Analytical solutions for coated circular inhomogeneity with non-uniform axisymmetric eigenstrain distribution

Yan, Jiyang; Zhu, Junbei; Ma, Lifeng

Abstract

In this paper, a general model for coated circular inhomogeneous inclusion problems is proposed and studied, where non-uniform axisymmetric eigenstrains are independently distributed within the circular zone and annular zone (coating layer). The main difficulties are from the dissimilarity of three-phase materials, the non-uniform axisymmetric eigenstrain distribution, and the presence of intermediate annularity, which are hardly treated within the classical Eshelby inclusion mechanics. By employing the equivalent eigenstrain principle, these challenges can be completely tackled, and a general explicitly analytical solution is obtained. From this solution, a couple of solutions for typical inclusion problems are readily degenerated, which have been derived with great efforts in literature. With the general model and its solution, the analytical solution for the coated hollow-cored inhomogeneous inclusion problem with non-uniform axisymmetric eigenstrain is provided, and an eigenstrain-based nano-inclusion model is subsequently proposed. The applications of coated circular inhomogeneity with eigenstrains can be found in coated fiber composites, thermoelastic problems, and micro- & nano-mechanics.

Citation

Yan, J., Zhu, J., & Ma, L. (2022). Analytical solutions for coated circular inhomogeneity with non-uniform axisymmetric eigenstrain distribution. International Journal of Solids and Structures, 243, Article 111567. https://doi.org/10.1016/j.ijsolstr.2022.111567

• Journal Article Type: Article
• Acceptance Date: Mar 11, 2022
• Online Publication Date: Mar 19, 2022
• Publication Date: May 15, 2022
• Deposit Date: Jun 30, 2023
• Publicly Available Date: Jul 10, 2023
• Journal: International Journal of Solids and Structures
• Print ISSN: 0020-7683
• Electronic ISSN: 1879-2146
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 243
• Article Number: 111567
• DOI: https://doi.org/10.1016/j.ijsolstr.2022.111567
• Keywords: Applied Mathematics; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; General Materials Science; Modeling and Simulation
• Public URL: https://nottingham-repository.worktribe.com/output/22454095
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0020768322001123?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Analytical solutions for coated circular inhomogeneity with non-uniform axisymmetric eigenstrain distribution; Journal Title: International Journal of Solids and Structures; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.ijsolstr.2022.111567; Content Type: article; Copyright: © 2022 Elsevier Ltd. All rights reserved.