By Vladimír Kompiš

This booklet provides new leads to the information and simulations for composite nano-materials. It comprises chosen, prolonged papers awarded within the thematic ECCOMAS convention on Composites with Micro- and Nano-Structure (CMNS) – Computational Modelling and Experiments. It includes atomistic and continuum numerical equipment and experimental validation for composite fabrics strengthened with debris or fibres, porous fabrics, homogenization and different very important subject matters.

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Extra resources for Composites with Micro- and Nano-Structure: Computational Modeling and Experiments (Computational Methods in Applied Sciences)

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E. the individuals with the best fitness value. The selected individuals form the parent generation, and they produce offsprings by rules like mutation, crossover, or gene replacement (for details, see, Sch¨oneburg [23]). The algorithm stops after a specified number of generations or if a certain fitness value is obtained for the best individual. 3) and the whole set of parameters corresponds to one individual. As fitness function, the square difference between the microscopic and macroscopic system response is used.

It represents a gradient-based optimization technique. g. [10, 24]. In the following presented examples, the gradient is calculated by finite differences. Gradient based algorithms often exhibit weaknesses in non-convex 4 Effective Properties of Non-Convex Microstructured Materials 53 problems, which means that they run into local minima of the search space. Therefore, also a global optimization technique a Genetic Algorithm is applied to the optimization problem. As expected from literature, tests have shown that the Genetic Algorithm is the robustest (but slowest) technique also compared with Neural Networks as alternative global optimization tool.

But for the purpose of quantitative evaluation of the influence of fibre reinforcement the models give sufficient information. Some results are presented in the next figures. All displacement, strain and stress fields given in the figures are the local components of corresponding fields. Recall that the far fields have to be added in to obtain the total quantities. 10 show the local fields in the vicinity of the fibre of interest (the coordinates’ origin is in the middle of the fibre) for L = 1,000 R with overlay and the distance ∆3 = 200 R.

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