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The boundary conditions for the normal displacement w and its derivatives are given in the figure. The compressive loads U are distributed uniformly along the vertical and horizontal edges.
This and the next 2 images are from:
G. Parry, A. Cimetiere, C. Coupeau, J. Colin, J. Grilhe (Laboratoire de Métallurgie Physique, UMR 6630 du CNRS, Université de Poitiers, BP 30179, 86962 Futuroscope Cedex, France),
“Stability diagram of unilateral buckling patterns of strip-delaminated films”, Phys. Rev. E, 74 (2006), p. 066601, https://doi.org/10.1103/PhysRevE.74.066601
ABSTRACT: Thin films deposited on substrates are usually submitted to large residual compression stresses, causing delamination and buckling of the film into various patterns. The present study is focused on the different equilibria arising on strip-shaped delaminated areas. The three most common types of buckling patterns observed on such strips are known as the straight-sided wrinkles, bubble pattern, and telephone cord blisters. The stability of those equilibria as a function of the two stress components of the loading is investigated. The Föppl–Von Karman model for elastic plates is used for theoretical aspects. The post-critical equilibrium paths of the buckling patterns are investigated numerically by means of the finite-element method. The substrate is assumed to be rigid and the contact to be frictionless. The equilibrium solutions can be classified into families of homologous equilibria allowing the identification of dimensionless parameters for the study of stability. A mapping of the different stable post-critical equilibria is given. It is shown that the straight-sided wrinkles and the bubbles are associated with anisotropy of stresses and/or of elastic properties, whereas the telephone cords are stable at high isotropic stresses. The morphological transitions are experimentally evidenced by in situ atomic force microscopy observations of a nickel 50−nm-thick film under stress.
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