Multiscale method for fracture
During my PhD, I developed a code for multiscale modelling of fracture in polycrystalline materials under the supervision of Professor Stephane Bordas and Dr Pierre Kerfriden. In this link the Failure of polycrystalline microstructure has been simulated by developing a thermodynamically consistent cohesive law for grain interfaces. However, because of the large size of engineering structures, these problems cannot be solved completely at the micro-level, i.e. by resolving the micro structure explicitly on the whole domain of interest.
In this work, we propose an adaptive hybrid multiscale method for modeling fracture in a heterogeneous material composed of orthotropic grains with cohesive interfaces between grains. Instead of a direct solver the FE2 method, derived from the homogenisation technique, is employed to compute the efective behaviour of the heterogeneous microscopic medium at a much coarser scale in the non-critical region where the modelling error due to the homogenisation is still low. The coarse scale is discretised with non-structured triangular nite elements, and adaptive mesh renement is used to control the discretization error. While the coarse mesh renement retains the discretization error at a certain level, the modeling error increases due to the fact that the ner the coarse elements, the less the scale separation assumption is fulfilled, which is a key issue for homogenization.
The accuracy of homogenization is examined by measuring the second gradient of displacement which is ignored in the rst order homogenisation. A critical zone emerges when the second displacement gradient reaches the critical value, or if the underlying RVE (representative volume element of microstructure) of the element loses stability due to localisation. Thereafter, a zoom-in process is triggered to replace the corresponding coarse elements of the critical zone with a high resolution microscale mesh and gluing it to the coarse scale mesh through a strong coupling technique using Lagrange multipliers. The high resolution region can gradually be extended to the newly emerged critical zones. A local arc-length technique is adopted to control the opening of microscopic cohesive cracks.
- A Akbari R, P Kerfriden, SPA Bordas, An adaptive multiscale strategy to simulate fracture of composite structures, CFRAC, Prague, Czech Republic 5-7 June 2013
- P Kerfriden, A Akbari R, O Goury, SPA Bordas, L Margetts, Addressing lack of scale separation in fracture simulations, IUTAM 2012 Symposium Fracture Phenomena in Nature and Technology 1-5 July
- A Akbari R, P Kerfriden, S Bordas, Scale selection in nonlinear fracture mechanics of heterogeneous materials, Philosophical Magazine (submitted)
- A Akbari R, Error Controlled Adaptive Multiscale Method for Fracture in Polycrystalline Materials, Cardiff University 2014