Fast statistical homogenization procedure (FSHP) for particle random composites using virtual element method

Abstract

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.

Homogenization of Random Porous Materials With Low-Order Virtual Elements

“…In this Section, the steps of the automated so-called Fast Statistical Homogenization Procedure (FSHP) [1], based on the statistical homogenization procedure previously developed in [23] and briefly described in Section 1, are detailed. FSHP allows to compute overall homogenized mechanical parameters, in particular the anisotropic elasticity tensor.…”

“…FSHP with virtual element of k = 1 is particularly suitable for analysing low contrast materials [1], and in this paper a very low value of contrast (c → 0) is adopted, with the purpose of simulating a material with randomly distributed voids. Referring to the properties adopted in [11], an high value of Poisson coefficient has been adopted for the inclusions.…”

“…In particular, we use the development of the above mentioned procedure, the Fast Statistical Homogenization Procedure (FSHP) based on Virtual Element Method (VEM) provided in [1]. In FSHP the statistical procedure is automatized and integrated in a completely in house specifically developed code, that makes it possible to quickly and efficiently perform a high number of parametric analyses.…”

“…In this paper, low order virtual elements are used: the adoption of virtual elements of order one is particularly suitable for low contrast materials, as porous materials, as shown in [1], because the stresses are concentrated in the stiffer matrix and constant stress/strain over the elements do not affect homogenization results.…”

Micromodels for the in-plane failure analysis of masonry walls: Limit Analysis, FEM and FEM/DEM approaches

“…Most of the existing approaches are devoted to the mechanical behavior of periodic (i.e. regular) masonries, for which a suitably defined unit cell plays the role of RVE, but there exist also different homogenization techniques for both linear and nonlinear analyses of random microstructures, already applied or directly applicable to irregular masonry structures [21][22][23]. Other multiscale strategies have been proposed that exploit different homogenization techniques based on the so-called Cauchy rule, and its, generalizations [24] that allowed the derivation of both classical and generalized continua able to properly represent scale effects, that in masonry materials are prominent [25][26][27][28][29].…”