We are interested in this paper in recovering lacking data on some part of a domain boundary, from the knowledge of Cauchy data on the other part. It is first proved that the desired solution is the unique fixed point of some appropriate operator, which naturally gives rise to an iterative process that is proved to be convergent. Discretization provides an additional regularization: the algorithm reads as a least square fitting of the given data, with a regularization term the effect of which fades as iterations go on. Displayed numerical results highlight its accuracy, as well as its robustness.
An asymptotic expansion method is applied to nonlinear three-dimensional elastic straight slender rods. Nonlinear ordinary differential equations for approximate displacements and explicit formulas for approximate stress distributions are obtained. Mathematical properties of these models are studied.R~sum~. On applique la m&hode des d6veloppements asymptotiques ~ des poutres tridimensionnelles droites, 61anc+es et non lin6airement 61astiques. On en d6duit des 6quations diff6ren-tielles ordinaires non lin6aires pour des d~placements approch+s, ainsi que des formules explicites pour des approximations des distributions de contraintes. On 6tudie les propri6t6s math6matiques de ces mod61es.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.