Homogenization of Random Porous Materials With Low-Order Virtual Elements

Abstract

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.

Statistical homogenization of polycrystal composite materials with thin interfaces using virtual element method

“…More specifically, taking advantage of the encouraging results found in [36,37], we here exploit an efficient evolution of the above mentioned procedure, i.e. the Fast Statistical Homogenization Procedure (FSHP) based on Virtual Element Method (VEM).…”

“…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. VEM [38,39] is an innovative and very promising computational method that find many engineering and structural mechanics applications [40,41,42,41]: from linear [43,44,45] to non-linear elasticity [46,47,48], elastodynamic [49], topology optimization [50,51], contact problem [52], plates [53], fracture and damage [54,55], as well as in homogenization of heterogeneous materials [56,57,36,37].…”

“…Here, the procedure is to specifically account for the microstructural topology exhibited by polycrystalline composites with thin interphases, making the most of VEM to improve the computational efficiency. The result is a powerful numerical tool suitable for analyses of large portions of random microstrure, very important in the case materials with very high or low contrast [37]. In particular the strategy proposed is to use a single virtual element for each grain (polygons of any shape with n-nodes) with a significant reduction of the computational burden, while the interconnecting layer is discretized with a fine mesh of triangular elements.…”

Micromodels for the In-Plane Failure Analysis of Masonry Walls with Friction: Limit Analysis and DEM-FEM/DEM Approaches

“…micro-macro, continuum models represent a very promising approach for the analysis of masonry structures since they can accurately retain memory of the the mechanical and geometrical properties of the material (microstructure) together with the capability to contain the computational effort compared to a fully micromechanical model [25,36,20,33]. These models are often derived by considering two material scales: a microscale where, after deducing the mechanical properties of the components through experimental tests, a material representative volume element (RVE) is defined and a macroscale structural level, where a homogeneous continuum is obtained by performing a homogenization procedure based on the solution of boundary conditions problems for the RVE [2,1,16,17,33,30,29]. Other multiscale strategies have been proposed that exploit different homogenization techniques exploiting the so-called Cauchy rule, and its, generalizations [9] that allowed the derivation of generalized continua able to properly represent scale effects, that in masonry materials are prominent [25,35,28,15,19].…”

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].…”