In the last 10 years, a new finite element methodology, the virtual element method (VEM), has been proposed by Brezzi, Beirao da Veiga and coworkers. The VEM is more flexible than standard FEM, as it is possible to discretize the domain by polygons characterized by any number of edges, without constraints. Moreover, it has also been proved that VEM presents several advantages with respect to classical FEM, such as ability to accurately deal with complex geometries, flexibility in mesh generation, no need of a parent element, easy polynomial degree elevation, very good performances for distorted meshes. The lectures are devoted to the development of a virtual element method with application in fracture mechanics. The basic concepts of the VEM and the construction of all operators involved in the construction of the mathematical formulation will be explained during the course. Some detail concerning the VEM implementation in a Python framework will be given in order to enable the course participants to implement a virtual element. Then, a procedure for reproducing the nucleation and propagation of fracture in 2D cohesive media, combining the virtual element technique with a splitting methodology and a minimal remeshing procedure will be discussed and possible applications will be illustrated.
June 23-24, 2025 - 9:00am-11:00am, June 26-27, 2025 - 2:00pm-6:00pm
The course will take place in blended mode: in presence at the Aula Seminary - DISG, Faculty of Architecture, via Gramsci 53, Rome and online via Zoom at the following link: https://uniroma1.zoom.us/j/89127395440
For all courses supplied by the PhD Program of the DISG credits are not provided: a certificate of in person attendance will be produced upon request (only after a check of the effective presence). Certificate of online attendance will not be provided.