Free Damage Propagation with Memory
- 295 Downloads
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.
KeywordsNonlocal model Damage Memory Peridynamics
Mathematics Subject Classification74R05 74R10
The authors would like to thank the anonymous referees for their comments.
- 11.Jha, P.K., Lipton, R.: Numerical analysis of peridynamic models in Hölder space. arXiv:1701.02818 (2017)
- 14.Lipton, R., Silling, S., Lehoucq, R.: Complex fracture nucleation and evolution with nonlocal elastodynamics. arXiv:1602.00247 (2016)
- 16.Oterkus, E., Guven, I., Madenci, E.: Fatigue failure model with peridynamic theory. In: IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, NV, June 2010, 1–6 (2010) Google Scholar
- 20.Silling, S.A., Askari, E.: Peridynamic model for fatigue cracking. Sandia Report, SAND2014–18590 (2014) Google Scholar