Analytical derivation of cosserat moduli via homogenization of heterogeneous elastic materials

被引：0
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作者：
Bigoni, D. [1 ]
Drugan, W.J. [1 ,2 ]
机构：
[1] Dipartimento di Ingegneria Meccanica e Strutturale, Universita di Trento, Via Mesiano 77, 38050 Povo, Trento, Italy
[2] Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706-1687
来源：
Journal of Applied Mechanics, Transactions ASME | 2007年 / 74卷 / 04期
关键词：
Why do experiments detect Cosserat-elastic effects for porous; but not for stiff-particlereinforced; materials? Does homogenization of a heterogeneous Cauchy-elastic material lead to micropolar (Cosserat) effects; and if so; is this true for every type of heterogeneity? Can homogenization determine micropolar elastic constants? If so; is the homogeneous (effective) Cosserat material determined in this way a more accurate representation of composite material response than the usual effective Cauchy material? Direct answers to these questions are provided in this paper for both two- (2D) and three-dimensional (3D) deformations; wherein we derive closed-form formulae for Cosserat moduli via homogenization of a dilute suspension of elastic spherical inclusions in 3D (and circular cylindrical inclusions in 2D) embedded in an isotropic elastic matrix. It is shown that the characteristic length for a homogeneous Cosserat material that best mimics the heterogeneous Cauchy material can be derived (resulting in surprisingly simple formulae) when the inclusions are less stiff than the matrix; but when these are equal to or stiffer than the matrix; Cosserat effects are shown to be excluded. These analytical results explain published experimental findings; correct; resolve and extend prior contradictory theoretical (mainly numerical and limited to two-dimensional deformations) investigations; and provide both a general methodology and specific results for determination of simple higher-order homogeneous effective materials that more accurately represent heterogeneous material response under general loading conditions. In particular; it is shown that no standard (Cauchy) homogenized material can accurately represent the response of a heterogeneous material subjected to a uniform plus linearly varying applied traction; while a homogenized Cosserat material can do so (when inclusions are less stiff than the matrix). Copyright © 2007 by ASME;
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页码：741 / 753
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