Sensitivity analysis of homogenized characteristics for some elastic composites

The main goal of the paper is to present theoretical aspects and the finite element method implementation of sensitivity analysis in homogenization of composite materials with linear elastic components using the effective modules approach. The sensitivity analysis of effective material properties is presented in a general form for n-component periodic composite and is illustrated using the examples of periodic 1D as well as 2D heterogeneous structures. The sensitivity coefficients are determined for the effective Young’s modulus and the effective elasticity tensor components. The structural response functional for the fiber-reinforced elastic composite is proposed in the form of total strain energy resulting from some uniform strain state of the composite representative volume element (RVE). The results of sensitivity analysis presented in the paper confirm the usefulness of the homogenization method in computational analysis of composite materials and its application in composite optimization, identification, shape sensitivity studies and, after some probabilistic extensions, in stochastic analysis of random composites.