scholarly journals Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials

2014 ◽  
Vol 372 (2023) ◽  
pp. 20130186 ◽  
Author(s):  
Yichao Xu ◽  
Vitali F. Nesterenko
Keyword(s):  
Power Law ◽  
Elastic Moduli ◽  
Dynamic Behaviour ◽  
Spherical Particles ◽  
Short Pulses ◽  
One Dimensional ◽  
Linear Elastic ◽  
Strongly Nonlinear ◽  
Granular Chains ◽  
Different Levels

The propagation of short pulses with wavelength comparable to the size of a unit cell has been studied in a one-dimensional discrete metamaterial composed of steel discs alternating with toroidal nitrile O-rings under different levels of precompression using experiments, numerical simulations and theoretical analysis. This strongly nonlinear metamaterial is more tunable than granular chains composed of linear elastic spherical particles and has better potential for attenuation of dynamic loads. A double power-law relationship for compressed O-rings was found to describe adequately their quasi-static and dynamic behaviour with significantly different elastic moduli. It is demonstrated that the double power-law metamaterial investigated allows a dramatic increase in sound speed and acoustic impedance of three to four times using a moderate force.

Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. F13-F20 ◽  
Author(s):  
Xavier García ◽  
Ernesto A. Medina
Keyword(s):  
Cyclic Loading ◽  
Bulk Modulus ◽  
Power Law ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Hysteretic Behavior ◽  
Dynamics Simulation ◽  
Spherical Particles ◽  
Elastic Response ◽  
Power Law Exponent

When Hertz-Mindlin force laws are considered in the context of the effective-medium theory, the predictions yield a constant Poisson coefficient and bulk/shear elastic moduli that scale with pressure with a 1/3 power law exponent [Formula: see text]. This prediction contradicts early and recent experimental findings that conclude moduli grow faster with a 1/2 power law exponent ([Formula: see text]). Such a conclusion is also reached by recent second-order corrections to linear elastic theory. In this work we use a discrete-particle method to study the elastic response of a model of sand that is unconsolidated because of cyclic loading. We use a detailed molecular dynamics simulation that accounts for Hertz-type grain interactions and history-dependent shear forces. The porous sand model is constructed from spherical particles whose size distribution mimics well-sorted unconsolidated sands. The geometry of the model is obtained by simulating critical processes in sedimentary rock formations. Hysteretic behavior and relations between the sample bulk modulus, strain, and stress are obtained. The simulated sample reproduces experimental transient and stationary loading-unloading behavior. We find good correspondence of pressure and strain dependence of elastic moduli in our model with semilinear elasticity theory predictions. Simple arguments explain low coordination numbers observed on force-transmitting samples and the tendency to reduce dissipation under cyclic loading. Our approach clearly shows that a Hertz-Mindlin grain interaction is not inconsistent with the experimental [Formula: see text] behavior of the bulk modulus.

scholarly journals Polystyrene-Based Nanocomposites with Different Fillers: Fabrication and Mechanical Properties

Polymers ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 2457
Author(s):  
Olga A. Moskalyuk ◽  
Andrey V. Belashov ◽  
Yaroslav M. Beltukov ◽  
Elena M. Ivan’kova ◽  
Elena N. Popova ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Elastic Moduli ◽  
Spherical Particles ◽  
Linear Elastic ◽  
Rigid Particles ◽  
Different Types ◽  
Non Linear ◽  
Multi Walled Carbon Nanotubes ◽  
Carbon Fillers ◽  
Walled Carbon Nanotubes

The paper presents a comprehensive analysis of the elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and mica), and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Block samples of composites with different filler concentrations were fabricated by melt technology, and their linear and non-linear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of a composite, with the highest rise of about 80% obtained with carbon fillers. Non-linear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than linear ones. A non-linearity modulus βs comprising the combination of linear and non-linear elastic moduli of a material demonstrated considerable changes correlating with those of the Young’s modulus. The changes in non-linear elasticity of fabricated composites were compared with parameters of bulk non-linear strain waves propagating in them. Variations of wave velocity and decay decrement correlated with the observed enhancement of materials’ non-linearity.

