This works encompasses a broad review of the basic aspects of the Discrete Element Method for its application to general granular material handling problems with special emphasis on the topics of particle-structure interaction and the modelling of cohesive materials. On the one hand, a special contact detection algorithm has been developed for the case of spherical particles representing the granular media in contact with the finite elements that discretize the surface of rigid structures. The method, named Double Hierarchy Method, improves the existing state of the art in the field by solving the problems that nonsmooth contact regions and multi contact situations present. This topic is later extended to the contact with deformable structures by means of a coupled DE-FE method. To do so, a special procedure is described aiming to consistently transfer the contact forces, which are first calculated on the particles, to the nodes of the FE representing the solids or structures. On the other hand, a model developed by Oñate et al. for the modelling of cohesive materials with the DEM is numerically analysed to draw some conclusions about its capabilities and limitations.

In parallel to the theoretical developments, one of the objectives of the thesis is to provide the industrial partner of the doctoral programme, CITECHSA, a computer software called DEMPack (www.cimne.com/dem/) that can apply the coupled DE-FE procedure to real engineering projects. One of the remarkable applications of the developments in the framework of the thesis has been a project with the company Weatherford Ltd. involving the simulation of concrete-like material testing.

The thesis is framed within the first graduation (2012-13) of the Industrial Doctorate program of the Generalitat de Catalunya. The thesis proposal comes out from the agreement between the company CITECHSA and the research centre CIMNE from the Polytechnical University of Catalonia (UPC).