  Hierarchical (first-order) structured deformations are studied from the
variational point of view. The main contributions of the present research are
the first steps, at the theoretical level, to establish a variational framework
to minimize mechanically relevant energies defined on hierarchical structured
deformations. Two results are obtained here: (i) an approximation theorem and
(ii) the assignment of an energy to a hierarchical structured deformation by
means of an iterative procedure. This has the effect of validating the proposal
made in [Deseri & Owen: Elasticity with hierarchical disarrangements: a field
theory that admits slips and separations at multiple submacroscopic levels.
J.~Elast., 135 (2019), 149--182] to study deformations admitting slips and
separations at multiple submacroscopic levels. An explicit example is provided
to illustrate the behavior of the proposed iterative procedure and relevant
directions for future research are highlighted.
