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Peridynamic Modeling of Frictional Contact

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Abstract

This paper reviews several existing peridynamic models for frictional contact (previously documented only in the gray literature), and extends them to remedy various shortcomings. In particular, we introduce a state-based nonlocal friction formulation that corrects for loss of angular momentum balance and objectivity in a widely used frictional extension of short-range contact forces. We demonstrate the properties of various peridynamic contact models by applying them in finite element and meshfree peridynamic analyses of benchmark problems and an impact/penetration test.

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Notes

  1. We differ in convention from [13, (17)] by including an explicit factor of 1/2, to make the interpretation of ϕ in self-contact more consistent with the two-body contact energy [13, (1)].

  2. While \(\dot {\mathbf {r}}_{1\to 2}\) is not objective, the rate of change of bond length, , is objective, which is both clear from physical intuition and easily derived by invoking the antisymmetry of Ω.

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Acknowledgments

We thank the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported in this paper.

Funding

D. Kamensky and Y. Bazilevs were supported through AFOSR Award No. FA9550-16-1-0131. M. Behzadinasab and J.T. Foster were supported by AFOSR Award No. ONRBAA12-020. M. Behzadinasab also received fellowship funding from The University of Texas at Austin.

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Authors and Affiliations

  1. School of Engineering, Brown University, Providence, RI, 02912, USA

    David Kamensky & Yuri Bazilevs

  2. Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, Austin, TX, 78712, USA

    Masoud Behzadinasab & John T. Foster

  3. Hildebrand Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    John T. Foster

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  1. David Kamensky
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  2. Masoud Behzadinasab
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  3. John T. Foster
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  4. Yuri Bazilevs
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Correspondence to David Kamensky.

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D. Kamensky and Y. Bazilevs were supported through Air Force Office of Scientific Research (AFOSR) Award No. FA9550-16-1-0131. M. Behzadinasab and J. T. Foster were supported by AFOSR Award No. ONRBAA12-020.

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Kamensky, D., Behzadinasab, M., Foster, J.T. et al. Peridynamic Modeling of Frictional Contact. J Peridyn Nonlocal Model 1, 107–121 (2019). https://doi.org/10.1007/s42102-019-00012-y

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