Titlebook: Continuum Micromechanics; Theory and Applicati Dazhi Jiang Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive licen

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,Eshelby’s Inclusion and Inhomogeneity Problem,nd orientation during deformation. We discuss the powerful method of John Douglas Eshelby (1916–1981) in this Chapter which solves the problem of a deformable ellipsoid. The point force and equivalent inclusion method of Eshelby’s can be applied to many other problems, such as deformation in and aro

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Viscous Inclusions in Anisotropic Materials,ials. In Chap. ., we presented the solutions for the classic inclusion/inhomogeneity problem (Eshelby, Proc R Soc Lond Ser A- 241(1226):376–396, 1957; Eshelby, Proc R Soc Lond Ser A- 252(1271):561–569, 1959) of an elastic inclusion/inhomogeneity in an isotropic elastic medium. The solutions have bee

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Two-Dimensional Inclusion Problems,sing the Green function and integral formalism as Chap. . for 3D problems..In Chaps. . and ., we have developed formal and, where possible, explicit solutions for a 3D elastic (or viscous) ellipsoid in an infinite elastic (or viscous) medium. Two-dimensional (2D) inclusion problems may be regarded a

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Effective Stiffnesses of Heterogeneous Materials, and strain. We introduced the Voigt and Reuss averages, which are, respectively, based on the uniform strain and uniform stress assumptions. These two averages are upper and lower bounds for the properties of the “average” material. In Earth Sciences, phenomenological approaches have been proposed

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Application Example 1: An Elastic Prolate Object in a Viscous Matrix,ased on Jeffery’s (Proc R Soc Lond Ser A-Containing Papers of a Mathematical and Physical Character 102(715):161–179, 1922) original equations on the traction forces the viscous fluid exerts on the object’s surface [Forgacs and Mason (J Colloid Sci 14(5):457–472, 1959); Goldsmith and Mason (The micr

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Panacea

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,Generalization of Eshelby’s Formalism and a Self-Consistent Model for Multiscale Rock Deformation,linear rheology (either elastic or Newtonian viscous). We have also presented methods to evaluate the formal solutions numerically. In Chaps. .–., we applied the theory to some geology problems, assuming that the rheology is linear and the problems can be approximated by “a single ellipsoid in an in

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Rotation of Rigid Objects in Homogeneous Flows,a rigid ellipsoid in slow viscous flows is combined with the rotation equation to form an initial value problem for the motion of a rigid ellipsoid in viscous flow. The problem is solved analytically for a spheroid in monoclinic flows. The problem is solved numerically for more general situations. M