An enriched homogenized model is developed based on a proposed homogenization strategy, to describe the wave propagation behaviour through periodic layered composites. The intrinsic parameters characterising the micro-inertia effect and non-local interactions are defined transparently in terms of the constituent materials’ properties and volume fractions. The framework starts with the introduction of an additional kinematic field to characterise the displacement of the stiff layer, before setting up macro kinematic fields to account for the average deformation of the constituent materials within a segmented unit cell. Relationships between these macro average strain fields are determined based on suitable micro-mechanical arguments. The Hill–Mandel condition is next applied to translate the energy statements from micro to macro. A system of coupled governing equations of motion is finally extracted naturally at the macro level via Hamilton’s Principle. Through a series of benchmark examples, it is shown that the proposed model exhibits excellent predictive capabilities over a broad range of loading frequencies.

中文翻译：

---

周期层状复合材料中粘弹性平面波传播的富集均质模型

在提出的均质化策略的基础上，建立了丰富的均质化模型，以描述通过周期性分层复合材料的波传播行为。根据组成材料的性质和体积分数，透明地定义了表征微惯性效应和非局部相互作用的内在参数。该框架从引入额外的运动场开始，以表征硬质层的位移，然后建立宏观运动场以说明分段单元内组成材料的平均变形。这些宏观平均应变场之间的关系是根据合适的微机械参数确定的。接下来应用Hill–Mandel条件将能量表述从微观转化为宏观。最终，通过汉密尔顿原理在宏观水平上自然地提取了耦合的运动控制方程组。通过一系列基准示例，表明所提出的模型在广泛的加载频率范围内显示出出色的预测能力。