The problem of a functionally graded plane with a circular inclusion under a uniform antiplane eigenstrain is investigated, where the shear modulus varies exponentially along the direction. By introducing a new function which satisfies the Helmholtz equation, the general solution to the original problem is derived in terms of series expansion. Numerical results are then presented which demonstrate clearly that for a functionally graded plane, the strain and stress fields inside the circular inclusion under uniform antiplane eigenstrains are intrinsically nonuniform. This phenomenon differs from the corresponding homogeneous material case where both the strain and stress fields are uniform inside the circular inclusion.
A Functionally Graded Plane With a Circular Inclusion Under Uniform Antiplane Eigenstrain
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Wang, X., Pan, E., and Roy, A. K. (January 11, 2008). "A Functionally Graded Plane With a Circular Inclusion Under Uniform Antiplane Eigenstrain." ASME. J. Appl. Mech. January 2008; 75(1): 014501. https://doi.org/10.1115/1.2745391
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