Vol. 12, No. 4, 2017

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Polarization approximations for elastic moduli of isotropic multicomponent materials

Duc Chinh Pham, Nguyen Quyet Tran and Anh Binh Tran

Vol. 12 (2017), No. 4, 391–406

Polarization approximations (PA) are proposed for the macroscopic elastic moduli of d-dimensional (d = 2 or 3) isotropic multicomponent materials. Specifically we use Hashin–Shtrikman-type polarization trial fields, which were constructed earlier from the minimum energy principles to bound the effective moduli of the composites, as the approximate solutions to the field equations. The approximations contain free reference parameters, which can be found analytically, numerically, or experimentally, from the reference effective moduli at dilute and/or finite volume proportions of the component materials. In the basic one-point reference parameter version, the approximations should obey Hashin–Shtrikman (HS) bounds for all the ranges of the volume proportions of the component materials. In the refined versions involving variable reference parameters to improve the accuracy of the scheme, the approximations satisfy HS bounds over the ranges of components’ volume proportions between the extreme reference points. We provide numerous numerically and experimentally based examples to illustrate the applications of the proposed approach.

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isotropic composite material, macroscopic elastic moduli, polarization approximation, reference parameter
Received: 4 July 2016
Revised: 5 March 2017
Accepted: 27 March 2017
Published: 20 May 2017
Duc Chinh Pham
Institute of Mechanics
Vietnam Academy of Science and Technology
264 Doi Can
Ba dinh
Graduate University of Science and Technology – VAST
18 Hoang Quoc Viet
Nguyen Quyet Tran
Department of Applied Mechanics
Hanoi University of Industry
298 Cau Dien
Graduate University of Science and Technology – VAST
18 Hoang Quoc Viet
Anh Binh Tran
Department of Applied Informatics in Construction
National University of Civil Engineering
55 Giai phong
Graduate University of Science and Technology – VAST
18 Hoang Quoc Viet