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Estimating effective conductivity of unidirectional transversely isotropic composites

Three-point correlation bounds are constructed on effective conductivity of unidirectional composites, which are isotropic in the transverse plane. The bounds contain, in addition to the properties and volume proportions of the component materials, three-point correlation parameters describing the micro-geometry of a composite, and are tighter those obtained in [1]. The bounds, applied to some disordered and periodic composites, keep inside the numerical homogenization results obtained by Fast Fourier method. | Volume 35 Number 3 3 Vietnam Journal of Mechanics, VAST, Vol. 35, No. 3 (2013), pp. 203 – 213 ESTIMATING EFFECTIVE CONDUCTIVITY OF UNIDIRECTIONAL TRANSVERSELY ISOTROPIC COMPOSITES Nguyen Trung Kien1,∗ , Nguyen Van Luat2 , Pham Duc Chinh3 1 University of Transport and Communication, Hanoi, Vietnam 2 Hanoi University of Industry, Vietnam 3 Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam ∗ E-mail: ntkien@utc.edu.vn Abstract. Three-point correlation bounds are constructed on effective conductivity of unidirectional composites, which are isotropic in the transverse plane. The bounds contain, in addition to the properties and volume proportions of the component materials, three-point correlation parameters describing the micro-geometry of a composite, and are tighter those obtained in [1]. The bounds, applied to some disordered and periodic composites, keep inside the numerical homogenization results obtained by Fast Fourier method. Keywords: Effective conductivity, three-point correlation, numerical homogenization. 1. INTRODUCTION Effective (thermal, electrical,.) conductivity of multicomponent materials depends on their often complicated irregular micro-structure, hence is hard to be determined exactly. Variational approach has been developed to construct upper and lower bounds in the effective conductivity of composites [1-13]. The bounds contain the properties and volume fractions of the components and possibly correlation information about the microgeometries of the composites. On the other side, numerical homogenization methods have been developed to estimate effective properties of particular composites, mostly, the twocomponent ones [11-14]. An effective method to deal with the homogenization problem is the Fast-Fourier one [14-16]. Le and Pham [1] developed a variational approach to estimate effective conductivity of transversely isotropic composites. In this work we modify the approach of Pham [7] to derive bounds tighter than those .