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56
Bounds and extremal microstructures for twocomponent composites: A unified treatment based on the translation method
, 1996
"... ..."
2004 Eshelby problem of polygonal inclusions in anisotropic piezoelectric full and halfplanes
 J. Appl. Phys
, 2003
"... This paper studies the twodimensional Eshelby problem in anisotropic piezoelectric bimaterials. Assuming that the inclusion is an arbitrarily shaped polygon with uniform eigenstrain and eigenelectric fields, we derive the exact closedform solution by integrating analytically the linesource Gree ..."
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This paper studies the twodimensional Eshelby problem in anisotropic piezoelectric bimaterials. Assuming that the inclusion is an arbitrarily shaped polygon with uniform eigenstrain and eigenelectric fields, we derive the exact closedform solution by integrating analytically the linesource Green functions in the corresponding bimaterials. The required linesource Green functions are obtained in terms of the Stroh formalism and include six different interface models. Since the induced elastic and piezoelectric fields due to the eigenstrain and eigenelectric fields are given in the exact closed form in terms of simple elementary functions, those due to multiple inclusions can be superposed together. Benchmark numerical examples are also presented for the induced elastic and piezoelectric fields within a square inclusion due to a uniform hydrostatic eigenstrain with the bimaterials being made of typical quartz and ceramic.
EFFECTIVE STIFFNESS TENSOR OF COMPOSITE MEDIA: II. APPLICATIONS TO ISOTROPIC DISPERSIONS
, 1998
"... Accurate approximate relations for the effective elastic moduli of two and threedimensional isotropic dispersions are obtained by truncating, after thirdorder terms, an exact series expansion for the effective sti}ness tensor of ddimensional twophase composites "obtained in the _rst paper ..."
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Accurate approximate relations for the effective elastic moduli of two and threedimensional isotropic dispersions are obtained by truncating, after thirdorder terms, an exact series expansion for the effective sti}ness tensor of ddimensional twophase composites "obtained in the _rst paper # that perturbs about certain optimal dispersions. Our thirdorder approximations of the effective bulk modulus K e and shear modulus G e are compared to benchmark data, rigorous bounds and popular selfconsistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third!order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to
MarketShare Models
 Handbooks in Operations Research and Management Science
, 1993
"... polycrystals of grains containing cracks: ..."
Mixture Theories for Rock Properties
 Physics and Phase Relations, A Handbook of Physical Constants, Am. Geophys
, 1995
"... this article within bounds, we will say very little about anisotropy. Likewise, frequency dependent results and estimates (or bounds) for complex constants will be largely ignored. ..."
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Cited by 7 (3 self)
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this article within bounds, we will say very little about anisotropy. Likewise, frequency dependent results and estimates (or bounds) for complex constants will be largely ignored.
Averaging Theorems in Finite Deformation Plasticity
 Mechanics of Materials
, 1999
"... The transition from micro to macrovariables of a representative volume element (RVE) of a finitely deformed aggregate (e.g., a composite or a polycrystal) is explored. A number of exact fundamental results on averaging techniques, valid at finite deformations and rotations of any arbitrary hetero ..."
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Cited by 5 (0 self)
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The transition from micro to macrovariables of a representative volume element (RVE) of a finitely deformed aggregate (e.g., a composite or a polycrystal) is explored. A number of exact fundamental results on averaging techniques, valid at finite deformations and rotations of any arbitrary heterogeneous continuum, are obtained. These results depend on the choice of suitable kinematical and dynamical variables. For finite deformations, the deformation gradient and its rate, and the nominal stress and its rate, are optimally suited for the averaging purposes. A set of exact identities is presented in terms of these variables. An exact method for homogenization of an ellipsoidal inclusion in an unbounded finitely deformed homogeneous solid is presented, generalizing Eshelby’s method for application to finite deformation problems. In terms of the nominal stress rate and the rate of change of the deformation gradient, measured relative to any arbitrary state, a general phasetransformation problem is considered, and the concepts of eigenvelocity gradient and eigenstress rate are introduced. It is shown that the velocity gradient (and hence the nominal stress rate for rateindependent models) in an ellipsoidal region within an unbounded uniform and uniformly deformed solid, remains uniform when this region undergoes a uniform phase transformation corresponding to a constant eigenvelocity gradient. The generalized Eshelby tensor and its conjugate are defined and used to obtain the field quantities in an ellipsoidal inclusion which is embedded in an unbounded, uniformly deformed medium, leading to exact expressions for
Modeling and simulation of magnetic shapememory polymer composites
, 2006
"... gemeinschaft getragenen Sonderforschungsbereiches 611 an der Universität Bonn entstanden und als Manuskript vervielfältigt worden. Bonn, Oktober 2006 Modeling and simulation of magnetic shapememory polymer composites ..."
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gemeinschaft getragenen Sonderforschungsbereiches 611 an der Universität Bonn entstanden und als Manuskript vervielfältigt worden. Bonn, Oktober 2006 Modeling and simulation of magnetic shapememory polymer composites
The Composite Eshelby Tensors and Their Application to Homogenization,” submitted
, 2007
"... Summary. In recent studies, the exact solutions of the Eshelby tensors for a spherical inclusion in a finite, spherical domain have been obtained for both the Dirichlet and Neumann boundary value problems, and they have been further applied to the homogenization of composite materials [15], [16]. T ..."
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Summary. In recent studies, the exact solutions of the Eshelby tensors for a spherical inclusion in a finite, spherical domain have been obtained for both the Dirichlet and Neumann boundary value problems, and they have been further applied to the homogenization of composite materials [15], [16]. The present work is an extension to a more general boundary condition, which allows for the continuity of both the displacement and traction field across the interface between RVE (representative volume element) and surrounding composite. A new class of Eshelby tensors is obtained, which depend explicitly on the material properties of the composite, and are therefore termed ‘the Composite Eshelby Tensors’. These include the Dirichlet and the NeumannEshelby tensors as special cases. We apply the new Eshelby tensors to the homogenization of composite materials, and it is shown that several classical homogenization methods can be unified under a novel method termed the ‘Dual Eigenstrain Method’. We further propose a modified HashinShtrikman variational principle, and show that the corresponding modified HashinShtrikman bounds, like the Composite Eshelby Tensors, depend explicitly on the composite properties. 1
A circular inclusion in a finite domain I. The Dirichlet–Eshelby problem
 Acta Mech
, 2005
"... Summary. This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, selfsi ..."
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Summary. This is the first paper in a series concerned with the precise characterization of the elastic fields due to inclusions embedded in a finite elastic medium. A novel solution procedure has been developed to systematically solve a type of Fredholm integral equations based on symmetry, selfsimilarity, and invariant group arguments. In this paper, we consider a twodimensional (2D) circular inclusion within a finite, circular representative volume element (RVE). The RVE is considered isotropic, linear elastic and is subjected to a displacement (Dirichlet) boundary condition. Starting from the 2D plane strain Navier equation and by using our new solution technique, we obtain the exact disturbance displacement and strain fields due to a prescribed constant eigenstrain field within the inclusion. The solution is characterized by the socalled DirichletEshelby tensor, which is provided in closed form for both the exterior and interior region of the inclusion. Some immediate applications of the DirichletEshelby tensor are discussed briefly. 1