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Direct numerical simulation of complex Representative Volume Elements (RVEs): Generation, Resolution and Homogenization

Abstract : The influence of microstructural heterogeneities on material processing is an issue of prime importance, which explains the need to generate a digital material, statistically equivalent to the considered microstructure, and to connect this digital description to finite element (FE) calculations. For this reason, a multi-physical virtual microstructure generator which can simultaneously generate cells and spherical particles is created. This generator is based on Laguerre tessellations and advancing front method, level-set description of interfaces and anisotropic meshing adaptation. The capability of its tools to respect statistical data could be insured by the advancing front method coupled with an optimization procedure depending on the nature of the considered microstructure. Moreover, a graph coloration technique is applied in order to reduce the number of level-set functions used in anisotropic mesh adaptation. Furthermore, the high cost of a fully coupled micro-macro simulation can be significantly reduced when restricting the attention to a fully uncoupled analysis. In this context, the response of the Representative Volume Element (RVE) when subject to a given macroscopic loading path is of the main interest. RVEs of elastic Voronoï honeycombs and fiber arrays are considered in the manuscript. The first is used to simulate the compression of an elastic foam subject to a biaxial load. In this case, a fluid structure interaction (FSI) problem occurs between a compressible fluid, the air inside the foam's cells, and an elastic compressible solid, the foam's skeleton. A monolithic formulation is used for solving this problem where a single grid is considered and one set of equations with different material properties is solved. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations, which are solved by a mixed finite element method with a P1+/P1 interpolation, coming from the presence of the structure in the fluid. The second RVE is used to compute the permeability of disordered fiber arrays. In this case, flows through unidirectional fibrous media are simulated and the fibers are considered as rigid discs. Also, a monolithic formulation is used for solving this problem. Therefore the Stokes equations are solved in the whole domain using a penalization method. After using volume average techniques, Darcy's law is obtained giving the possibility to compute the permeability tensor.
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Submitted on : Tuesday, February 7, 2012 - 3:58:26 PM
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  • HAL Id : pastel-00667428, version 1

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Karim Hitti. Direct numerical simulation of complex Representative Volume Elements (RVEs): Generation, Resolution and Homogenization. Materials. École Nationale Supérieure des Mines de Paris, 2011. English. ⟨NNT : 2011ENMP0054⟩. ⟨pastel-00667428⟩

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