Congratulations, Olivier, it was fantastic to have you here, and we hope that you’re fairing well at Inria with Christian Duriez.
Thank you to Dr Pierre Kerfriden for the excellent supervision provided to Olivier.
Computational time savings in multiscale fracture mechanics using model order reduction
Engineering problems are very often characterised by a large ratio between the scale of the structure and the scale at which the phenomena of interest need to be described. In fracture mechanics, the initiation and propagation of cracks is the result of localised microscopic phenomena. This local nature of fracture leads to large numerical models. Projection-based reduced order modelling is an increasingly popular technique for the fast solution of parametrised problems. However, traditional model order reduction methods are unable to reliably deal with either the initiation or the propagation of a crack or a local zone with high damage concentration. In this thesis, we look at the general problem of applying model order reduction to fracture/ damage mechanics, in the pursuit of rationalising the computational time involved in these kind of simulations. The first contribution of this thesis is the development of a reduced-order modelling for computational homogenisation, which is a general multiscale method used to take microscopic data into account when deriving an engineeringscale model. A specific strategy is used to reduce the cost of solving the representative element volume (RVE) boundary value problem traditionally formulated in this method. The second contribution was made by developing a partitioned reduced-order procedure for the case of parametrised nonlinear material deformations involving a local lack of correlation, which typically happens with fracture. The method allows to reduce the regions undergoing little non-linearities whilst computational work can be concentrated on regions of high non-linearity.