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ISSN: 1940-4352 Online

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Year 2004, Volume 2 / Issue 1

DOI: 10.1615/IntJMultCompEng.v2.i1

Pages: 172

DOI: 10.1615/IntJMultCompEng.v2.i1.20

Article price - $35.00

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

Q.-S. 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.

pages 12

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