||Based on the thermodynamic theory and the postulates of Jiles and Atherton, a general coupled magnetic-elastic-thermal free-energy model with hysteretic nonlinearity is established for Terfenol-D rods, in which the effect of Weiss molecular field is incorporated. The quantitative agreement between numerical simulation results predicted by the free-energy model and existing experimental data confirms the validity and reliability of the obtained nonlinear theoretical model, and indicates that the free-energy model can accurately capture the nonlinear hysteresis characteristic of Terfenol-D. Meanwhile, the free-energy model is employed to investigate the influences of mechanical stress and the temperature on the magnetostrictive effect of Terfenol-D in detail, and its predictions are coincident with some well-known experimental results including the temperature-dependent saturation nonlinearity and "overturn phenomenon". It indicates that the free-energy model can also effectively capture the nonlinear magnetic-elastic-thermal coupling characteristic of Terfenol-D. Some important physical parameters, such as the maximum magnetostrictive strain, the maximum piezomagnetic coefficient, are summarized, which can be used to optimize the performance of Terfenol-D in practical application. In addition, the free-energy model uses simple differential equation and algebraic equations, in which all of parameters have definite physical implications and can be easily determined by experiments. Thus, the free-energy model established in this article has very strong and wide practicability.