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The Peridynamic Jacobian

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Abstract

In this brief note we propose a simple formula for the peridynamic Jacobian providing a physical justification along with demonstrating consistency with the classical Jacobian.

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Notes

  1. this allows for computing volume scalings that include discontinuities in the deformation

  2. details omitted for brevity

References

  1. Bobaru F, Foster J, Geubelle P, Silling S (2016) Handbook of peridynamic modeling. No. ISBN 9781482230437 in Advances in Applied Mathematics, CRC Press

  2. Silling S (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209. https://doi.org/10.1016/S0022-5096(99)00029-0

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  3. Silling S, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elasticity 88:151–184. https://doi.org/10.1007/s10659-007-9125-1

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Authors and Affiliations

  1. The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA

    Xiao Xu & John T. Foster

Authors
  1. Xiao Xu
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  2. John T. Foster
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Contributions

X.X. and J.F. wrote and reviewed the manuscript equally.

Corresponding author

Correspondence to John T. Foster.

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Xu, X., Foster, J.T. The Peridynamic Jacobian. J Peridyn Nonlocal Model 5, 491–496 (2023). https://doi.org/10.1007/s42102-022-00091-4

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  • DOI: https://doi.org/10.1007/s42102-022-00091-4

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