Scale selection in nonlinear fracture mechanics of heterogeneous materials

Abstract

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.

Keywords:

• multiscale
• fracture
• adaptive mesh
• homogenization error
• discretization error

Acknowledgements

The authors would also like to thank the financial support of the School of Engineering at Cardiff University for Dr Ahmad Akbari Rahimabadi PhD. Ahmad Akbari would also like to acknowledge the financial support of the Framework Programme 7 under IRSES exchange programme for his visit to the University of Witwatersrand in Johannesburg, South Africa.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author thanks the financial support of the UK EPSRC under grant [grant number EP/J01947X/1] “Toward rationalised computational expense for simulating fracture over multiple scales”. The last two authors thank 1) the EPSRC under grant [grant number EP/G042705/1] “Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method” and 2) the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) entitled “Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery“.