scholarly journals Quasiperiodic granular chains and Hofstadter butterflies

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170139 ◽  
Author(s):  
Alejandro J. Martínez ◽  
Mason A. Porter ◽  
P. G. Kevrekidis
Keyword(s):  
Fractal Dimension ◽  
Contact Angles ◽  
Spherical Particles ◽  
Localization Transition ◽  
Strongly Nonlinear ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Lattices ◽  
Granular Chains ◽  
A Chain ◽  
Cylindrical Particles

We study quasiperiodicity-induced localization of waves in strongly precompressed granular chains. We propose three different set-ups, inspired by the Aubry–André (AA) model, of quasiperiodic chains; and we use these models to compare the effects of on-site and off-site quasiperiodicity in nonlinear lattices. When there is purely on-site quasiperiodicity, which we implement in two different ways, we show for a chain of spherical particles that there is a localization transition (as in the original AA model). However, we observe no localization transition in a chain of cylindrical particles in which we incorporate quasiperiodicity in the distribution of contact angles between adjacent cylinders by making the angle periodicity incommensurate with that of the chain. For each of our three models, we compute the Hofstadter spectrum and the associated Minkowski–Bouligand fractal dimension, and we demonstrate that the fractal dimension decreases as one approaches the localization transition (when it exists). We also show, using the chain of cylinders as an example, how to recover the Hofstadter spectrum from the system dynamics. Finally, in a suite of numerical computations, we demonstrate localization and also that there exist regimes of ballistic, superdiffusive, diffusive and subdiffusive transport. Our models provide a flexible set of systems to study quasiperiodicity-induced analogues of Anderson phenomena in granular chains that one can tune controllably from weakly to strongly nonlinear regimes. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

2015 ◽  
Vol 114 (12) ◽  
Author(s):  
A. S. Campbell ◽  
D. M. Gangardt ◽  
K. V. Kheruntsyan
Keyword(s):  
Power Law ◽  
Bose Gas ◽  
Sudden Expansion ◽  
One Dimensional

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

2021 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Lower Bound ◽  
Case Studies ◽  
Power Law ◽  
Elastic Moduli ◽  
New Method ◽  
Stress Distributions ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Thick Cylinder ◽  
Better Than

Abstract An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

Mechanical response of double-stranded DNA to dynamic excitation

2021 ◽  
pp. 107754632110458
Author(s):  
Hamze Mousavi ◽  
Moein Mirzaei ◽  
Samira Jalilvand
Keyword(s):  
Mechanical Behavior ◽  
Mechanical Response ◽  
Actual Condition ◽  
Dimensional System ◽  
One Dimensional ◽  
Linear Elastic ◽  
Dynamic Excitation ◽  
Double Stranded Dna ◽  
Elastic Forces ◽  
Mass Spring

The present work investigates the vibrational properties of a DNA-like structure by means of a harmonic Hamiltonian and the Green’s function formalism. The DNA sequence is considered as a quasi one-dimensional system in which the mass-spring pairs are randomly distributed inside each crystalline unit. The sizes of the units inside the system are increased, in a step-by-step approach, so that the actual condition of the DNA could be modeled more accurately. The linear-elastic forces mimicking the bonds between the pairs are initially considered constant along the entire length of the system. In the next step, these forces are randomly shuffled so as to take into account the inherent randomness of the DNA. The results reveal that increasing the number of mass-spring pairs in the crystalline structure decreases the influence of randomness on the mechanical behavior of the structure. This also holds true for systems with larger crystalline units. The obtained results can be used to investigate the mechanical behavior of similar macro-systems.

scholarly journals Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2013 ◽  
Vol 88 (13) ◽  
Author(s):  
Alejandro M. Lobos ◽  
Masaki Tezuka ◽  
Antonio M. García-García
Keyword(s):  
Power Law ◽  
Phase Coherence ◽  
Electron Hopping ◽  
One Dimensional
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