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In this article, the dynamic magnetostrictive effect of giant magnetostrictive materials is studied and a novel general nonlinear transient constitutive model is established, in which the eddy current effects are incorporated. The validity and reliability of the obtained nonlinear transient constitutive model are verified by comparing its predicted results with existing experimental data. The excellent agreements between predicted results and experimental data indicate that the nonlinear transient constitutive model with eddy current effects can accurately capture frequency-dependent hysteretic behavior exhibited by giant magnetostrictive materials under different applied magnetic field amplitudes and frequencies. Moreover, the obtained constitutive model can also effectively capture the nonlinear magnetic-elastic-thermal coupling effect of giant magnetostrictive materials, since the stress and temperature-dependencies are incorporated in the nonlinear transient constitutive model. In such a case, the influences of exciting frequency and temperature on the dynamic magnetostrictive effect of giant magnetostrictive materials are discussed in detail by using this nonlinear transient constitutive model. The numerical simulation results evidence the notable dependences of dynamic magnetostrictive effect on exciting frequency and temperature, which indicate that the effects of eddy current and temperature on the dynamic magnetostrictive effect can not be ignored. Therefore, the nonlinear transient constitutive model with eddy current effects established in this article has great practical value for both theoretical researches and engineering applications of giant magnetostrictive materials.