Anomalous strain energy transformation pathways in mechanical metamaterials.
| Autor: | Karpov EG; Department of Civil and Materials Engineering, University of Illinois, Chicago, IL 60607, USA., Danso LA; Department of Civil and Materials Engineering, University of Illinois, Chicago, IL 60607, USA., Klein JT; Department of Civil and Materials Engineering, University of Illinois, Chicago, IL 60607, USA. |
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| Jazyk: | angličtina |
| Zdroj: | Proceedings. Mathematical, physical, and engineering sciences [Proc Math Phys Eng Sci] 2019 Jun; Vol. 475 (2226), pp. 20190041. Date of Electronic Publication: 2019 Jun 05. |
| DOI: | 10.1098/rspa.2019.0041 |
| Abstrakt: | 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. Competing Interests: We declare we have no competing interests. |
| Databáze: | MEDLINE |
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