Abstract
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.
Highlights
The group of non-homogeneous materials includes, e.g., composite materials, liquid mixtures, media with liquid and solid particles, as well as porous media
The present results based on the numerical homogenization for the square and hexagonal arrays are contrasted with results from micromechanical models such as Vanin model [61] (see Equation (A1))
The present paper discussed the application of numerical homogenization and optimization in
Summary
The group of non-homogeneous materials includes, e.g., composite materials, liquid mixtures, media with liquid and solid particles, as well as porous media. The assumption of Reuss [5] known as the series model is based on constant stress and gives the lower-bounds [2] These approximations consider only the elastic properties of constitutes and their volume fractions. Hashin and Shtrikman [10] proposed how to determine narrower bonds for the homogenized elastic properties for composite with isotropic constituents taking into account the interaction between the elastic properties They applied the principle of minimum potential energy and the idea of polarization. Explicit expressions of the components of Eshelby’s tensor are presented in work by Mura [15] Both Bensoussan et al [16] and Suquet [17] discussed an asymptotic homogenization theory being a mathematical description of periodic composites. Analyzed problem (3) and (4)the will be preceded short introduction on the 2D the analyzed problem (3)
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