Sensitivities of effective properties computed using micromechanics differential schemes and high-order Taylor series: Application to piezo-polymer composites

This paper presents an approach using micromechanics differential schemes to compute the effective properties of composite materials and their first order sensitivities. The approach is based on a high-order Taylor series expansion of the initial value problem of the differential schemes and the usage of automatic differentiation tools. Numerical results are presented for electro-elastic properties of two-phase piezo-polymer composite materials. The comparison of the results to those obtained by CVODES which is one of the most advanced dynamic sensitivity solvers show the effectiveness of the method. This approach may be useful for microstructure sensitive design by a gradient-based optimization method or may be used to carry out sensitivity analysis around the optimal point after an optimal microstructure design.