Analysis with mixed finite elements (Truly Mixed). Implementation of finite element codes using the Hellinger-Reissner formulation for the solution challenging of structural problems (PEERS element and Arnold-Winther element, etc.):in plane elasticity, viscoelasticity, and plasticity.
Second gradient problems and application. Characterized materials with internal length scale: porous materials, composites or fractured media.
Isogeometric analysis. Numerical analysis technique that exploits the definition of exact geometry of the domain and high regularity. Thanks to these characteristics is used for the solution of fourth order problems such as plates and shells.
Project GeoPDEs. Implementation of parts of the code in the program for the isogeometric analysis GeoPDEs. In particular, the part relating to the problems of fourth order (see http://rafavzqz.github.io/geopdes/contributors/).
Topology Optimization. Study and Implementation of codes for topology optimization using mixed finite elements.
VEM elements. Study and implementation of codes using Virtual Element Method applied to topology optimization and homogenization of random composite materials. In this project we implement a program in Python (PyVEM) for 2-D linear elasticity (isotropic and orthotropic) and enriched continuum such as Cosserat continuum.
Random composite materials. Study random materials made of matrix and inclusions (particles); examples of such materials are polymer, ceramic, metal matrix composites, but also granular materials, concrete, masonry made of crushed stones casually arranged in the mortar and even porous rocks.
