Anomalous strain energy transformation pathways in mechanical metamaterials

Area of Science:

• Solid Mechanics
• Materials Science
• Metamaterials

Background:

• Lattice materials with periodic internal structures exhibit unique mechanical properties.
• Understanding strain energy distribution is crucial for predicting material behavior under load.
• Continuum mechanics may not fully capture the complexities of discrete lattice responses.

Purpose of the Study:

• To present a mechanics version of Parseval's energy theorem for discrete lattice materials.
• To establish a relationship between strain energy distributions and spectral entropy.
• To investigate anomalies in energy distribution and deformation in lattice materials.

Main Methods:

• Application of Parseval's energy theorem to various lattice structures (microtruss, grid, frame, origami, tessellation).
• Analysis of volumetric and spectral energy distributions in reciprocal space.
• Calculation of spectral entropy of lattice deformation and its variance.

Main Results:

• A direct link between spectral energy distribution and spectral entropy (Shannon's type).
• Spectral entropy quantifies information loss about surface loads within the material.
• Observed anomalies include selective Raleigh wave filtering, Saint-Venant effect inversion, 'hiding pockets' of low deformation, and strain energy redirection.

Conclusions:

• Spectral entropy serves as a measure of mechanical response complexity in metamaterials.
• Lattice materials exhibit distinct behaviors compared to continuum materials, particularly concerning energy distribution.
• Anomalous energy redirection has potential applications in impact protection for mechanical metamaterials.