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See detailScale selection in nonlinear fracture mechanics of heterogeneous materials
Akbari Rahimabadi, Ahmad; Kerfriden, Pierre; Bordas, Stéphane UL

in Philosophical Magazine (2015), 95(28-30), 3328-3347

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and ... [more ▼]

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and modelling errors. In the failure problems, the discretization error increases due to the strain localization which is also a source for the error in the homogenization of the underlying microstructure. In this paper, the discretization error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz–Zhu technique, and the modelling error, which is the resultant of homogenization of microstructure, is controlled by replacing the macroscopic model with the underlying heterogeneous microstructure. The scale adaptation criterion which is based on an error indicator for homogenization is employed for our non-linear fracture problem. The control of both discretization and homogenization errors is the main feature of the proposed multiscale method. [less ▲]

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See detailError Controlled Adaptive Multiscale Method For Fracture Modelling in Polycrystalline materials
Akbari, Ahmad; Kerfriden, ierre; Bordas, Stéphane UL

in Philosophical Magazine (2015)

In this paper an adaptive multiscale method is presented in an attempt to address the lack of separation of scales in simulation of fracture. This method is set in the context of FE2 [20] for which ... [more ▼]

In this paper an adaptive multiscale method is presented in an attempt to address the lack of separation of scales in simulation of fracture. This method is set in the context of FE2 [20] for which computational homogenisation breaks down upon loss of material stability (softening). The lack of scale separation due to the coalescence of microscopic cracks in a certain zone is tackled by a full discretisation of the microstructure in this zone. Polycrystalline materials are considered with cohesive cracks along the grain boundaries as a model problem. Adaptive mesh refinement of the coarse region and adaptive initiation and growth of fully resolved regions are performed based on discretisation error and homogenisation error criteria, respectively. In order to follow sharp snap-backs in load-displacement paths, a local arc-length technique is developed for the adaptive multiscale method. The results are validated against direct numerical simulation. [less ▲]

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