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International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002527
pages 689-706

ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY

Pablo Seleson
Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120, USA
Michael Parks
Applied Mathematics and Applications, Sandia National Laboratories, Albuquerque, New Mexico 87185-1320, USA

RESUMO

The influence function in the peridynamic theory is used to weight the contribution of all the bonds participating in the computation of volume-dependent properties. In this work, we use influence functions to establish relationships between bond-based and state-based peridynamic models. We also demonstrate how influence functions can be used to modulate nonlocal effects within a peridynamic model independently of the peridynamic horizon. We numerically explore the effects of influence functions by studying wave propagation in simple one-dimensional models and brittle fracture in three-dimensional models.

Referências

  1. Aksoylu, B. and Parks, M. L., Variational theory and domain decomposition for nonlocal problems. DOI: 10.1016/j.amc.2011.01.027

  2. Alali, B., Multiscale Analysis of Heterogeneous Media for Local and Nonlocal Continuum Theories.

  3. Arndt, M. and Griebel, M., Derivation of higher order gradient continuum models from atomistic models for crystalline solids. DOI: 10.1137/040608738

  4. Askari, E., Bobaru, F., Lehoucq, R. B., Parks, M. L., Silling, S. A., and Weckner, O., Peridynamics for multiscale materials modeling. DOI: 10.1088/1742-6596/125/1/012078

  5. Bobaru, F., Yang, M., Alves, L. F., Silling, S. A., Askari, E., and Xu, J., Convergence, adaptive refinement, and scaling in 1D peridynamics. DOI: 10.1002/nme.2439

  6. Dehnen, W., Towards optimal softening in three-dimensional N-body codes. I. Minimizing the force error. DOI: 10.1046/j.1365-8711.2001.04237.x

  7. Du, Q. and Zhou, K., Mathematical analysis for the peridynamic nonlocal continuum theory. DOI: 10.1051/m2an/2010040

  8. Emmrich, E. andWeckner, O., The peridynamic equation of motion in non-local elasticity theory. DOI: 10.1007/1-4020-5370-3_62

  9. Emmrich, E. and Weckner, O., On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity.

  10. Eringen, A. C., Nonlocal Continuum Field Theories.

  11. Foster, J. T., Silling, S. A., and Chen, W. W., Viscoplasticity Using Peridynamics. DOI: 10.1002/nme.2725

  12. Gunzburger, M. and Lehoucq, R. B., A nonlocal vector calculus with application to nonlocal boundary value problems. DOI: 10.1137/090766607

  13. Ha, Y. D. and Bobaru, F., Studies of dynamic crack propagation and crack branching with peridynamics. DOI: 10.1007/s10704-010-9442-4

  14. Kröner, E., Elasticity theory of materials with long range cohesive forces. DOI: 10.1016/0020-7683(67)90049-2

  15. Kunin, I. A., Elastic media with microstructure. I: One-dimensional models. DOI: 10.1007/978-3-642-81748-9

  16. Kunin, I. A., Elastic media with microstructure. II: Three-dimensional models. DOI: 10.1007/978-3-642-81960-5

  17. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity.

  18. Parks, M. L., Lehoucq, R. B., Plimpton, S. J., and Silling, S. A., Implementing peridynamics within a molecular dynamics code. DOI: 10.1016/j.cpc.2008.06.011

  19. Rogula, D., Introduction to nonlocal theory of material media.

  20. Seleson, P., Gunzburger, M., and Parks, M. L., Coupling local and nonlocal diffusion models across interfaces.

  21. Seleson, P., Parks, M. L., Gunzburger, M., and Lehoucq, R. B., Peridynamics as an Upscaling of Molecular Dynamics. DOI: 10.1137/09074807X

  22. Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces. DOI: 10.1016/S0022-5096(99)00029-0

  23. Silling, S. A. and Askari, E., A meshfree method based on the peridynamic model of solid mechanics. DOI: 10.1016/j.compstruc.2004.11.026

  24. Silling, S. A., Epton, M., Weckner, O., Xu, J., and Askari, E., Peridynamic States and Constitutive Modeling. DOI: 10.1007/s10659-007-9125-1

  25. Zhou, K. and Du, Q., Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions. DOI: 10.1137/090781267


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