A Multiscale Homogenization Scheme with the Virtual Element Method

Abstract

Evaluations and predictions of the responsive behavior of complex heterogeneous materials such as cementitious mortars, soils, rocks or concretes, require a multi-scale approach. The overall characteristics of these materials strongly depend on processes that are occurring at different length scales, mostly reflecting the macro, meso and micro-scale levels. Various scale-levels are required to account for the different mechanisms that control the behaviour at different levels of detail. Among the different multi-scale schemes, those based on a homogenization procedures are more commonly used due to their versatility. In this research, a consistent homogenized multiscale approach is proposed for modelling mechanical and transport phenomena. A multiscale model, based in the Virtual Element Method (VEM), is implemented in a VEM2 setting. VEM allows for a great flexibility in the mesh, and is a powerful tool to characterize the complex RVEs geometries, reducing the amount of elements needed and hence saving time and resources.