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 is that in reality there are uncertainties either in the execution of the work (geometric errors or material quality) or during its subsequent use (loads not contemplated or its value has been estimated incorrectly) that can lead to the collapse of the structure. This is why the study of the failure of structures is inherently interesting and, once is known, its design can be improved to 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 lies in the breakage or cracking of a medium. Within the mining engineering we can enumerate several processes of this nature, namely: hydraulic fracture processes or fracking, blasting for tunnels, explosion of slopes in open pit mines, among others. Equally relevant is the analysis of structural failures due to natural disasters, such as large avenues or even tsunamis impacting protection structures such as walls or dikes. In this work numerous implementations and studies have been made in relation to the mentioned processes.
That said, the objective of this work is to develop an advanced numerical method capable of simulating multi-fracture processes in materials and structures. The general approach of the proposed method can be seen in various publications made by the author and directors of this work. This methodology is meant to cover the maximum spectrum of engineering applications possible. For this purpose, a coupled formulation of the Finite Element Method (FEM) and the Discrete Element Method (DEM) is used, which employs an isotropic damage constitutive model to simulate the initial degradation of the material and, once the strength of the material has been completely exhausted, those Finite Element (FE) are removed from the FEM mesh and a set of Discrete Element (DE) are generated at its nodes. In addition to ensure the conservation of the mass of the system, these DE prevent the indentation between the fissure planes thanks to the frictional repulsive forces calculated by the DEM, if any. Additionally, in this work it has been studied how the proposed coupled method named FEM-DEM together with the smoothing of stresses based on the super-convergent patch is able to obtain reasonably meshindependent results but, as one can imagine, the crack width is directly related to the size of the elements that have been removed. This favours the inclusion of an adaptive remeshing technique that will refine the mesh where it is required (according to the Hessian of a nodal indicator of interest) thus improving the discretization quality of the crack obtained and thereby optimizing the simulation cost. In this sense, the procedures for mapping nodal and internal variables as well as the calculation of the nodal variable of interest will be discussed.
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 aforementioned method FEM-DEM and one Computational Fluid Dynamics (CFD) formulation commonly referred to as Particle Finite Element Method (PFEM) has been implemented. With this strong coupled formulation, many cases of wave impacts and fluid flows have been simulated against solid structures such as walls and dikes, among others.