“…Using asymptotic analysis, several classical reduced models have been mathematically developed over the years. The asymptotic method was originally introduced by Lions [22] and since then it has been extensively used to derive and justify reduced models for elastic plates and shells [10][11][12], elastic beams [4,19,21,31,[40][41][42][43], viscoelastic beams [28,29] and also for elastic beams in contact with a foundation (see [20,30,44,47], the last two to justify and generalize contact models found in [17,37]). The success of this method is due to the inherent small geometrical parameters involved (thickness of plates and shells and diameter of the cross-section in beams).…”