Study of three-dimensional elastic metamaterials based on a lattice system

2021 ◽  
Vol 150 (4) ◽  
pp. A109-A109
Author(s):  
Zachary Mumme ◽  
Jiadi Fan ◽  
Sheng Sang
Keyword(s):  
Three Dimensional ◽  
Lattice System ◽  
Elastic Metamaterials

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Y. Y. Chen ◽  
G. L. Huang ◽  
C. T. Sun
Keyword(s):  
Band Gap ◽  
Elastic Waves ◽  
Low Frequency ◽  
Lattice System ◽  
Band Gaps ◽  
Negative Capacitance ◽  
Bending Waves ◽  
Stiffness Constant ◽  
Elastic Metamaterials ◽  
Gap Control

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices

2019 ◽  
Vol 25 (2) ◽  
pp. 475-497
Author(s):  
Vincent Picandet ◽  
Noël Challamel
Keyword(s):  
Difference Equations ◽  
Differential Operators ◽  
Scale Effects ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Continuous Model ◽  
Lattice System ◽  
Discrete Problem ◽  
Linear Difference Equations ◽  
One Dimensional

The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

Crystallographic Features of the C-Type Orbital-Ordered, and Charge- and Orbital-Ordered States in the Simple Perovskite Manganite Ca1-xLaxMnO3

2012 ◽  
Vol 706-709 ◽  
pp. 1612-1617
Author(s):  
Yasuhide Inoue ◽  
Masazumi Arao ◽  
Daisuke Shiga ◽  
Yasumasa Koyama
Keyword(s):  
Three Dimensional ◽  
Electronic System ◽  
Lattice System ◽  
Perovskite Manganite ◽  
Orbital Ordering ◽  
Transverse Lattice ◽  
Type Orbital ◽  
Antiferromagnetic Ordering ◽  
Monoclinic Distortion ◽  
Highly Correlated

The C-type orbital-ordered (CTOO), and charge-and orbital-ordered (COO) states are present in the simple perovskite manganite Ca1-xLaxMnO3, which has a three-dimensional highly-correlated electronic system. In this study, the crystallographic features of the CTOO and COO states have been investigated mainly by transmission electron microscopy to understand responses of a lattice system to these orderings. Of these two states, the cooling from the disordered orthorhombic Pnma (DO) state around x = 0.20 resulted in the CTOO state with the monoclinic P21/m symmetry. As a result of the monoclinic distortion as a response of the lattice system, the CTOO state consisted of a banded structure that was characterized by an alternating array of two monoclinic domains with different β values. In 0.30 < x < 0.50, on the other hand, the appearance of the COO state from the DO state on cooling accompanied a transverse lattice modulation with q = []DO as a response to orbital ordering in the COO state. The subsequent cooling in the COO state led to the antiferromagnetic ordering with a large lattice dilatation. In other words, no change in the crystal symmetry occurs in the appearance of the antiferromagnetic ordering.

Elastic Metamaterials With Low-Frequency Passbands Based on Lattice System With On-Site Potential

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yongquan Liu ◽  
Xiaohui Shen ◽  
Xianyue Su ◽  
C. T. Sun
Keyword(s):  
Elastic Waves ◽  
Present Method ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Lattice System ◽  
Two Dimensional ◽  
High Frequencies ◽  
Elastic Metamaterials

An elastic metamaterial with a low-frequency passband is proposed by imitating a lattice system with linear on-site potential. It is shown that waves can only propagate in the tunable passband. Then, two kinds of elastic metamaterials with double passbands are designed. Great wave attenuation performance can be obtained at frequencies between the two passbands for locally resonant type metamaterials, and at both low and high frequencies for the diatomic type metamaterials. Finally, the strategy to design two-dimensional (2D) metamaterials is demonstrated. The present method can be used to design new types of small-size waveguides, filters, and other devices for elastic waves.

Scattering of waves by three-dimensional obstacles in elastic metamaterials with zero index

2016 ◽  
Vol 94 (22) ◽  
Author(s):  
Fengming Liu ◽  
Feng Zhang ◽  
Wei Wei ◽  
Ni Hu ◽  
Gang Deng ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Elastic Metamaterials ◽  
Zero Index
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