Design of Reinforcement in Nano- and Microcomposites

The application of numerical homogenization and optimization in the design of micro- and nanocomposite reinforcement is presented. The influence of boundary conditions, form of a representative volume element, shape and distribution of reinforcement are distinguished as having the crucial influence on a design of the reinforcement. The paper also shows that, in the optimization problems, the distributions of any design variables can be expressed by n-dimensional curves. It applies not only to the tasks of optimizing the shape of the edge of the structure or its mid-surface but also dimensional optimization or topology/material optimization. It is shown that the design of reinforcement may be conducted in different ways and 2D approaches may be expanding to 3D cases.