Ignacio Romero’s research while affiliated with Universidad Politécnica de Madrid and other places

Ignoring crack tip effects, the stability of the X-FEM discretizations is trivial for open cracks but remains a challenge if we constrain the crack to be closed (i.e., the bi-material problem). Here, we develop a formulation for general cohesive interactions between crack faces within the X-FEM framework. The stability of the new formulation is demonstrated for any cohesive crack stiffness (including the closed crack) and illustrated for a nonlinear cohesive softening law. A benchmark of the new model is carried out with simpler approaches for a closed crack (i.e., Lagrange multipliers) and for a cohesive crack (i.e., penalty approach). Due to the analogies between stable cohesive X-FEM and Nitsche's methods, the new method simplifies the implementation and is attractive in dynamic explicit codes. Copyright © 2014 John Wiley & Sons, Ltd.

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

The effect of the integration time step and the introduction of a cut-off velocity for the dislocation motion was analysed in discrete dislocation dynamics (DD) simulations of a single crystal microbeam. Two loading modes, bending and uniaxial tension, were examined. It was found that a longer integration time step led to a progressive increment of the oscillations in the numerical solution, which would eventually diverge. This problem could be corrected in the simulations carried out in bending by introducing a cut-off velocity for the dislocation motion. This strategy (long integration times and a cut-off velocity for the dislocation motion) did not recover, however, the solution computed with very short time steps in uniaxial tension: the dislocation density was overestimated and the dislocation patterns modified. The different response to the same numerical algorithm was explained in terms of the nature of the dislocations generated in each case: geometrically necessary in bending and statistically stored in tension. The evolution of the dislocation density in the former was controlled by the plastic curvature of the beam and was independent of the details of the simulations. On the contrary, the steady-state dislocation density in tension was determined by the balance between nucleation of dislocations and those which are annihilated or which exit the beam. Changes in the DD imposed by the cut-off velocity altered this equilibrium and the solution. These results point to the need for detailed analyses of the accuracy and stability of the dislocation dynamic simulations to ensure that the results obtained are not fundamentally affected by the numerical strategies used to solve this complex problem.

A model was developed to simulate the mechanical behavior of non-woven felts. The material was represented as a bidimensional network of straight fibres of finite length. The intersections between fibres formed the nodes of the model. Adjacent nodes were connected through bars that transferred load in the fibre direction. Spring elements were also added to penalize the variation of the angle between neighbour fibres. The model was applied to study the deformation mechanism of a non-woven felt made up of polyethylene fibres deformed in tension. The simulation results showed that the initial fibre orientation with respect to the load axis and their reorientation during deformation played a crucial role in the mechanical behaviour of these materials. 1. INTRODUCCIÓN