On sensitivity analysis in homogenization of some composite materials

Main purpose of the paper is to present theoretical aspects and Finite Element Method implementation of the sensitivity analysis in homogenization of multicomponent materials in the linear range; the problem is solved by using of the effective modules homogenization approach. The deterministic sensitivity analysis is worked out in general form and is illustrated on the example of some material parameters such as the heat conductivity coefficients and Young moduli of the component materials, for instance, as well as for particular 1 d periodic two-component composite. The results of sensitivity analysis presented in the paper may be successfully applied to computational optimization of engineering composites, to the shape sensitivity studies and, after some extensions, to random composites analysis.