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Finite element implementation of ordinary state-based peridynamics with variable horizon

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Abstract

This study presents an ordinary state-based peridynamic (OSB PD) analysis within the finite-element framework while considering implicit/explicit solvers. The present PD formulation permits non-uniform discretization with a variable horizon and eliminates the use of external surface and volume correction factors. An implicit solver is employed until immediately before damage emerges, and then an adaptive time-stepping explicit solver for crack initiation and propagation. The major advantage of the present approach is the reduction in computational time. The PD interactions lead to a sparsely populated global stiffness matrix. The BiConjugate Gradient Stabilized (BICGSTAB) method is employed to determine the solution of the system equations. Damage onset and its evolution is investigated using the critical stretch criterion. The efficacy of the present approach is established by considering two different geometric configurations and loading/boundary conditions. The PD predictions for the crack patterns compare well with those of the analytical results and experimental observations.

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Acknowledgements

This study was performed as part of the ongoing research at the MURI Center for Material Failure Prediction through Peridynamics at the University of Arizona (AFOSR Grant No. FA9550-14-1-0073) and it was supported by Erciyes University Scientific Research Projects Coordination Unit (Grant No. 11070).

Funding

This work was funded by Erciyes Üniversitesi (Grant no. 11070); Air Force Research Laboratory (Grant no. FA9550-14-1-0073).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Erciyes University, Kayseri, Turkey

    Mehmet Dorduncu

  2. Department of Mechanical Engineering, University of Arizona, Tucson, AZ, USA

    Erdogan Madenci

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  1. Mehmet Dorduncu
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Correspondence to Mehmet Dorduncu.

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Dorduncu, M., Madenci, E. Finite element implementation of ordinary state-based peridynamics with variable horizon. Engineering with Computers 39, 641–654 (2023). https://doi.org/10.1007/s00366-022-01641-6

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