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A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes

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Abstract

Large-scale simulation of separation phenomena in solids such as fracture, branching, and fragmentation requires a scalable data structure representation of the evolving model. Modeling of such phenomena can be successfully accomplished by means of cohesive models of fracture, which are versatile and effective tools for computational analysis. A common approach to insert cohesive elements in finite element meshes consists of adding discrete special interfaces (cohesive elements) between bulk elements. The insertion of cohesive elements along bulk element interfaces for fragmentation simulation imposes changes in the topology of the mesh. This paper presents a unified topology-based framework for supporting adaptive fragmentation simulations, being able to handle two- and three-dimensional models, with finite elements of any order. We represent the finite element model using a compact and “complete” topological data structure, which is capable of retrieving all adjacency relationships needed for the simulation. Moreover, we introduce a new topology-based algorithm that systematically classifies fractured facets (i.e., facets along which fracture has occurred). The algorithm follows a set of procedures that consistently perform all the topological changes needed to update the model. The proposed topology-based framework is general and ensures that the model representation remains always valid during fragmentation, even when very complex crack patterns are involved. The framework correctness and efficiency are illustrated by arbitrary insertion of cohesive elements in various finite element meshes of self-similar geometries, including both two- and three-dimensional models. These computational tests clearly show linear scaling in time, which is a key feature of the present data-structure representation. The effectiveness of the proposed approach is also demonstrated by dynamic fracture analysis through finite element simulations of actual engineering problems.

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Notes

  1. For reference, the tests were run on a dual-processor AMD Opteron 248 (2 × 2,193.78 MHz, 64 bits, and 16 Gb RAM).

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Acknowledgments

Paulino gratefully acknowledges the support from NASA-Ames, Engineering for Complex Systems Program, and the NASA-Ames Chief Engineer (Dr. Tina Panontin) through grant NAG 2-1424. Both Celes and Espinha would like to thank the Tecgraf laboratory at PUC-Rio, which is mainly funded by the Brazilian oil company, Petrobras.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, MC-250, 205 North Mathews Avenue, Urbana, IL, 61801-2397, USA

    Glaucio H. Paulino & Zhengyu (Jenny) Zhang

  2. Tecgraf/PUC-Rio—Computer Science Department, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ, 22450-900, Brazil

    Waldemar Celes & Rodrigo Espinha

Authors
  1. Glaucio H. Paulino
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  2. Waldemar Celes
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  3. Rodrigo Espinha
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  4. Zhengyu (Jenny) Zhang
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Correspondence to Glaucio H. Paulino.

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Paulino, G.H., Celes, W., Espinha, R. et al. A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes. Engineering with Computers 24, 59–78 (2008). https://doi.org/10.1007/s00366-007-0069-7

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  • DOI: https://doi.org/10.1007/s00366-007-0069-7

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