Applications of the Virtual Element Method for Cracking Analysis of Cement-Based Composites Using Interface Elements

Abstract

The very recently introduced Virtual Element Method (VEM) is a numerical method for solving partial differential equations that was created out of the mimetic difference method, but was later reformulated into the Galerkin framework. It is a generalization of the standard Finite Element Method (FEM) to general meshes made up by arbitrary polyhedra. The greatest advantage of VEM is to be able to deal with very complex geometries, i.e., made up by elements of any number of edges not necessarily convex, hanging nodes, flat angles, collapsing nodes, etc, while retaining the same approximation properties of FEM. In this paper we propose the simulating of the mechanical response of cement-based composites by means of a Virtual Element approach for discretization of the domain, along with a novel interaction between zero-thickness interface element for meso-scale analysis within the framework of the so-called discontinuous-based approach. Following a similar modeling approach already available in literature for FEM and iso-parametric interface elements, the formulation of the VEM for elasticity problems is a novelty that can be used to capture the key mechanical phenomena controlling concrete heterogeneity by taking advantage of the versatility of polyhedral meshes.