Justification and refinement of Winkler-Fuss hypothesis

Kaplunov, J.; Prikazchikov, D.; Sultanova, L.

Abstract

Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that the Winkler-Fuss hypothesis is valid only for a sufficiently high contrast in the stiffnesses of the layer and the half-space. As an alternative, a uniformly valid non-local approximation is proposed. Higher-order corrections to the Winkler-Fuss formulation, such as the Pasternak model, are also studied.

Citation

Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2018). Justification and refinement of Winkler-Fuss hypothesis. Zeitschrift für Angewandte Mathematik und Physik, 69, Article 80. https://doi.org/10.1007/s00033-018-0974-1

• Journal Article Type: Article
• Acceptance Date: May 1, 2018
• Publication Date: May 28, 2018
• Journal: Zeitschrift fur angewandte Mathematik und Physik
• Print ISSN: 0044-2275
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 69
• Article Number: 80
• DOI: https://doi.org/10.1007/s00033-018-0974-1
• Keywords: soft thin coating, Asymptotic, Winker-Fuss model, Contrast, Substrate
• Publisher URL: https://doi.org/10.1007/s00033-018-0974-1