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)
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 ). 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.