Automatic differentiation of micromechanics incremental schemes for coupled fields composite materials: Effective properties and their sensitivities

A modeling approach based on automatic differentiation and micromechanics incremental schemes for coupled fields composite materials is presented in this work. In the multi-sites framework, the micromechanics incremental schemes presented herein are able to account for the anisotropic behavior of the constituents, the morphological and the topological textures and the strong contrast between the properties of the individual phases of these composite materials. By applying automatic differentiation to these micromechanics incremental schemes, the first order and high order sensitivities of the effective material properties can be easily computed in the same analysis. An application on three-phase magneto-electro-elastic composite material is presented in the framework of mono-site micromechanics to show the effectiveness of this composite materials modeling approach. The details on the implementation of this modeling approach in the multi-sites framework will be discussed in a future work. The composite materials modeling methodology reported here may be used for material microstructure sensitive design in material by design strategies.