Eshelby tensors for a spherical inclusion in microelongated elastic fields |
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| Affiliation: | 1. Faculty of Science and Letters, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey;2. Faculty of Art and Sciences, Işık University, 34398, Maslak, Istanbul, Turkey;1. Laboratory of Strength of Materials and Micromechanics, Department of Civil Engineering University of Thessaly, Volos, 38336, Greece;2. Mechanics Division, National Technical University of Athens, 5 Heroes of Polytechnion Ave., Zographou, GR-15773, Greece;1. Research Scholar, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India;2. Professor, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India;1. Department of Electrical Energy, Systems and Automation, Faculty of Engineering and Architecture, Ghent University, Belgium;2. Faculty of Computer Science and Systems Engineering, Department of Creative Informatics, Kyushu Institute of Technology, Japan;3. Polytechnic University of Marche, Ancona, Italy;4. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;5. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;6. Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde 903, B-9052 Zwijnaarde, Belgium |
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| Abstract: | Eshelby tensors are found for a spherical inclusion in a microelongated elastic field. Here, a special micromorphic model is introduced to describe the damaged material which defines the damage as the formation and the growth of microcracks and microvoids occurred in the material at the microstructural level. To determine the new material coefficients of the model, an analogy is established between the damaged body and the composite materials and then Mori–Tanaka homogenization technique is considered to obtain overall material moduli. Following this idea, the determination of the Eshelby tensors which establish the relation between the strains of the matrix material and of the inclusion becomes the first task. Introducing the concept of eigenstrain and microeigenstrain, the general constitutive theory is given for a homogeneous isotropic centrosymmetric microelongated media with defects. Then by the use of Green’s functions, micro and macro elastic fields are presented for the case of spherical inclusions embedded in an infinite microelongated material. Thus, the Eshelby tensors are obtained for a microelongated elastic field with a spherical inclusion and it is also shown that the classical Eshelby tensors can be obtained as a limit case of the microelongation. |
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