  Coupling effects among different physical fields substantially reflect the
conversion of energies from one form into another. For simple physical
processes, their governing or constitutive equations all satisfy the law of
conservation of energy. Then, analysis is extended to coupling effects. First,
it is found 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, energies are converted via work terms,
$(\beta_{ijk} E_i )_{,k} v_j$ and $(\gamma_{ijk} H_i)_{,k} v_j$, rather than
via 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, it is argued both effects are induced by
the Maxwell stress; moreover, their energy is purely electromagnetic and thus
both have no converse effects. During these processes, energy can be converted
in three different ways, i.e., via non-potential forces, via cross-dependence
of energy terms and directly via the electromagnetic interactions of ions and
electrons. In the end, general coupling processes which involve elastic,
electromagnetic fields and diffusion are also analyzed. The advantage of using
this energy formulation is that it facilitates discussions of the conversion of
energies and provides better physical insights into the mechanisms of these
coupling effects.
