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Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

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Abstract

We introduce a framework for modeling dynamic fracture problems using cohesive polygonal finite elements. Random polygonal meshes provide a robust, efficient method for generating an unbiased network of fracture surfaces. Further, these meshes have more facets per element than standard triangle or quadrilateral meshes, providing more possible facets per element to insert cohesive surfaces. This property of polygonal meshes is advantageous for the modeling of pervasive fracture. We use both Wachspress and maximum entropy shape functions to form a finite element basis over the polygons. Fracture surfaces are captured through dynamically inserted cohesive zone elements at facets between the polygons in the mesh. Contact is enforced through a penalty method that is applied to both closed cohesive surfaces and general interpenetration of two polygonal elements. Several numerical examples are presented that illustrate the capabilities of the method and demonstrate convergence of solutions.

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Acknowledgements

This research was supported by the National Science Foundation through contract Grant CMMI-1334783 to the University of California at Davis. Additional research support from Sandia National Laboratories is also acknowledged. EBC is grateful for the financial support from the ARCS Foundation Northern California. JEB was supported by Sandia National Laboratories and RVG was supported by the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under contract DE-AC52-06NA25396. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA

    Eric B. Chin & N. Sukumar

  2. Sandia National Laboratories, Albuquerque, NM, 87123, USA

    Joseph E. Bishop

  3. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Rao V. Garimella

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  1. Eric B. Chin
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  4. N. Sukumar
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Correspondence to N. Sukumar.

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Chin, E.B., Bishop, J.E., Garimella, R.V. et al. Finite deformation cohesive polygonal finite elements for modeling pervasive fracture. Int J Fract 214, 139–165 (2018). https://doi.org/10.1007/s10704-018-0325-4

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