Homogenization of a 1D nonlinear dynamical problem for periodic composites

被引：30

作者：

Andrianov, Igor V. ^{[1
]}

Danishevs'kyy, Vladyslav V. ^{[2
]}

Topol, Heiko ^{[1
]}

Weichert, Dieter ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Inst Gen Mech, Templergraben 64, D-52062 Aachen, Germany

[2] Prydniprovska State Acad Civil Engn & Architectur, Dept Mat Sci, UA-49600 Dnepropetrovsk, Ukraine

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2011年 / 91卷 / 06期

关键词：

Composite material; asymptotic homogenization; nonlinear wave; 3RD-ORDER ELASTIC-CONSTANTS; WAVE-PROPAGATION; MEDIA;

D O I：

10.1002/zamm.201000176

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study wave propagation through a composite material built up of a periodically repeated one-dimensional structure of coated inclusions and matrix material by the application of the asymptotic homogenization method. We take into account geometrical nonlinearity, which is described by the Cauchy-Green strain tensor and physical nonlinearity by the Murnaghan elastic potential. We take into account structural nonlinearity by considering the bonding between two materials to be imperfect. As a result we obtain homogenized equations for the low-frequency range. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：523 / 534

页数：12

共 38 条

[1]

Achenbach JD., 1982, Journal of Nondestructive Evaluation, V3, P229

[2] Improved Continuous Models for Discrete Media [J].

Andrianov, I. V. ;

Awrejcewicz, J. ;

Weichert, D. .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2010, 2010

[3] Higher order asymptotic homogenization and wave propagation in periodic composite materials [J].

Andrianov, Igor V. ;

Bolshakov, Vladimir I. ;

Danishevs'kyy, Vladyslav V. ;

Weichert, Dieter .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2008, 464 (2093) :1181-1201

[4]

[Anonymous], 1978, ASYMPTOTIC ANAL PERI

[5] Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations [J].

Bertoldi, K. ;

Boyce, M. C. .

PHYSICAL REVIEW B, 2008, 78 (18)

[6] Homogenization estimates for fiber-reinforced elastomers with periodic microstructures [J].

Brun, M. ;

Lopez-Pamies, O. ;

Castaneda, P. Ponte .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2007, 44 (18-19) :5953-5979

[7] Measurement of elastic nonlinearity of soft solid with transient elastography [J].

Catheline, S ;

Gennisson, JL ;

Fink, M .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2003, 114 (06) :3087-3091

[8]

Cattani C, 2007, WAVELET WAVE ANAL AP

[9] Homogenization Techniques and Micromechanics. A Survey and Perspectives [J].

Charalambakis, Nicolas .

APPLIED MECHANICS REVIEWS, 2010, 63 (03) :1-10

[10] A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales [J].

Chen, W ;

Fish, J .

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2001, 68 (02) :153-161

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