Journal of Elasticity

, Volume 133, Issue 2, pp 129–153 | Cite as

Free Damage Propagation with Memory

  • Robert LiptonEmail author
  • Eyad Said
  • Prashant Jha


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.


Nonlocal model Damage Memory Peridynamics 

Mathematics Subject Classification

74R05 74R10 



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


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA

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