Improved method for zero-energy mode suppression in peridynamic correspondence model
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The peridynamic correspondence model provides a general formulation to incorporate the classical local model and, therefore, helps to solve mechanical problems with discontinuities easily. But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor. To suppress zero-energy modes, previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory, which requires a bond-based peridynamic micro-modulus. In this work, we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model. Hence, the bond-based peridynamic micro-modulus is abandoned. This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials. Several examples are presented to demonstrate its performance in simulating crack propagation, and numerical results show its efficiency and effectiveness.
KeywordsPeridynamic correspondence model Zero-energy modes Anisotropic material Damage
This work was supported by the National Natural Science Foundation of China (Grants 11472196, 11172216 and 11772237).
- 7.Oterkus, E., Guven, I., Madenci, E.: Fatigue failure model with peridynamic theory. In: 2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, Las Vegas, June 2–5 (2010)Google Scholar
- 9.Zhu, F., Zhao, J.: A peridynamic investigation on crushing of sand particles. Géotechnique. 69, 529–540 (2019)Google Scholar
- 20.Littlewood, D.J.: Simulation of dynamic fracture using peridynamics, finite element modeling, and contact. In: ASME 2010 International Mechanical Engineering Congress and Exposition, Vancouver, November 12–18 (2010)Google Scholar
- 21.Littlewood, D.J.: A nonlocal approach to modeling crack nucleation in AA 7075-T651. In: ASME 2011 International Mechanical Engineering Congress and Exposition, Denver, November 11–17 (2011)Google Scholar