AI 中文总结
该研究提出界面惯性增强的松弛微形态模型，解决超材料均匀化的尺度分离失效问题，可区分体性质相同但界面构型不同的有限尺寸试样，复现边界依赖响应。
AI 中文摘要
均匀化连续介质模型被广泛用于描述力学超材料中的波传播和带隙行为，无需显式解析其微观结构。然而，这类模型的有效性通常依赖于经典的尺度分离假设，即传播扰动的波长远大于单胞的特征尺寸。在有限尺寸的超材料样品及更高频率下，该假设逐渐失效，动态响应受微观结构在外部边界处截断方式的强烈影响。本研究在力学超材料的均匀化描述中引入全新概念：宏观界面的惯性贡献。研究表明，同一晶格的不同截断会产生具有不同质量分布的边界，导致有限尺寸试样的动态响应出现可测量差异。为在均匀化框架中捕捉这一复杂机制，研究扩展了松弛微形态模型，在研究对象的边界引入定义的动能表面能，这在边界条件中产生额外惯性项，可视为微观结构截断产生的界面惯性的均匀化对应物。因此，该均匀化模型如今可区分体性质相同但仅界面构型不同的有限尺寸试样，所提公式保留了松弛微形态模型的变分结构，同时使连续介质能复现全解析模拟中观察到的边界依赖响应，尤其在频率区间内。
英文摘要
Homogenized continuum models are widely used to describe wave propagation and band-gap behavior in mechanical metamaterials without explicitly resolving their microstructure. Their validity, however, typically relies on the classical separation of scales assumption, according to which the wavelength of the propagating disturbance is much larger than the characteristic size of the unit cell. In finite-size metamaterial samples and at higher frequencies, this assumption progressively breaks down, and the dynamic response becomes strongly influenced by the way the microstructure is truncated at the external boundaries. In this work we introduce a fundamentally new concept in the homogenized description of mechanical metamaterials: the inertial contribution of macroscopic interfaces. We show that different truncations of the same lattice generate boundaries with distinct mass distributions, which lead to measurable differences in the dynamic response of finite-sized specimens. To capture this complex mechanism in a homogenized framework, we extend the relaxed micromorphic model by introducing a kinetic surface energy defined on the boundary of the considered body. This generates an additional inertial term in the boundary conditions that can be seen as the homogenized counterpart of the interface inertia produced by the truncation of the microstructure. As a result, the homogenized model can now distinguish between finite-sized specimens that share identical bulk properties but differ only in the configuration of their interfaces. The proposed formulation preserves the variational structure of the relaxed micromorphic model while enabling the continuum to reproduce boundary-dependent responses observed in fully resolved simulations, particularly in frequency regimes ....... See the PDF for the full abstract.
