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Free Damage Propagation with Memory

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Abstract

We introduce a simple model for free damage propagation based on non-local potentials. The model is developed using a state based peridynamic formulation. The resulting evolution is shown to be well posed. At each instant of the evolution we identify the damage set. On this set the local strain has exceeded critical values either for tensile or hydrostatic strain and damage has occurred. For this model the damage set is nondecreasing with time and associated with damage variables defined at each point in the body. We show that energy balance holds for this evolution. For differentiable displacements away from the damage set we show that the nonlocal model converges to the linear elastic model.

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Acknowledgements

The authors would like to thank the anonymous referees for their comments.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Robert Lipton, Eyad Said & Prashant Jha

Authors
  1. Robert Lipton
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  2. Eyad Said
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  3. Prashant Jha
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Correspondence to Robert Lipton.

Additional information

This material is based upon work supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF1610456.

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Lipton, R., Said, E. & Jha, P. Free Damage Propagation with Memory. J Elast 133, 129–153 (2018). https://doi.org/10.1007/s10659-018-9672-7

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  • DOI: https://doi.org/10.1007/s10659-018-9672-7

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