Stress field of a functionally graded coated inclusion of arbitrary shape
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Based on the theory of complex variable functions, the stress field in an infinite matrix containing an arbitrary shape inclusion with a functionally graded coating is analyzed. The elastic properties in the functionally graded coating change continuously and arbitrarily along the normal direction of the inclusion. By using the method of piecewise homogeneous layers and the technique of conformal mapping, the complex potential functions in the matrix, coating and inclusion are derived in the form of Laurent series and Faber series, respectively. The influences of different varying Young’s modulus on the interfacial stresses are discussed by numerical examples for various shape inclusions, including ellipse, triangle, square and rectangle. It is shown that the magnitude and distribution of interfacial stresses for arbitrary shape inclusions can be successfully designed and controlled by adding a functionally graded coating with proper varying elastic properties along the normal direction. The results for some special cases are compared with previous literature and found in good agreement.
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