Universal relations for an elastic elliptical inclusion under arbitrary plane loading

Conference · Sun Dec 31 04:00:00 EST 1995

OSTI ID:175313

Gong, S X ^[1]

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1. Univ. of Regina, Saskatchewan (Canada)

Inclusion and inhomogeneity problems play an important role in the micromechanical analysis of advanced composite materials which contain in their microstructure various defects or inhomogeneities in the form microcracks, microvoids, transformed inclusions and reinforcing fibers. Since the pioneering work of Eshelby, considerable effort has been devoted to the determination of the elastic fields induced by inclusions and inhomogeneities. However, most of the available solutions are restricted to a single inclusion, an infinite matrix and special loading conditions such as remote uniform loading. Recent developments have been made for the analysis of circular inhomogeneities under arbitrary loading, and general relations have also been derived for an elastic elliptical inclusion under arbitrary antiplane loading. In the present paper, a unified treatment is provided for an elastic elliptical inclusion undergoing uniform eigenstrains inside the inclusion and subjected to arbitrary plane loading in the surrounding matrix. The analysis is based on the complex potentials of Muskhelishvili, Laurent series expansion method and the conformal mapping technique. New stress-free displacement potentials are introduced to simplify the complex variable formulation where both inclusion and inhomogeneity problems are treated within the same framework. General forms of the stress functions inside the inclusion and the matrix are derived in both transformed and physical planes. These relations are universal in the sense of being applicable to arbitrary loading conditions and being valid for both finite and infinite matrix. The relations can be used as building blocks for dealing with more complex problems involving a wide variety of geometry and loading conditions.

• OSTI ID: 175313
• Report Number(s): CONF-950686--
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
COMPOSITE MATERIALS
CONFORMAL MAPPING
CRACKS
DEFECTS
DISLOCATIONS
FIBERS
INCLUSIONS
MICROSTRUCTURE
SERIES EXPANSION