Mechanical behaviour of particle composite materials is growing of interest to engineering applications. A computational homogenization procedure in conjunction with a statistical approach have been successfully adopted for the definition of the Representative Volume Element (RVE) size, that in random media is an unknown of the problem, and of the related equivalent elastic moduli. Drawback of such a statistical approach to homogenization is the high computational cost, which prevents the possibility to perform series of parametric analyses. In this work, we 2 M. Pingaro et al.propose a so-called Fast Statistical Homogenization Procedure (FSHP) developed within an integrated framework that automates all the steps to perform. Furthermore within the FSHP, we adopt the numerical framework of the Virtual Element Method (VEM) for numerical simulations to reduce the computational burden. The computational strategies and the discretization adopted allow us to efficiently solve the series (hundreds) of simulations and to rapidly converge to the RVE size detection.
A fast statistical homogenization procedure (FSHP) based on virtual element method (VEM)—previously developed by the authors has been successfully adopted for the homogenization of particulate random composites, via the definition of the representative volume element (RVE), and of the related equivalent elastic moduli. In particular, the adoption of virtual elements of degree one for modeling the inclusions provided reliable results for materials with low contrast, defined as the ratio between mechanical properties of inclusions and matrix. Porous media are then here described as bimaterial systems in which soft circular inclusions, with a very low value of material contrast, are randomly distributed in a continuous stiffer matrix. Several simulations have been performed by varying the level of porosity, highlighting the effectiveness of FSHP in conjunction with virtual elements of degree one.
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