The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle
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...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Metals |
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| Online Access: | https://www.mdpi.com/2075-4701/12/4/582 |
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| author | Lifeng Ma Alexander M. Korsunsky |
| author_facet | Lifeng Ma Alexander M. Korsunsky |
| author_sort | Lifeng Ma |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T10:32:11Z |
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| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-03-09T10:32:11Z |
| publishDate | 2022-03-01 |
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| spelling | doaj.art-8c2ccea8e3e943cc8dd8185b310e9bde2023-12-01T21:13:49ZengMDPI AGMetals2075-47012022-03-0112458210.3390/met12040582The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain PrincipleLifeng Ma0Alexander M. Korsunsky1Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UKDepartment of Engineering Science, University of Oxford, Oxford OX1 3PJ, UKIn 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.https://www.mdpi.com/2075-4701/12/4/582equivalent eigenstrain principleinhomogeneous inclusionGreen’s function methodnonelliptical inclusionarbitrary load |
| spellingShingle | Lifeng Ma Alexander M. Korsunsky The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle Metals equivalent eigenstrain principle inhomogeneous inclusion Green’s function method nonelliptical inclusion arbitrary load |
| title | The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle |
| title_full | The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle |
| title_fullStr | The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle |
| title_full_unstemmed | The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle |
| title_short | The Fundamental Formulation for Inhomogeneous Inclusion Problems with the Equivalent Eigenstrain Principle |
| title_sort | fundamental formulation for inhomogeneous inclusion problems with the equivalent eigenstrain principle |
| topic | equivalent eigenstrain principle inhomogeneous inclusion Green’s function method nonelliptical inclusion arbitrary load |
| url | https://www.mdpi.com/2075-4701/12/4/582 |
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