anomalous strain energy transformation pathways in metamaterials
Introduction
Mechanics version of Parseval's energy theorem
provides simple relationship between the strain energy volumetric and spectral distributions in the reciprocal space
Spectral energy distribution
leads directly to a spectral entrophy of lattice deformation (Shannon's type)
also a basic measure of complexity of mechanical responses of metamaterials to surface and body loads
transformation of the energy volumetric and spectral distributions with a material coordinate pointed away from a surface load
Selective filtering of Rayleigh waves (sinusoidal pressure patterns)
Saint-Venant effect inversion illustrated by energy spectral dist contours
Occurance of 'hiding pockets' of low deformation
redirection of strain energy maximum away from axis of a concentrated surface load
Metamaterials
properties of interest
negative poisson's ratio
negative bulk modulus
negative longitudinal stiffness and compliance
Reverse Saint-Venant effect
cause of variation of properties
internal structure
topology
geometric architecture
design of metamaterials
application of large amount of deformation
stiffness modulations
functional properties due to internal structure design of lattice materials
reconfigurabilitiy
multistability
polymorphism
symmetry breaking
deformation
strain energy reprogramming
control
reprogramming
redistribution
polymorphic metamaterials may well perform as superdampers
their unusual quasi-static performances could complement fast aperiodic impact loads
frequency spectra extend far beyond reasonable acoustical metamaterial's bandgap
this impact load could be damped in supersonic regime by controlling instantaneous strain energy distributions in the material before any oscillatory process is established.
harnessing these mechanisms would also suggest opportunities to employ spatial profiles of impact loads, frequency spectra for highly efficient damping performance
Objectives
discussion of some novel analytical tools and concepts enabling a systematic analysis of strain energy transformation in any periodic material system
universal strain energy representation
Rayleigh decay spectrum
strain energy spectral distribution
a spectral theorem that connects volumetric and spectral distributions
shannon's entropy of lattice deformation
analogous to Parseval's theorem
interpreted as purity of signal or used to distinguish between artificial and natural signals
It's variance with a material coordinate represents the decrease of info about surface loads in the material interior
lattice associate cell
utility of these new analytical tools for a systematic analysis of strain energy transformation behavior of materials with periodic internal structure
qualitative shapes of this determine how the material translates the instantaneous strain energy of deformation between two points in space