Metamaterial Systems and Routing of Elastic Waves in Engineered Structures

UK Success Stories in Industrial Mathematics ◽

10.1007/978-3-319-25454-8_14 ◽

2016 ◽

pp. 107-113

Author(s):

Natalia V. Movchan ◽

Alexander B. Movchan ◽

Ross C. McPhedran ◽

Michele Brun ◽

Ian S. Jones

Keyword(s):

Elastic Waves ◽

Engineered Structures

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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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Micromechanics Measurements Applied to Integrated Circuit Microelectronics

MRS Proceedings ◽

10.1557/proc-473-27 ◽

1997 ◽

Vol 473 ◽

Cited By ~ 2

Author(s):

David R. Clarke

Keyword(s):

Integrated Circuits ◽

Integrated Circuit ◽

Fracture Resistance ◽

Interface Fracture ◽

New Techniques ◽

Fracture Properties ◽

Engineered Structures ◽

Mechanical And Fracture Properties ◽

Interconnect Lines ◽

Metallic Interconnect

ABSTRACTAs in other engineered structures, fracture occasionally occurs in integrated microelectronic circuits. Fracture can take a number of forms including voiding of metallic interconnect lines, decohesion of interfaces, and stress-induced microcracking of thin films. The characteristic feature that distinguishes such fracture phenomena from similar behaviors in other engineered structures is the length scales involved, typically micron and sub-micron. This length scale necessitates new techniques for measuring mechanical and fracture properties. In this work, we describe non-contact optical techniques for probing strains and a microscopic “decohesion” test for measuring interface fracture resistance in integrated circuits.

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