Equivalent circuit model including magnetic and thermo sources for the thermo–magneto–electric coupling effect in magnetoelectric laminates

The nonlinear thermo–magneto–mechanical magnetostrictive constitutive and the linear thermo–mechanical-electric piezoelectric constitutive are adopted in this paper. The bias magnetic field and ambient temperature are equivalent to a magnetic source and a thermo source, respectively. An equivalent circuit, which contains a magnetic source and a thermo source at the input, for the thermo–magneto–electric coupling effect in magnetoelectric（ME） laminates, is established. The theoretical models of the output voltage and static ME coefficient for ME laminates can be derived from this equivalent circuit model. The predicted static ME coefficient versus temperature curves are in excellent agreement with the experimental data available both qualitatively and quantitatively. It confirms the validity of the proposed model. Then the models are adopted to predict variations in the output voltages and ME coefficients in the laminates under different ambient temperatures, bias magnetic fields, and the volume ratios of magnetostrictive phases. This shows that the output voltage increases with both increasing temperature and increasing volume ratio of magnetostrictive phases; the ME coefficient decreases with increasing temperature; the ME coefficient shows an initial sharp increase and then decreases slowly with the increase in the bias magnetic field, and there is an optimum volume ratio of magnetostrictive phases that maximize the ME coefficient.This paper can not only provide a new idea for the study of the thermo–magneto–electric coupling characteristics of ME laminates, but also provide a theoretical basis for the design and application of ME laminates, operating under different sensors.