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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v2.i1.20
12 pages

Green's Function and Eshelby's Fields in Couple-Stress Elasticity

Quanshui Zheng
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Z.-H. Zhao
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China


Conventional micromechanical schemes for estimating effective properties of composite materials in the matrix-inclusion type have no dependence upon absolute sizes of inclusions. However, there has been more and more experimental evidence that severe strain-gradient may result in remarkable size effects to mechanical behavior of materials. The strain field of an unbounded isotropic homogeneous elastic body containing a spherical inclusion subject to a uniform farfield stress may have very sharp strain-gradient within a surrounding matrix region of the inclusion, whenever the inclusion size would be very small. Consequently, the strain field variation in the whole matrix region of a composite with highly concentrated very small inclusions would be violent. Therefore, it is necessary to develop a micromechanical scheme in which the matrix phase is treated as a nonconventional material, and both the inclusion phases and the composite itself as an effective medium are treated as conventional materials. Such a scheme has been reported, with interesting applications. This scheme is based on the results of Green's functions and Eshelby's fields in couple-stress elastic theory. A thorough derivation of these results is given in the present paper. The main reason for choosing the couple-stress theory among various nonconventional theories of elasticity is that it contains the least number of material constants, in order to establish a simplest possible micromechanical scheme for taking account of absolute sizes.