Abstract
This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and spectral distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior. Spectral entropy is also a basic measure of complexity of mechanical responses of metamaterials to surface and body loads. Considering transformation of the energy volumetric and spectral distributions with a material coordinate pointed away from a surface load, several interesting anomalies are seen even for simple lattice materials, when compared to continuum materials. These anomalies include selective filtering of surface Raleigh waves (sinusoidal pressure patterns), Saint–Venant effect inversion illustrated by energy spectral distribution contours, occurrence of ‘hiding pockets’ of low deformation, and redirection of strain energy maximum away from axis of a concentrated surface load. The latter phenomenon can be significant for impact protection applications of mechanical metamaterials.
Highlights
The science of mechanical metamaterials emerged at the interface of applied mechanics and materials engineering, inspired by the earlier research in optics, acoustics and electromagnetism [1,2,3,4,5,6,7,8,9,10,11], to explore opportunities for materials with exotic mechanical2019 The Authors
Internal structure design of lattice materials, foams, granular materials, origamis kirigamis, tessellations, tensegrities and minimal surface may lead to a range of functional properties, such as reconfigurability, multistability, polymorphism, symmetry breaking, deformation and strain energy reprogramming
We have discussed several non-standard analytical tools that could facilitate a systematic analysis of arbitrary periodic materials: associate substructure, Raleigh wave solution and decay royalsocietypublishing.org/journal/rspa Proc
Summary
The science of mechanical metamaterials emerged at the interface of applied mechanics and materials engineering, inspired by the earlier research in optics, acoustics and electromagnetism [1,2,3,4,5,6,7,8,9,10,11], to explore opportunities for materials with exotic mechanical. Their unusual quasi-static performances could complement acoustical metamaterials for fast aperiodic impact loads, whose frequency spectra extend far beyond any reasonable acoustical metamaterial’s bandgap Such an impact load could be more efficiently damped in a supersonic regime, by controlling instantaneous strain energy distributions in the material even before any oscillatory process is established. It is important to understand, if mechanical metamaterials can provide a mechanism to control the strain energy distribution and transformation Harnessing these mechanisms would suggest opportunities to employ spatial profiles of impact loads [22,31], in addition to their frequency spectra, for highly efficient damping performance. One of them can provide selective surface pressure blockage, and another leads to strain energy redirection out of the axis of a concentrated surface load Such functionalities of mechanical metamaterials can be interesting for a range of military, civil and mechanical engineering applications
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