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