On the Asymptotic Derivation of Winkler-Type Energies from 3D Elasticity

We show how bilateral, linear, elastic foundations (i.e., Winkler foundations) often regarded as heuristic, phenomenological models, emerge asymptotically from standard, linear, three-dimensional elasticity. We study the parametric asymptotics of a non-homogeneous linearly elastic bi-layer attached to a rigid substrate as its thickness vanishes, for varying thickness and stiffness ratios. By using rigorous arguments based on energy estimates, …