Energy functional is total energy of a certain system, as a functional of the system's state.
In the energy methods of simulating the dynamics of complex structures, a state of the system is often described as an element of an appropriate function space. To be in this state, the system pays a certain cost in terms of energy required by the state. This energy is a scalar quantity, a function of the state, hence the term functional. The system tends to develop from the state with higher energy (higher cost) to the state with lower energy, thus local minima of this functional are usually related to the stable stationary states. Studying such states is part of the optimization problems, where the terms energy functional or cost functional are often used to describe the objective function.
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