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Mathematics and Mechanics of Solids
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An Elliptic Inhomogeneity Subjected to a General Class of Nonuniform Remote Loadings in Finite Elasticity

C.I. Kim

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada

P. Schiavone

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada

We consider a composite material containing an elastic elliptic inhomogeneity which is assumed to be perfectly bonded to a surrounding matrix of similar elastic material. In fact, both the inhomogeneity and the matrix belong to the same class of compressible hyperelastic materials of harmonic-type but each has its own distinct material properties. We consider finite plane deformations of the inhomogeneity-matrix system and obtain the complete solution when the system is subjected to classes of nonuniform remote (Piola) stress characterized by stress functions described by general polynomials of order n ≥ 1 in the corresponding complex variable z used to describe the matrix.

Key Words: Elastic inhomogeneity • finite elasticity • harmonic materials • nonuniform remote loading • complex variable methods

This version was published on June 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 4, 421-442 (2009)
DOI: 10.1177/1081286507081494
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