Functionally Graded Materials
A functionally graded material (FGM) is a type of material whose composition and/or function is designed to change continuously within the solid. In nature, we can see examples of FGMs in bamboo, bones, and teeth. In each case, there is a hard wear-resistant exterior that smoothly transitions to a soft interior.
With respect to manufactured items, FGMs are constructed for complex requirements, such as the heat shield of a rocket or bone implants for humans. The gradual transition between the heat or corrosion resistant outer layer (often made of a ceramic material) and the tough metallic base material increases in most cases the lifetime of the component. FGMs are of interest for a wide range of applications: thermal barrier coatings for turbine blades (electricity production), armor protection for military applications, fusion energy devices, biomedical, etc.
Oak Ridge National Laboratory has developed a unique 3D code for elastic analysis in an FGM. The algorithm is based on a boundary integral equation formulation for exponential grading, utilizing the FGM Green's function (derived in previous ASCR sponsored research) and its derivative. The calculations were run on the Oak Ridge Institutional Cluster, which consists of 526 dual core 3.4 GHz Intel Xeon processors, for a total of 1052 cpus with a peak performance of 7.154 Teraflops. Each dual node/core has 4 gigabytes of RAM.
A domain decomposition strategy allows the analysis of FGMs where in the grading direction is spatially varying. Although successful finite element codes for modeling FGMs exist, the integral equation formulation facilitates more accurate simulations by significantly simplifying the required re-meshing task for certain key problems (e.g., crack propagation analysis, design optimization). By using simulations to provide the information needed to optimize the grading function of the FGM, engineers and scientists are able to avoid costly trial and error experiments.
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