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Modelling interfacial cracking with non-matching cohesive interface elements

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Abstract

Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these interfacial cracks usually employs compatible or matching cohesive interface elements. In this paper, incompatible or non-matching cohesive interface elements are proposed for interfacial fracture mechanics problems. They allow non-matching finite element discretisations of the opposite crack faces thus lifting the constraint on the compatible discretisation of the domains sharing the interface. The formulation is based on a discontinuous Galerkin method and works with both initially elastic and rigid cohesive laws. The proposed formulation has the following advantages compared to classical interface elements: (i) non-matching discretisations of the domains and (ii) no high dummy stiffness. Two and three dimensional quasi-static fracture simulations are conducted to demonstrate the method. Our method not only simplifies the meshing process but also it requires less computational demands, compared with standard interface elements, for problems that involve materials/solids having a large mismatch in stiffnesses.

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Notes

  1. Based on the author’s own experiences in implementing XFEM, [10], and cohesive interface elements [41, 42] it can be concluded without any doubt the latter is much more easier to implement.

  2. The force terms are standard and thus omitted for sake of presentation.

  3. Searching for neighbouring elements is efficiently done using the technique of bounding boxes.

  4. Herein we made an assumption that the geometry of the interface \(\varGamma ^*\) has been well represented by the geometrically approximate FE domain meshes. This is to ensure that Eq. (34) has solutions. In case that this assumption cannot be guaranteed one needs to find the closest point projection of \(\mathbf {x}_k\) on \(\varOmega ^2\), commonly used in contact mechanics, readers are referred to the pre-processing algorithm in [48] for details.

  5. Jem-Jive has become open sourced since February 2016 at http://jive.dynaflow.com.

  6. The two domains separated by the interfacial crack are meshed independently using a Matlab script and the input required by the procedure described in Sect. 5 is also generated by this script.

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Acknowledgments

Funding support from the Australian Research Council via project DE160100577 (Vinh Phu Nguyen) is gratefully acknowledged. Stephane Bordas is sincerely grateful for the financial support of the European Research Council Starting Independent Research Grant (ERC grant agreement no. 279578): Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery. The authors 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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Authors and Affiliations

  1. Department of Civil Engineering, Monash University, Clayton, VIC, 3800, Australia

    Vinh Phu Nguyen, Chi Thanh Nguyen & Amin Heidarpour

  2. Faculté des Sciences, de la Technologie et de la Communication, University of Luxembourg, 6, rue Richard, Coudenhove-Kalergi, 1359, Luxembourg City, Luxembourg

    Stéphane Bordas

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  1. Vinh Phu Nguyen
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Nguyen, V.P., Nguyen, C.T., Bordas, S. et al. Modelling interfacial cracking with non-matching cohesive interface elements. Comput Mech 58, 731–746 (2016). https://doi.org/10.1007/s00466-016-1314-y

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