# Dynamic Damage Propagation with Memory: A State-Based Model

## Abstract

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.

## Keywords

Damage model Nonlocal interactions Energy dissipation State-based peridynamics## Notes

### Acknowledgements

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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