The existence of nonlinearity within materials manifests richer wave propagation compared to their linear counterpart in the form of amplitude-dependent material response and energy transfer between frequencies. While these properties have been extensively studied in the case of continuous and discrete nonlinear phononic materials (PMs), individually, the behavior of continuum PMs with discrete nonlinearities, which could open new opportunities for wave propagation control via discrete–continuum coupling, is relatively unexplored. In this article, we investigate nonlinear wave propagation through one-dimensional continuum PMs with periodic contacts. Specifically, the periodicity is in the form of pre-compressed rough contacts resulting in nonlinearly coupled linear finite thickness elastic layers. We analyze the system using full-scale time-domain finite element simulations by treating the contacts as spring-equivalent nonlinear thin elastic layers. The model considers a power-law pressure-gap relationship at the rough contacts. The evolution of propagating nonlinear waves within the weakly nonlinear regime is illustrated, emphasizing the generation of zero (DC), self-demodulated low, and second harmonic frequencies for excitation in different zones of the dispersion relation. The continuum between discrete contact nonlinearities exhibits local DC reduction and second harmonic increment, not observed in discrete PMs such as granular phononic crystals. The intertwined effects of nonlinearity, periodicity, and finiteness on nonlinear wave propagation are also explored, which results in maximum DC amplitude at the finite boundaries of the PMs and mode-based second harmonic characteristics. Finally, we demonstrate the flexibility of the proposed nonlinear PMs by characterizing the dependence of nonlinear wave propagation on different arrangements of embedded contacts. The concept of discretely embedding nonlinear interfaces, such as rough contacts, within an elastic continuum, opens opportunities to control the global nonlinear response of the PMs through local microstructural nonlinearities.

与线性对应物相比，材料中非线性的存在表现出更丰富的波传播，其形式为振幅相关的材料响应和频率之间的能量转移。虽然这些特性已经在连续和离散非线性声子材料 (PM) 的情况下进行了广泛研究，但单独而言，具有离散非线性的连续 PM 的行为可能为通过离散-连续耦合控制波传播开辟新的机会，但相对未开发. 在本文中，我们通过具有周期性接触的一维连续介质研究非线性波传播。具体而言，周期性采用预压缩粗糙接触的形式，导致非线性耦合的线性有限厚度弹性层。我们通过将接触视为弹簧等效非线性薄弹性层，使用全尺寸时域有限元模拟来分析系统。该模型考虑了粗糙接触处的幂律压力间隙关系。说明了在弱非线性范围内传播非线性波的演变，强调了零 (DC)、自解调低和二次谐波频率的生成，用于在色散关系的不同区域进行激励。离散接触非线性之间的连续体表现出局部 DC 降低和二次谐波增量，这在离散 PMs（如粒状声子晶体）中没有观察到。还探讨了非线性、周期性和有限性对非线性波传播的交织影响，这导致在 PM 和基于模式的二次谐波特性的有限边界处的最大直流幅度。最后，我们通过表征非线性波传播对嵌入式接触的不同布置的依赖性来证明所提出的非线性 PM 的灵活性。在弹性连续体中离散嵌入非线性界面（例如粗糙接触）的概念为通过局部微观结构非线性控制 PM 的全局非线性响应提供了机会。