High order imperfect interface modeling of thin layers in two-dimensional potential and linear elasticity problems

Abstract

The dissertation develops a novel complex variable-based implementation of the Bövik-Benveniste methodology. This approach is used to derive higher order imperfect interface models for two-dimensional potential and linear elasticity problems with thin layers. The major advantage of the proposed approach over existing asymptotic approaches is straightforward derivation of jump conditions that involve high order surface differential operators. Additionally, this dissertation analyzes the main assumptions of the Bövik-Benveniste methodology and discusses the advantages of higher order models. Unlike lower order models, the derived higher order models can accurately represent layers that are significantly softer or stiffer than the adjacent bulk materials or exhibit varying curvature. For potential problems, a clear hierarchy of arbitrary order imperfect interface models is formulated and explicit expressions of jump conditions associated with the models up to the third order are provided. For the problems of elasticity, the models are formulated up to the third order. All models are obtained with proposed approach are compared with existing models of different orders, their limiting behavior is validated with respect to known interface regimes, and improved accuracy of higher order models is illustrated for benchmark examples. The developed higher order models could be used for i) establishing the links between phenomenological- and asymptotic-based imperfect interface models, ii) expanding current classification of imperfect interfaces, and iii) revealing the links between imperfect interface models and the beam, shell, and plate theories, thus, clarifying the applicability of those theories for modeling thin layers.