A multiscale model for electro-thermo-elasto-plastic piezoelectric metal matrix multifunctional composites

A multiscale model was developed to analyze the deformation of piezoelectric multifunctional composites with metal matrix. In view of the thermo-inelastic deformation of metal matrix, this model was constructed using an incremental formulation based on the variational-asymptotic method. Although this study adopted the classical plasticity theory to model the metal matrix, it could easily be extended to include viscoplasticity theory as well. The microstructure of composites is assumed to be periodic. Taking advantage of the small size of the microstructure, we formulate a variational statement of energy change of the unit cell through an asymptotic analysis of the functional to predict the effective instantaneous tangential electromechanical matrix of the composites. The present model can recover the local fields using a set of algebraic relations obtained in the process of calculating the effective instantaneous tangential electromechanical matrix. Numerical examples are used to demonstrate the application of the present modeling technique.