Mechanical responses of solid materials are governed by their material properties. The solutions for estimating and predicting the mechanical responses are extremely difficult, in particular for non-homogeneous materials. Among these, there is a special type of materials whose properties are variable only along one direction, defined as graded materials or functionally graded materials (FGMs). Examples are plant stems and bones. Artificial graded materials are widely used in mechanical engineering, chemical engineering, biological engineering, and electronic engineering.

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