Resumen de A fully lagrangian formulation for fluid-structure interaction between free-surface flows and multi-fracturing solids
It is well known that in civil engineering structures are designed so that they remain,whenever possible, in an elastic regime and with their mechanical properties intact. The truth isthat in reality there are uncertainties either in the execution of the work (geometric errors ormaterial quality) or during its subsequent use (loads not contemplated or its value has beenestimated incorrectly) that can lead to the collapse of the structure. This is why the study of thefailure of structures is inherently interesting and, once is known, its design can be improvedto be the less catastrophic as possible or to dissipate the maximum energy before collapsing.Another area of application of fracture mechanics is that of processes of which interest liesin the breakage or cracking of a medium. Within the mining engineering we can enumerateseveral processes of this nature, namely: hydraulic fracture processes orfracking, blasting fortunnels, explosion of slopes in open pit mines, among others. Equally relevant is the analysis ofstructural failures due to natural disasters, such as large avenues or even tsunamis impactingprotection structures such as walls or dikes. In this work numerous implementations and studieshave been made in relation to the mentioned processes.That said, the objective of this thesis is to develop an advanced numerical method capableof simulating multi-fracture processes in materials and structures. The general approach ofthe proposed method can be seen in various publications made by the author and directorsof this thesis. This methodology is meant to cover the maximum spectrum of engineeringapplications possible. For this purpose, a coupled formulation of theFinite Element Method(FEM) and theDiscrete Element Method(DEM) is used, which employs an isotropic damageconstitutive model to simulate the initial degradation of the material and, once the strength ofthe material has been completely exhausted, thoseFinite Element(FE) are removed from theFEMmesh and a set ofDiscrete Element(DE) are generated at its nodes. In addition to ensurethe conservation of the mass of the system, theseDEprevent the indentation between thefissure planes thanks to the frictional repulsive forces calculated by theDEM, if any.Additionally, in this thesis it has been studied how the proposed coupled method namedFEM-DEMtogether with the smoothing of stresses based on thesuper-convergent patchisable to obtain reasonably mesh-independent results but, as one can imagine, the crack width isdirectly related to the size of the elements that have been removed. This favours the inclusionof an adaptive remeshing technique that will refine the mesh where it is required (according tothe Hessian of a nodal indicator of interest) thus improving the discretization quality of the crackobtained and thereby optimizing the simulation cost. In this sense, the procedures for mappingnodal and internal variables as well as the calculation of the nodal variable of interest will bediscussed.As far as the studies of natural disasters are concerned, especially those related to free-surface water flows such as tsunamis, one more level of coupling between the aforementionedmethodFEM-DEMand oneComputational Fluid Dynamics(CFD) formulation commonlyreferred to asParticle Finite Element Method(PFEM) has been implemented. With this strongcoupled formulation, many cases of wave impacts and fluid flows have been simulated agains solid structures such as walls and dikes, among others.
