期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 50, 期 7-8, 页码 1141-1153出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2012.12.016
关键词
Spherical inhomogeneity; Gurtin-Murdoch interface; Multipole expansion; Unit cell model; Effective stiffness
类别
资金
- MTS Professorship Grant from the University of Minnesota, Minneapolis, USA
A complete solution has been obtained for periodic particulate nanocomposite with the unit cell containing a finite number of spherical particles with the Gurtin-Murdoch interfaces. For this purpose, the multipole expansion approach by Kushch et al. [Kushch, V.I., Mogilevskaya, S.G., Stolarski, H.K., Crouch, S.L., 2011. Elastic interaction of spherical nanoinhomogeneities with Gurtin-Murdoch type interfaces. J. Mech. Phys. Solids 59, 1702-1716] has been further developed and implemented in an efficient numerical algorithm. The method provides accurate evaluation of local fields and effective stiffness tensor with the interaction effects fully taken into account. The displacement vector within the matrix domain is found as a superposition of the vector periodic solutions of Lame equation. By using local expansion of the total displacement and stress fields in terms of vector spherical harmonics associated with each particle, the interface conditions are fulfilled precisely. Analytical averaging of the local strain and stress fields in matrix domain yields an exact, closed form formula (in terms of expansion coefficients) for the effective elastic stiffness tensor of nanocomposite. Numerical results demonstrate that elastic stiffness and, especially, brittle strength of nanoheterogeneous materials can be substantially improved by an appropriate surface modification. (C) 2013 Elsevier Ltd. All rights reserved.
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