Composites materials are used in many engineering applications and typically exhibit a micro-structure made of randomly distributed inclusions (particles) embedded into a dissimilar matrix. A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behaviour. Homogenization procedures may be adopted for the definition of equivalent moduli able to take into account at the macroscale the material properties emerging from the internal micro-structure. In the case of materials with random micro-structure it is not possible to a priori define a Representative Volume Element (RVE), this being an unknown of the problem in contrast to the classical homogenization approach. A possible way to solve this problem is to approach the RVE using finite-size scaling of intermediate control volume elements, named Statistical Volume Elements (SVEs), and proceed to homogenization. Here a homogenization procedure, consistent with a generalized Hill-Mandel condition, is adopted in conjunction with a statistical procedure, by which scale-dependent bounds on classical moduli are obtained using Dirichlet and Neumann boundary conditions for solving Boundary Value Problems (BVPs) [1]. The outlined procedure has provided significant results, also extended to non-classical continuum formulations, but with high computational cost which prevents the possibility to perform series of parametric analyses. We here propose a so-called Fast Statistical Homogenization Procedure (FSHP) developed within an integrated framework that automates all the steps to perform: from the simulations of each random realization of the microstructure to the solutions of the boundary value problems for the SVEs, up to the evaluation of the final size of the RVE for the homogenization of the random medium. Within the FSHP the BVPs has been solved numerically adopting a mixed Virtual-Finite Element Method (VEM-FEM), with a single Virtual Element for the inclusions and triangular Finite Elements for the matrix, determined using random mesh generators. The computational strategies and the discretization adopted allow us to very efficiently solve the series (hundred) of BVPs and to rapidly converge to the RVE size detection. Several simulations are then performed by modifying the material contrast (ratio between the moduli of the materials components) deriving the size of the RVE for performing homogenization on various kinds of two-phases random composites.

A Fast Statistical Homogenization Procedure (FSHP) for Random Composite

Emanuele Reccia
2018-01-01

Abstract

Composites materials are used in many engineering applications and typically exhibit a micro-structure made of randomly distributed inclusions (particles) embedded into a dissimilar matrix. A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behaviour. Homogenization procedures may be adopted for the definition of equivalent moduli able to take into account at the macroscale the material properties emerging from the internal micro-structure. In the case of materials with random micro-structure it is not possible to a priori define a Representative Volume Element (RVE), this being an unknown of the problem in contrast to the classical homogenization approach. A possible way to solve this problem is to approach the RVE using finite-size scaling of intermediate control volume elements, named Statistical Volume Elements (SVEs), and proceed to homogenization. Here a homogenization procedure, consistent with a generalized Hill-Mandel condition, is adopted in conjunction with a statistical procedure, by which scale-dependent bounds on classical moduli are obtained using Dirichlet and Neumann boundary conditions for solving Boundary Value Problems (BVPs) [1]. The outlined procedure has provided significant results, also extended to non-classical continuum formulations, but with high computational cost which prevents the possibility to perform series of parametric analyses. We here propose a so-called Fast Statistical Homogenization Procedure (FSHP) developed within an integrated framework that automates all the steps to perform: from the simulations of each random realization of the microstructure to the solutions of the boundary value problems for the SVEs, up to the evaluation of the final size of the RVE for the homogenization of the random medium. Within the FSHP the BVPs has been solved numerically adopting a mixed Virtual-Finite Element Method (VEM-FEM), with a single Virtual Element for the inclusions and triangular Finite Elements for the matrix, determined using random mesh generators. The computational strategies and the discretization adopted allow us to very efficiently solve the series (hundred) of BVPs and to rapidly converge to the RVE size detection. Several simulations are then performed by modifying the material contrast (ratio between the moduli of the materials components) deriving the size of the RVE for performing homogenization on various kinds of two-phases random composites.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/260249
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