Dynamic Damage Propagation with Memory: A State-Based Model

  • Robert LiptonEmail author
  • Eyad Said
  • Prashant K. Jha
Reference work entry


A model for dynamic damage propagation is developed using nonlocal potentials. The model is posed using a state-based peridynamic formulation. The resulting evolution is seen to be well posed. At each instant of the evolution, we identify a damage set. On this set, the local strain has exceeded critical values either for tensile or hydrostatic strain, and damage has occurred. The damage set is nondecreasing with time and is associated with damage state variables defined at each point in the body. We show that a rate form of energy balance holds at each time during the evolution. Away from the damage set, we show that the nonlocal model converges to the linear elastic model in the limit of vanishing nonlocal interaction.


Damage model Nonlocal interactions Energy dissipation State-based peridynamics 



This material is based upon the 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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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