Replication data for: "Wave characteristics and anisotropic homogenization theory of layered soft matter structures"

We investigate the wave characteristics and homogenization theory of soft-matter layered structures in the low-frequency P-wave limit. Using the potential method, we derive a closed-form dispersion relation and identify three distinct wave modes: quasi-static, resonance, and slip. These modes are governed by equivalent interface conditions—namely, a continuous interface for the quasi-static mode, a spring-like interface for the resonance mode, and a slip-like interface for the slip mode. Furthermore, we propose a simplified model that captures P-wave characteristics in the high-frequency S-wave regime. Our findings provide a unified framework for wave–structure interactions across solids, liquids, and soft-matter composites, enabling predictive design of metamaterials with programmable wave responses. This study offers new insight on the fundamental understanding of layered media and providing direct design principles for applications in acoustic cloaking, vibration damping, and biomedical imaging. This dataset is released under CC-BY-4.0 and is cited as DOI:10.5281/zenodo.16416852.”