期刊
METALS
卷 12, 期 4, 页码 -出版社
MDPI
DOI: 10.3390/met12040582
关键词
equivalent eigenstrain principle; inhomogeneous inclusion; Green's function method; nonelliptical inclusion; arbitrary load
资金
- National Natural Science Foundation of China [12072254, 41630634]
This paper proposes a fundamental formulation for inhomogeneous inclusion problems based on the equivalent homogeneous inclusions, which significantly reduces the workload and enables analytical solutions. It allows for solving problems with arbitrarily connected and-shaped inhomogeneous inclusions and any kind of external load. This formulation is applicable for evaluating the effective properties of composite materials.
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.
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