Design of functionally graded piezocomposites using topology optimization and homogenization – Toward effective energy harvesting materials

In the optimization of a piezocomposite, the objective is to obtain an improvement in its performance characteristics, usually by changing the volume fractions of constituent materials, its properties, shape of inclusions, and mechanical properties of the polymer matrix (in the composite unit cell). Thus, this work proposes a methodology, based on topology optimization and homogenization, to design functionally graded piezocomposite materials that considers important aspects in the design process aiming at energy harvesting applications, such as the influence of piezoelectric polarization directions and the influence of material gradation. The influence of the piezoelectric polarization direction is quantitatively verified using the Discrete Material Optimization (DMO) method, which combines gradients with mathematical programming to solve a discrete optimization problem. The homogenization method is implemented using the graded finite element concept, which takes into account the continuous gradation inside the finite elements. One of the main questions answered in this work is, quantitatively, how the microscopic stresses can be reduced by combining the functionally graded material (FGM) concept with optimization. In addition, the influence of polygonal elements is investigated, quantitatively, when compared to quadrilateral 4-node finite element meshes, which are usually adopted in material design. However, quads exhibit one-node connections and are susceptible to checkerboard patterns in topology optimization applications. To circumvent these problems, Voronoi diagrams are used as an effective means of generating irregular polygonal meshes for piezocomposite design. The present results consist of bi-dimensional unit cells that illustrate the methodology proposed in this work.