The Design of Functional Gradient Materials with Inverse Homogenization Method

Author(s):  
Shi Wei Zhou ◽  
Qing Li
2008 ◽  
Vol 32 ◽  
pp. 245-250 ◽  
Author(s):  
Shi Wei Zhou ◽  
Qing Li

This study systemically presents an inverse homogenization method in the design of functional gradient materials, which gained substantial attention recently due to their layer-by-layer defined physical properties. Each layer of these materials is unilaterally constructed by periodically extended microstructural elements (namely base cells), whose effective properties can be decided by the homogenization theory in accordance with the material distribution within the base cell. The design objective is to minimize the summation of the least squares of the difference between corresponded entries in target and effective elasticity tensors. The method of moving asymptote drives the minimization of this positive objective function, which forces the effective values approach to the targets as closely as possible. The sensitivity of the effective elasticity tensors with respect to the design variables is derived from the adjoint variable method and it guides the minimization algorithm efficiently. To guarantee the connectivity between adjacent layers, non-design domains occupied by solid materials acting as connective bars are fixed in the design of base cells. Furthermore, nonlinear diffusion technique is introduced to avoid checkerboard patterns and blur boundaries in the microstructures. A series of two-dimensional examples targeted for the elasticity tensors with same extreme Poisson ratios but different densities in each layer are illustrated to highlight the computational material design procedure.


2005 ◽  
Vol 494 ◽  
pp. 167-174 ◽  
Author(s):  
R. Steinhausen ◽  
H.Th. Langhammer ◽  
A.Z. Kouvatov ◽  
C. Pientschke ◽  
Horst Beige ◽  
...  

In the field of applications of piezoelectric materials properties, functional gradient materials (FGM) are suitable for bending devices due to reduced internal mechanical stresses and lower production costs as well as for ultrasonic transducers because of their increased band width. This paper reports both on preparation, poling, characterization of FGM actuators, and on the description of suitable models of the poling and the bending processes. The calculations of the bending behavior show that the deflection at the end of the cantilever with a continuous gradient still reaches 2/3 of the deflection of a bimorph, whereas the maximum stress goes to zero, which is the main advantage of FGM compared to the commonly used bimorph devices. As a model system with well-defined electromechanical and dielectric properties of the homogeneous components the solid solution of BaTi1-xSnxO3 (BTS) with 0.075 £ x £ 0.15 was chosen. The FGMs approximated by a layered system with a one-dimensional gradient of the Sn-content were prepared both by successive uniaxial powder pressing and by tape casting with the doctor blade method. The chemical gradient was transformed into a gradient of the piezoelectric properties by a poling process. Several models were developed for the description of the non-trivial problem of the poling process in layered systems. The calculated data were compared with experimental results. It was shown that the very small electrical conductivity of the single layers generally cannot be neglected during the poling process and must be incorporated into more sophisticated models. The bending properties of several poled BTS structures with up to 4 layers were measured and discussed.


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