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Inclusion problem in second gradient elasticity
Ma HS(马寒松); Hu GK; Wei YG(魏悦广); Liang LH(梁立红)
Source PublicationINTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
2018-11-01
Volume132Pages:60-78
ISSN0020-7225
AbstractThe Green's function and Eshelby tensors of an infinite linear isotropic second gradient continuum are derived for an inclusion of arbitrary shape. Particularly for spherical, cylindrical and ellipsoidal inclusions, Eshelby tensors and their volume averages are obtained in an analytical form. It is found that the Eshelby tensors are not uniform inside the inclusion even for a spherical inclusion, and their variations depend on the two characteristic lengths of second gradient theory. When size of inclusion is large enough compared to the characteristic lengths, the Eshelby tensor of the second gradient medium is reduced to the classical one, as expected. It is also demonstrated that the existing Green's functions and Eshelby tensors of couple stress theory, Aifantis, Kleinert and Wei-Hutchinson special strain gradient theories could be recovered as special cases. This work paves the way for constructing micromechanical method to predict size effect of composite materials, as shown for the effective modulus of particulate composite derived with the proposed theory. (C) 2018 Elsevier Ltd. All rights reserved.
KeywordGreen's function Eshelby tensor Second gradient Inclusion Effective modulus
DOI10.1016/j.ijengsci.2018.07.003
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Indexed BySCI ; EI
Language英语
WOS IDWOS:000446151900005
WOS KeywordPARTICLE-SIZE ; MATRIX COMPOSITES ; GREENS-FUNCTION ; FIELDS ; DEFORMATION ; PLASTICITY ; CONTINUA ; FRACTURE
WOS Research AreaEngineering, Multidisciplinary
WOS SubjectEngineering
Funding OrganizationNational Natural Science Foundation of China [11572329, 11432014, 11672301, 11372318, 11672296, 11521202] ; Strategic Priority Research Program of the Chinese Academy of Sciences [XDB22040501]
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/77933
Collection非线性力学国家重点实验室
Affiliation1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China
2.Beijing Inst Technol, Sch Aerosp Engn, Beijing 100081, Peoples R China
3.Peking Univ, Coll Engn, Beijing 100871, Peoples R China
Recommended Citation
GB/T 7714
Ma HS,Hu GK,Wei YG,et al. Inclusion problem in second gradient elasticity[J]. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE,2018,132:60-78.
APA 马寒松,Hu GK,魏悦广,&梁立红.(2018).Inclusion problem in second gradient elasticity.INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE,132,60-78.
MLA 马寒松,et al."Inclusion problem in second gradient elasticity".INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 132(2018):60-78.
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