High-frequency homogenization in periodic media with imperfect interfaces

Area of Science:

• Solid Mechanics
• Wave Propagation
• Materials Science

Background:

• High-frequency homogenization is a technique used to analyze wave propagation in periodic structures.
• Periodic media with imperfect interfaces present challenges due to discontinuities in displacement and stress.
• Understanding wave behavior in such media is crucial for designing advanced materials and devices.

Purpose of the Study:

• To extend high-frequency homogenization to 1D periodic media with imperfect interfaces.
• To develop asymptotic approximations for dispersion diagrams and wave fields.
• To provide a uniform approximation applicable to both Dirac and non-Dirac points.

Main Methods:

• Asymptotic analysis of periodic and antiperiodic solutions at the Brillouin zone edges.
• Development of second-order approximations for higher dispersion branches and leading-order for wave fields.
• Analysis of Dirac points and derivation of first-order dispersion and zeroth-order wave field approximations.
• Numerical validation using the Bloch-Floquet approach for monolayered and bilayered materials.

Main Results:

• Asymptotic approximations for dispersion diagrams and wave fields were derived.
• A novel uniform approximation was developed, valid for both Dirac and non-Dirac points.
• Numerical comparisons confirmed the accuracy of the uniform approximation, even away from Brillouin zone edges.
• Convergence measurements validated the proposed homogenization approach.

Conclusions:

• The extended high-frequency homogenization method accurately models elastic wave propagation in 1D periodic media with imperfect interfaces.
• The developed uniform approximation offers a robust tool for analyzing wave phenomena in these complex structures.
• The findings have implications for the design and analysis of acoustic and mechanical metamaterials.