The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle

Ma, Lifeng; Korsunsky, Alexander M.

Abstract

In this paper, and on the basis of the equivalent eigenstrain principle, a fundamental formulation for inhomogeneous inclusion problems is proposed, which is to transform the inhomogeneous inclusion problems into auxiliary equivalent homogenous inclusion problems. Then, the analysis, which is based on the equivalent homogenous inclusions, would significantly reduce the workload and would enable the analytical solutions that are possible for a series of inhomogeneous inclusion problems. It also provides a feasible way to evaluate the effective properties of composite materials in terms of their equivalent homogenous materials. This formulation allows for solving the problems: (i) With an arbitrarily connected and shaped inhomogeneous inclusion; (ii) Under an arbitrary internal load by means of the nonuniform eigenstrain distribution; and (iii) With any kind of external load, such as singularity, uniform far field, and so on. To demonstrate the implementation of the formulation, an oblate inclusion that interacts with a dilatational eigenstrain nucleus is analyzed, and an explicit solution is obtained. The fundamental formulation that is introduced here will find application in the mechanics of composites, inclusions, phase transformation, plasticity, fractures, etc.

Citation

Ma, L., & Korsunsky, A. M. (2022). The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle. Metals, 12(4), Article 582. https://doi.org/10.3390/met12040582

• Journal Article Type: Article
• Acceptance Date: Mar 25, 2022
• Online Publication Date: Mar 29, 2022
• Publication Date: 2022-04
• Deposit Date: Jun 30, 2023
• Publicly Available Date: Jul 6, 2023
• Journal: Metals
• Electronic ISSN: 2075-4701
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 4
• Article Number: 582
• DOI: https://doi.org/10.3390/met12040582
• Keywords: General Materials Science; Metals and Alloys
• Public URL: https://nottingham-repository.worktribe.com/output/22454107
• Publisher URL: https://www.mdpi.com/2075-4701/12/4/582