The influence of shear strain and hydrostatic stress on stability and elastic waves in a layer

We investigate the propagation of waves in dense static granular packings made of soft and stiff particles subjected to hydrostatic stress. Physical experiments in a triaxial cell equipped with broadband piezoelectric wave transducers have been performed at ultrasound frequencies. The time of flight is measured in order to study the combined effect of applied stress and rubber content on the elastic properties of the mixtures. The bulk stiffness deduced from the wave speed is nonlinear and non-monotonic with the increasing percentage of rubber with a more prominent effect at higher pressures. Moreover, in the frequency domain, a spectral analysis gives insights on the transition from a glass- to a rubber-dominated regime and the influence of rubber particles on the energy dissipation. Mixtures with rubber content below 30% show enhanced damping properties, associated with slightly higher stiffness and lighter weight.

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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THEORY OF THE ATTENUATION OF ELASTIC WAVES IN INHOMOGENEOUS SOLIDS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1981632 ◽

1981 ◽

Vol 42 (C6) ◽

pp. C6-102-C6-104

Author(s):

P. G. Klemens

Keyword(s):

Elastic Waves

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Analysis of magneto rheological elastomers for energy harvesting systems

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209350 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 439-446

Author(s):

Gildas Diguet ◽

Gael Sebald ◽

Masami Nakano ◽

Mickaël Lallart ◽

Jean-Yves Cavaillé

Keyword(s):

Magnetic Field ◽

Energy Harvesting ◽

Shear Strain ◽

Magnetic Induction ◽

Magnetic Particles ◽

Homogeneous Magnetic Field ◽

Electrical Signal ◽

Harvesting Systems ◽

Dc Bias ◽

Magneto Rheological

Magneto Rheological Elastomers (MREs) are composite materials based on an elastomer filled by magnetic particles. Anisotropic MRE can be easily manufactured by curing the material under homogeneous magnetic field which creates column of particles. The magnetic and elastic properties are actually coupled making these MREs suitable for energy conversion. From these remarkable properties, an energy harvesting device is considered through the application of a DC bias magnetic induction on two MREs as a metal piece is applying an AC shear strain on them. Such strain therefore changes the permeabilities of the elastomers, hence generating an AC magnetic induction which can be converted into AC electrical signal with the help of a coil. The device is simulated with a Finite Element Method software to examine the effect of the MRE parameters, the DC bias magnetic induction and applied shear strain (amplitude and frequency) on the resulting electrical signal.

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On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽

10.32964/tj17.04.231 ◽

2018 ◽

Vol 17 (04) ◽

pp. 231-240

Author(s):

Douglas Coffin ◽

Joel Panek

Keyword(s):

Shear Strain ◽

Transverse Shear ◽

Elastic Limit ◽

Experimental Results ◽

Transverse Shear Strain ◽

Maximum Strain ◽

Machine Direction ◽

Engineering Approach ◽

Wide Range ◽

Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

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