Sensitivity analysis of effective thermomechanical properties for periodic multicomponent composites with interface defects
Marcin Kamiński Politechnika Łódzka, Katedra Mechaniki Materiałów, al. Politechniki 6, 93-590 Łódź
Quarterly No. 4, 2005 pages 41-47
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abstract The main objective of this paper is to demonstrate the method of sensitivity gradients determination for the effective material parameters for the periodic multicomponent composites. This issue is analyzed from the point of view of thermomechanical properties with any finite number of the components in the periodicity cell and for fiber-reinforced composites with interface defects also (see Fig. 1). These defects are modeled as semi-elliptical regions lying with major axes on the fiber- matrix boundary. The homogenization method applied are based on the solution for the cell problem with the aid of Finite Element Method (FEM) to compute the homogenized elasticity tensor. The sensitivity gradients for the periodic superconducting composite with four components are determined using the homogenization-oriented FEM program MCCEFF Fig. 3). On the other hand, the effective material parameters for the interphase, the heat conductivity and heat capacity coefficients as well as upper and lower bounds for the effective elasticity tensor are computed symbolically thanks the system MAPLE. Using this methodology the effective Young modulus and Poisson ratio for the interphase with respect to flatness coefficients of the defects and with respect to the defects number on the interface are computed (Figs 2-5). the same time, the relevant gradients of the homogenized heat conduction and capacity coefficients with respect to the defects flatness and these coefficients for the defects in Figures 7-10 illustrate the opportunities of this model. The applied methodology may be successfully used for numerical determination of the sensitivity gradients with respect to the other design parameters, for various physical fields applied to composites and can be used further in conjunction with various FEM programs for structural and/or thermomechanical analysis of composites. Key words: homogenization method, interface defects, sensitivity analysis, Finite Element Method