Adaptive multiscale methods for multiple intergranular discontinuities

In order to simulate fracture in heterogeneous materials, one of the most promising approaches is to model the behaviour of the material at the scale of the material heterogeneities, which is usually called micro or meso-modelling. In a second step, these fine-scale features can be transferred to the scale of the structure by averaging techniques (on representative volume elements or unit cells) or homogenisation. However, in the case of fracture, these upscaling methods cannot be used in the vicinity of cracks, as the separation of scales necessary for their application is lost.

In the literature, two schools of thought aim at alleviating this problem. The first one tries to extend the applicability of averaging techniques to fracture (in the casa of established damage bands). The second one aims at analysing the zones where homogenisation fails directly at the microscopic scale, in a concurrent framework. Although the latter approach is more general, it is heavier in terms of computations, and requires the development of robust adaptivity procedures, which is the topic of this project.

From the PhD thesis of Ahmad Akbari R.

We propose to capture the initiation of the damage mechanisms at the macroscale using a classical FE2 approach. In order to control the precision of the simulations, an error estimation for the upscaling strategy is carried out at each step of the time integration algorithm. Based on this estimation, the macro elements are refined hierarchically where needed. When the size of a macro-element becomes of the order of the statistical volume ele- ment used in the FE2 method, the homogenisation step is bypassed. Instead, the corresponding process zone is modelled directly at the microscale and coupled to the homogenised region by a mortar-type gluing technique.

Simulations by Ahmad Akbari, P. Kerfriden and S.P.-A. Bordas


A Akbari Rahimabadi, P Kerfriden, S Bordas, Scale selection in nonlinear fracture mechanics of heterogeneous materials, Philosophical Magazine 95 (28-30), 3328-3347, 2015