This study presents a mathematical framework to predict the effective time-dependent behavior of three-phase smart composites with typical 0-3, 1-3, and 2-2 connectivities. A composite is composed of magnetostrictive and piezoelectric reinforcements that both show nonlinear multiphysics coupling and a polymer matrix that exhibits viscoelastic behavior. For dealing with nonlinear and time-dependent problems, a tangent linearization is employed to linearize the nonlinear constituents and a time-integration algorithm is applied to numerically determine the viscoelastic response of the matrix. A unified constitutive equation can be subsequently formulated to cover various phase constitutive laws following by a simplified unit-cell micromechanics model to set up a composite constitutive relation. The presented formulation is validated by limited experimental data available in literatures. Numerical results show that inclusion of a polymer matrix in a smart composite causes magnetoelectric coupling to be creep due to strain-mediated coupling among these three phases. The established unit-cell micromechanics model can be further integrated into a finite element framework to analyze composite structures, which is a great merit in a variety of practical applications. It will do so by implementing the presented micromechanics method at every integration point.
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