Complex variable step method for sensitivity analysis of effective properties in multi-field micromechanics

This paper shows an approach to computing the effective properties of multi-field composite materials and their first-order sensitivities. The approach is based on the application of the complex variable step method for the micromechanical Mori-Tanaka scheme; hence, the first-order sensitivities can be computed in the same analysis. Numerical results are presented for magnetoelectroelastic properties of piezoelectric-piezomagnetic composite materials. A comparison of the results to those obtained by other methods shows that the presented sensitivity analysis gives highly accurate and stable results, but the values of the results are dependent on the applied micromechanical model. The presented approach may be used to solve ill-posed problems of optimal design or identification in coupled fields micromechanics.