Abstract
This paper considers the unusual behavior of functionally graded materials/structures when the surface effect is involved. It is found that on the assumption that the surface energy is not positive semi-definite, the solution can be non-unique. Several examples are given for simple spherically-symmetric and axisymmetric FGM bodies with surface effects characterized by Gurtin-Murdoch surface elasticity. The results show that the conditions for non-uniqueness of solution emerge when the magnitude of negative effective surface modulus is of the order of a characteristic dimension of the problem multiplied by the bulk modulus near the surface, which is quite different from that for homogeneous materials.
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