Computational mechanics

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The past two decades have witnessed a dramatic growth in the development of computational tools for solid and fluid mechanics problems. One area that has attracted particular attention is computational fracture mechanics, given the challenges associated with modelling evolving discontinuities. Attention has shifted from the analysis of stationary cracks (computation of stress intensity factors and J-integral) to the modelling of crack growth and other complex features such as branching, merging or fragmentation. Our contributions can be classified into three fronts.

First, we have contributed to the success of cohesive zone models. On the one side, we developed new control algorithms that enable capturing crack growth using cohesive elements without convergence problems and eliminating the iterative procedure intrinsic to steady state analyses. This has enabled us to compute R-curves and explore the influence of crack tip dislocation hardening and plastic dissipation. On the other side, we have developed Abaqus2Matlab, a comprehensive piece of software that couples Abaqus and Matlab, enabling (for example) estimating the cohesive parameters by means of neural networks.

Second, we have contributed to the development of the eXtended Finite Element Method (X-FEM) by presenting a new X-FEM non-linear framework for elastic-plastic solids. The scheme is capable of capturing the stress elevation due to strain gradients by means of suitably defined asymptotic functions. In addition, it includes (i) higher order elements, (ii) a linear weighting function for the blending elements, (iii) an iterative solver for nonlinear systems and (iv) an appropriate triangular integration scheme.

Third, we have embraced the remarkable success of the phase field fracture method with relish. The phase field fracture method is a very robust tool, with sound underlying physics (based on the concepts of fracture energy and a process zone) and capable of capturing complex crack phenomena, such as crack nucleation at arbitrary sites, crack growth along complex trajectories, and branching and coalescence of multiple cracks. Our contributions lie in the development of (1) a phase field formulation for functionally graded materials, (2) a multi-physics deformation-diffusion-fracture framework, particularised to the case of hydrogen embrittlement, and (3) quasi-Newton monolithic solution schemes, that reveal notable computational gains.

A recent talk on this topic is given below:

Session 2 - Emilio Martinez Paneda

https://www.youtube.com/embed/wDD7KSnVz_A?wmode=opaque&controls=&rel=0&list=PLg7f-TkW11iXyrmX9k6beGGLJPsLfbTyO