Modern piezoelectric structures offer certain performance advantages over conventional ones due to their capability of converting electrical energy into mechanical energy and vice versa. In recent years composites with a continuously change of the material properties are getting increasing attention in advanced engineering applications. An important advantage over conventional laminates is that interfaces and stress discontinuities are avoided. Piezoelectric composites are very brittle and have a low fracture toughness. The analysis of functionally graded materials (FGMs) is mathematically complex and analytical solutions are possible only for very simple geometry and loading conditions. Therefore, efficient numerical methods are needed to solve more general problems.
The production methodology of alloyed quantum-dot (QD) structures introduced a new design degree of freedom for QD arrays which is the grading of the material composition in the QD growth direction. This enables QDs of same size to generate different colors when exposed to blue light based on the grading of each QD. The grading of the material composition affects the material properties as well as the lattice mismatch strain between the QDs and the host matrix. Previous studies modeled graded QDs by just considering graded lattice mismatch strain while the material properties were kept uniform. Because these previous studies were seeking analytical solutions, including a graded material property model would have complicated the solutions. In this paper, a fully-coupled thermo-electro-mechanical finite element model of a cylindrical functionally graded QD (FGQD) in a host piezoelectric matrix is developed with both graded material properties and graded lattice mismatch strain. Different cases are considered corresponding to separately increasing and decreasing the strength of the lattice mismatch strain and the material properties in the QD thickness direction. The grading function is expressed using the power law that enables fractional exponents. The results show the effect of grading on the electromechanical quantities and demonstrate the flexibility that grading can add to the design of QD arrays. This work contributes to the development of quantum dots with "grading-dependent color" rather than the traditional "size-dependent color." The model can be easily extended to other cases such as different shapes of QDs, addition of wetting layer, and any applied thermo-electro-mechanical loads.
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