）进行调整。这项工作中提出的模型和结果适用于一类广泛的非线性离散连续体接口，具有广泛的应用，例如，减震/爆炸，具有灵活边界的粒状容器和声学互不干扰。