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Mircomechanics of defects in solids. 2nd, rev. ed. (English) Zbl 0652.73010

Mechanics of Elastic and Inelastic Solids, 3. Dordrecht/Boston/Lancaster: Martinus Nijhoff Publishers, a member of the Kluwer Academic Publishers Group. XIII, 587 p.; Dfl. 345.00; $ 162.00; £113.95 (1987).
This book is the revised second edition of volume three in the series Mechanics of Elastic and Inelastic Solids. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications covering a broad area related to the mechanical behavior of materials: plasticity, fracture and fatigue, constitutive equations, composite materials, polycrystals, etc. These subjects are treated in this book by means of a unified method called by the author “eigenstrain method”, which is a generic name for such nonelastic strains as thermal expansion, phase transformation and misfit strains. In particular, problems related to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.
This book contains seven chapters and an appendix. In chapter 1 the definition of the eigenstrains is given and the general solutions for elastic fields for given eigenstrains are expressed by Fourier integrals and Green’s functions for static and dynamic cases. The general expressions of elastic fields for inclusions, dislocations and disclinations are given and the stress discontinuity on boundaries of inclusions and the incompatibility of eigenstrains are discussed as general theories. Chapter 2 is devoted to the elastic fields caused by ellipsoidal inclusions in an isotropic infinite body when the elastic moduli are the same for inclusions and matrices. In the 3rd chapter are investigated the elastic fields due to ellipsoidal inclusions in anisotropic materials. The presented results are applicable to any distribution of eigenstrains given in an ellipsoidal inclusion. In chapter 4 the ellipsoidal inhomogeneity is defined as an ellipsoidal subdomain of a material where the elastic moduli of the material differ from those of the matrix. Voids, cracks and precipitates might be examples of such inhomogeneities. The following chapter contains the analysis of the crack problem considered as a special case of an ellipsoidal void when one of the principal axes of the ellipsoid becomes vanishingly small. The Griffith fracture criterion and stress intensity factors of cracks are discussed. The elastic field caused by a dislocation loop and applications to the continuum plasticity are discussed in chapter six. In the last chapter the author shows how inclusion problems are applied to estimate macroscopic mechanical properties of aggregates, i.e. particle bearing materials and polycrystalline materials. In these materials internal stresses usually develop as a result of plastic deformation which is inherently heterogeneous due to the heterogeneity of the constituent medium. These internal stresses can be calculated in a straightforward manner by using the methods described above.
The readers of this book should not possess particular previous knowledge, as the necessary mathematics and physics implied are explained in the text and appendix. The subject matter is most clearly and rigorously treated. This monography is recommended to students or scientists interested in continuum mechanics especially in micromechanics of defects in the solid state.
Reviewer: N.Sandru

MSC:

74E05 Inhomogeneity in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74A60 Micromechanical theories
74M25 Micromechanics of solids
74E10 Anisotropy in solid mechanics