Elastic fields of inclusions in anisotropic media

Abstract

The displacement and stress fields caused by eigenstrains (thermal expansion, plastic strain, phase transformation, etc.) distributed uniformly inside a domain 8 of an infinitely extended anisotropic medium are expressed in a series form and also in an interesting integral form. These forms provide not only a method of stress analysis but also enable an investigation of Eshelby's proposition that the stress in an ellipsoidal domain is constant.The special case that SZ is a flat ellipse leads to an extremely simple result. Die Verschiebungs-und Spannungsfelder, die durch Eigendehnungen (thermische Ausdehnung, plastische Dehnung, Phasentransformation, etc.) verursacht werden, die gleichformig in einer Domane SZ in einem unendlich angedehntem Medium verteilt sind, werden in einer Reihenentwicklung und ebenfalls in einer interessanten Integralform ausgedruckt. Diese Formeln ergeben nicht nur eine Methode fur die Spannungsanalyse, sondern ermoglichen eine Untersuchung des Vorschlags von Eshelby, daB die Spannung in einer elliptischen Domane eine Konstante ist. Der Spexialfall, daB SZ eine flache Ellipse ist, fuhrt zu einem extrem einfachen Ergebnis. I) This research was supported by the Atomic Energy Commission through Northwestern 2, Leave of absence from Meiji University, Tokyo, Japan.University.

Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. II: The vigdergauz microstructure

“…The orientation and eccentricity of such an optimal ellipse is uniquely defined by the value of the average strain (Barnett et al, 1974;Kaganova and Roitburd, 1987;Kardonski and Roitburd, 1972;Kinoshita and Mura, 1971;Lee, Barnett and Aaronson, 1977;Pineau, 1976). The above calculation recovers those parameters precisely, by realizing the optimal ellipse as a limit of microstructures that are optimal for any volume fraction.…”

Substructures of Gas-Ion-Irradiation-Induced Surface Blisters in Silicon Studied by Cross-Sectional Transmission Electron Microscopy

“…5(a)], which suggests that the projected thickness is less along the defects. It has been known 23) that the shape and orientation of coherent precipitates in cubic metals and alloys are determined by the elastic anisotropy of the matrix: when the internal pressure is hydrostatic and the inequality C 0 ð¼ ðC 11 À C 12 Þ=2Þ < C 44 holds between the elastic constants of the matrix, the precipitate shape that is elastically most stable is the disc on the {001} plane. On the other hand, if C 0 > C 44 , the most stable shape is needle-like extending along the h111i direction.…”

Seismic velocity anisotropy in a medium cotaining oriented cracks. Transversely isotropic case.

“…Total strain is given by a summation of all strains including elastic strain, thermal strain, strain, eij, satisfies Hooke's law. Eigenstrain, a general name given by KINOSHITA and MURA (1971) for the stress-free strain in ESHELBY (1957), includes strains that are not related uniquely to stress, e.g., initial strains, plastic strains, strains due to phase transformations or thermal expansion, etc. (MURA and CHENG, 1977;MURA and MORI, 1976).…”