Abstract: Coupling effects among different physical fields reflect the conversion of energies from one field into another substantially. For simple physical processes, their governing or constitutive equations all satisfy the law of conservation of energy (LCE). Then, an analysis is extended to the coupling effects. First, for the linear direct and converse piezoelectric and piezomagnetic effects, their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields. However, the energies are converted via the work terms, $(\beta_{ijk} E_i)_{,k} v_j$ and $(\gamma_{ijk} H_i)_{,k} v_j$, rather than via the energy terms, $\beta_{ijk} E_i e_{jk}$ and $\gamma_{ijk} H_i e_{jk}$. Second, for the generalized Villari effects, the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy. Third, for electrostriction and magnetostriction, both effects are induced by the Maxwell stress. Moreover, their energies are purely electromagnetic and thus both have no converse effects. During these processes, the energies can be converted in three different ways, i.e., via the non-potential forces, via the cross-dependence of the energy terms, and directly via the electromagnetic interactions of ions and electrons. In the end, the general coupling processes which involve elastic, electromagnetic fields and diffusion are also analyzed. The advantages of using this energy formulation are that it facilitates discussion of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.

Key words: piezoelectricity, piezomagnetism, Villari effect, electrostriction, magnetostriction