Anisotropic peridynamic model—Formulation and implementation

Aylin Ahadi; Jakob Krochmal; Aylin Ahadi; Jakob Krochmal

doi:10.3934/matersci.2018.4.742

AIMS Materials Science

2018, Volume 5, Issue 4: 742-755. doi: 10.3934/matersci.2018.4.742

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Research article Special Issues

Anisotropic peridynamic model—Formulation and implementation

Aylin Ahadi ^,,
Jakob Krochmal

Division of Mechanics, Department of Mechanical Engineering Lund University, P.O. Box 118, S22100 Lund, Sweden

Received: 24 April 2018 Accepted: 20 June 2018 Published: 24 August 2018

In this work, anisotropy is introduced in a peridynamic model. The spherical influence function is replaced by an ellipsoidal influence function. The model is mathematically formulated and implemented into the source files of LAMMPS, extending the program in a straight-forward manner. The extension ca be applied to other peridynamic model and here it is introduced into elastoplastic peridynamic model in LAMMPS. The implemented model is tested through simulating beams loaded in compression. The model is found to alter the material behavior in the simulations compared to the original isotropic mode. A clear qualitative and quantitative difference in behavior is shown independently of pre-existing simulation parameters. The model is shown to be internally consistent. Finally we also demonstrated that the model can easily be extended to include several preferable direction opening for application as modeling elasticplastic deformation of anisotropic heterogeneous crystalline matter.
- peridynamics,
- anisotropy,
- implementation,
- PDLAMMPS
Citation: Aylin Ahadi, Jakob Krochmal. Anisotropic peridynamic model—Formulation and implementation[J]. AIMS Materials Science, 2018, 5(4): 742-755. doi: 10.3934/matersci.2018.4.742

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Abstract

In this work, anisotropy is introduced in a peridynamic model. The spherical influence function is replaced by an ellipsoidal influence function. The model is mathematically formulated and implemented into the source files of LAMMPS, extending the program in a straight-forward manner. The extension ca be applied to other peridynamic model and here it is introduced into elastoplastic peridynamic model in LAMMPS. The implemented model is tested through simulating beams loaded in compression. The model is found to alter the material behavior in the simulations compared to the original isotropic mode. A clear qualitative and quantitative difference in behavior is shown independently of pre-existing simulation parameters. The model is shown to be internally consistent. Finally we also demonstrated that the model can easily be extended to include several preferable direction opening for application as modeling elasticplastic deformation of anisotropic heterogeneous crystalline matter.

References

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