Computational modelling of structures using discrete and finite elements.

The objective of this thesis is the establishment of an objective comparison between the Finite Element Method and the Discrete Element Method when modelling the mechanical behaviour of the continuum, both for quasi-static and dynamic response. These two very different approaches to the same problem have increasingly gained popularity during the last years, becoming the distinction between the fields of application of each method each time more difficult. This research aims the assessment of the accuracy of the Discrete Element Method to solve problems that traditionally belong to the field of the Finite Element Method. This comparison has the ultimate purpose of determining the applicability of the first method to problems that involve a first stage when the material is elastic or elasto-plastic, followed by a second stage where actual physical separation of portions of the material occurs. The first part of this work comprises a review of the theoretical background and numerical techniques used to solve continuum mechanics problems using the Finite Element Method, both for quasi-static and dynamic loading. A description of the Discrete Element Method, encompassing its insights and the numerical strategies involved in its implementation constitute the second part of this work. The establishment of a methodology to model the continua using a Discrete Element Method based approach, namely the development of techniques to simulate elasto-plastic behaviour and crack path modelling, accompanied by illustrative benchmark examples, are the main pylons over which the third part of this research lays