Abstract
A continuum constitutive framework with embedded cohesive interface model is presented to describe the failure of quasi-brittle materials. Both cohesive behaviour for cracking inside the fracture process zone and elastic bulk behaviour are treated at integration points making implementation straightforward. In this sense, the proposed approach is simpler than existing ones that focus on element enrichments, such as the extended finite element method, while share similarities with smeared crack models, and offers the capability to correctly model quasi-brittle failure in post-peak regime at constitutive level. In this work, the formulation is introduced, numerical algorithms described and static and dynamic fracture simulations with complex crack patterns are conducted to demonstrate the capability and advantage of the proposed approach.
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Notes
One exception is the cohesive interface elements which are available in many FE packages such as Abaqus and LS-Dyna.
Reasons for this choice will be given later in the paper.
Einstein summation convention does not apply here.
Exceptions include Abaqus of Dassault Systemes and Systus of ESI.
The load-displacement curves were extracted from Nooru-Mohamed et al. (1993) using the software plotdigitizer which is freely available at http://plotdigitizer.sourceforge.net.
In Nguyen et al. (2015b) we presented simulations with finite thin interfaces to indicate that our model can be used without interface elements.
Periodicity was not considered simply because our microstructure generator is unable to generate periodic structures.
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Acknowledgments
Funding support from the Australian Research Council via projects DP140100945 (Luming Shen, Giang D. Nguyen, Vinh Phu Nguyen, Abbas El-Zein, Federico Maggi), FT140100408 (Giang D. Nguyen) and DE 150101703 (Daniel Dias-da-Costa) is gratefully acknowledged. Daniel Dias-da-Costa would like to extend his acknowledgements to the Portuguese Foundation for Science and Technology through Project No. FCOMP-01-0124-FEDER-020275-PTDC/ECM/119214/2010. VP Nguyen would like to express the gratitude towards Drs. Erik Jan Lingen and Martijn Stroeven at the Dynaflow Research Group, Houtsingel 95, 2719 EB Zoetermeer, The Netherlands for providing us the numerical toolkit jem/jive.
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Nguyen, V.P., Nguyen, G.D., Nguyen, C.T. et al. Modelling complex cracks with finite elements: a kinematically enriched constitutive model. Int J Fract 203, 21–39 (2017). https://doi.org/10.1007/s10704-016-0114-x
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DOI: https://doi.org/10.1007/s10704-016-0114-x