Functional Gradient Material (FGM) is one of the most promising heterogeneous materials for its spatial continuity of material properties and functional flexibility. FGM is a well-studied research topic. In this paper, we utilize Finite Element Analysis (FEA) method to model objects with spatially varying material property. A two-stage optimization framework including Monte Carlo based global optimizer and gradient descent based local optimizer is proposed to achieve the optimal material composition in response to different user defined objectives. An error diffusion based halftoning technique is utilized to convert the continuous material distribution into discrete material distribution for viable manufacturing. The transition of the material properties are governed by predefined equations and only a few coefficients instead of large number of elements are to be optimized, therefore this optimization process is more computationally efficient than traditional techniques. Meanwhile it can automatically guarantee the smoothness of material transition along the body. Such design and optimization method has the potential to enable interactive multiple material modeling and simulation. Several experiments are carried out to demonstrate its efficiency and effectiveness.

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