Phase field methods for fracture mechanics in coupled problems

Nowadays, cutting-edge industry processes cannot thrive with- out the integration of multidisciplinary perspectives in all its associated processes. Even the field of Mechanics is not ex- empt from such approaches, since most recent studies now incorporate considerations spanning multiple size scales (multi- scale) and encompassing various branches such as Chemistry, Biology, Electricity, and Magnetism, among others (multi-physics). This is what constitutes the very essence of a coupled prob- lem in Mechanics. The principal objective of this thesis is to specifically explore their impact on structural integrity and reliability in the field of Fracture Mechanics. Consequently, it is necessary to establish a robust mathematical framework to assess the mechanical behavior and failure strength, con- sidering the intricate influence of the multi-scale and multi- physics fields associated with each problem. To accomplish this mission, we have primarily utilized the phase-field ap- proach for fracture, alongside the continuum damage me- chanics technique. Our efforts have been devoted to shed light on representative coupled problems in Fracture Mechanics. To exemplify the breadth of this field, our research comprises a diverse spec- trum of topics. First, the research deals on the problem of hy- drogen embrittlement in polycrystalline materials. Moreover, the residual stress influence on the integrity of soft cylindrical tubes has been investigated. Furthermore, a computational framework for incompressible materials has been proposed. The final topic concerns the application of this last formula- tion in the simulation of swelling of thermoresponsive hydro- gels.