TY - JOUR

T1 - Nonlinear effects in the extension of an elastic space containing a wavy layer inclusion

AU - Chiskis, A.

AU - Parnes, R.

N1 - Funding Information:
The authors wish to thank Prof. Leonid Slepyan for several useful discussions during the course of this investigation. This research was partially supported by Grant No. 9673-1-96 from the Ministry of Science, Israel and by Grant No. 94-00349 from the United States-israel Binational Science Foundation (BSF), Jerusalem, Israel.

PY - 1998/7

Y1 - 1998/7

N2 - two-dimensional problem of extension of an infinite isotropic elastic space (the matrix) containing an infinite, solitary, elastic, periodically wavy layer inclusion, having both bending and axial rigidities, is considered. Geometric nonlinearity of the layer and the matrix are taken into account as well as physical nonlinearity of the matrix material. A general procedure for an arbitrary periodic inclusion is developed. Explicit analytical solutions for a typical case of a cosinusoidal inclusion having small initial waviness are presented and are found to depend solely on parameters defined by stiffness and thickness ratios of the matrix/inclusion system. Numerical results describing the deformation of the layer and the stress field in the matrix are presented for a wide range of the matrix/inclusion parameters. It is shown that within the range of small to moderate strains physical nonlinearity can have significant influence on the behavior and be a controlling factor in possible modes of failure, namely by delamination or crack initiation in the matrix.

AB - two-dimensional problem of extension of an infinite isotropic elastic space (the matrix) containing an infinite, solitary, elastic, periodically wavy layer inclusion, having both bending and axial rigidities, is considered. Geometric nonlinearity of the layer and the matrix are taken into account as well as physical nonlinearity of the matrix material. A general procedure for an arbitrary periodic inclusion is developed. Explicit analytical solutions for a typical case of a cosinusoidal inclusion having small initial waviness are presented and are found to depend solely on parameters defined by stiffness and thickness ratios of the matrix/inclusion system. Numerical results describing the deformation of the layer and the stress field in the matrix are presented for a wide range of the matrix/inclusion parameters. It is shown that within the range of small to moderate strains physical nonlinearity can have significant influence on the behavior and be a controlling factor in possible modes of failure, namely by delamination or crack initiation in the matrix.

KW - A. delamination

KW - B. finite strain

KW - B. layered material

KW - B. nonlinear constitutive behavior

KW - B. strain compatibility

UR - http://www.scopus.com/inward/record.url?scp=0032115377&partnerID=8YFLogxK

U2 - 10.1016/S0022-5096(98)00012-X

DO - 10.1016/S0022-5096(98)00012-X

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AN - SCOPUS:0032115377

SN - 0022-5096

VL - 46

SP - 1213

EP - 1251

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 7

ER -