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A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation

Abstract

Peridynamics has attractive features for solving several fracture mechanics problems. On the other hand, to ensure the accuracy, a large amount of particles (material points) is required. Introduction of variable horizon is an alternative approach by changing the horizon size over the problem domain. In the present study, we propose a novel variable horizon concept. It is known that an undesired “ghost” force arises along the transition region of different horizons. In order to suppress the ghost force, the gradual variation in the horizon size over a certain region, called smoothing length, is introduced between different scale particle distributions. Efficiency of the smoothed variable horizon peridynamics is demonstrated by several numerical studies employing the ordinary state-based peridynamics. As a basic case, a linear displacement field is considered. It is observed that the proposed approach significantly reduces the ghost forces along the interface of different spatial discretizations. Additionally, the dynamic stress intensity factors of stationary cracks are carefully examined. The path independence of the fracture parameters in the variable horizon peridynamics is ensured. The efficiency of the presented method is then discussed. It is monitored that introduction of the smoothing length concept significantly reduces the computational costs in the peridynamic modeling.

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Acknowledgements

The present research was partially supported by the JSPS Grant-in-Aid for JSPS Fellows (19J14053) and Grants-in-Aid for Scientific Research (C)(18K04582), which the authors gratefully acknowledge.

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Correspondence to S. Tanaka.

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Imachi, M., Takei, T., Ozdemir, M. et al. A smoothed variable horizon peridynamics and its application to the fracture parameters evaluation. Acta Mech 232, 533–553 (2021). https://doi.org/10.1007/s00707-020-02863-9

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