Micromechanics modeling of time-dependent, nonlinear and multiphysics response of metal core piezoelectric and piezomagnetic fibers reinforced polymer matrix composites

In order to effectively simulate the time-dependent, nonlinear and multiphysics response of the new type of multi-functional smart materials-metal core piezoelectric and piezomagnetic fiber reinforced polymer matrix composite (MPPF/PMC), an incremental micromechanics model was developed based on the variational asymptotic method. Firstly, the incremental constitutive equations of polymer, piezoelectric/piezomagnetic materials and metal materials were derived respectively, and a unified constitutive equation was established. Considering the time-dependent and nonlinear characteristics of composites, an incremental procedure in conjunction with an instantaneous tangential electro-magneto-mechanical matrix of composites was established. The fluctuate functions of field variables were solved by minimizing the approximate energy functional and realized by finite element method, resulting in a micromechanics model as close as possible to the physical and engineering authenticity. The numerical example of aluminum core piezoelectric (BaTiO₃) and piezomagnetic (CoFe₂O₄) polymer matrix shows that this constructed model can be used to simulate the effective response of MPPF/PMCs under different physical fields and can accurately capture the stress mutation phenomenon between the fiber and the matrix.