Phase-Field modelling of ramdomly representative volume elements

Resumo

Real-world engineering materials are usually heterogeneous in nature. Taking concrete as an example,
it is composed of sand, gravel, a cementitious matrix, in addition to various voids and imperfections caused by
chemical hardening reactions inherent of the material itself. To model those kinds of materials, the Phase-Field
Modelling has been widely used by the scientific community due to the advantages presented by it like the ability
to detect crack nucleation and to obtain its full path. For that, this model considers the smeared variational form
of Griffith’s sharp crack that spreads over a portion of the domain according to a length scale parameter. The
Phase-Field is inserted into the problem through an additional equation that solves, for each degree of freedom,
its variable that varies from 0 to 1 and indicates the damage. The purpose of this article is to use the Phase-Field
Models with heterogeneous material to study the behaviour of RVE for different sizes and grading curves. All the
implementation was done in INSANE, an open-source software, developed in Java at the Structural Engineering
Department of the Federal University of Minas Gerais. Numerical results will be presented.