A numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures |
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| Affiliation: | 1. Energy Department, Politecnico di Milano, Via Ponzio 34/2, 20133 Milan, Italy;2. Aramis S.r.l., Via Viviani 8, Milano, Italy;3. Fondation EDF, Centrale Supelec, France;1. Engineering Research Center of Technical Textiles, Ministry of Education, Donghua University, Shanghai 201620, China;2. Key Laboratory of Textile Science & Technology, Ministry of Education, Donghua University, Shanghai 201620, China;3. Zhejiang Provincial Key Laboratory of Novel Textiles Research and Development, Hangzhou 310001, China;4. Laboratory for Clothing Physiology and Ergonomics, National Engineering Laboratory for Modern Silk, Soochow University, Suzhou 215123, China;1. Department of Mathematical Sciences, University of Liverpool, Peach Street, L69 7ZL, UK;2. Institute for Risk and Uncertainty, University of Liverpool, UK;1. Faculty of Applied Engineering, University of Antwerp, Belgium;2. Institute of Stochastics, TU Bergakademie Freiberg, Germany |
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| Abstract: | The present work is dedicated to a numerical investigation of the connection between state of dispersion and percolation and its effect on the elastic properties of 2D random microstructures. The main objective consists in checking out the link between percolation and mechanical response in the context of a heterogeneous medium the reinforcements of which are not homogeneously dispersed. Besides, the influence of the stiffness of inclusions is also investigated since this could impact on the percolation effects. For these purposes, large samples of volume elements are generated according to the Monte Carlo method. We consider the low cost framework of 2D random grids which enables large and in-depth investigations. Besides, the spatial distribution of heterogeneities is simulated with the help of the 2-scale Boolean scheme of disks which is a powerful tool for modelling and studying several states of dispersion. The numerical results highlight beneficial mechanical reinforcements for a heterogeneous dispersion when the percolation phenomenon is enhanced. This improvement is highly sensitive to the stiffness of heterogeneities. |
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| Keywords: | Percolation Elastic properties Homogenisation Volume elements (VE) Finite element analysis (FEA) |
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