Abstract
This work is concerned with the application of two different particle methods, the state-based peridynamics and the reproducing kernel particle method, to model the nonlocal multiresolution continuum. It is shown that both methods lead to the same results in uniform grids, and that they can offer an alternative to the finite element method based multiscale analysis. The equivalence between the two methods is explained in a comparison study, which shows that the state-based peridynamics may have better computational efficiency, but the RKPM synchronized derivative approach may have the possibility of faster convergence.
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Notes
- 1.
Note that this equation is presented by using an abbreviated notation in this paper where the time dependence of each term is suppressed.
- 2.
Note that this deformation gradient is a nonlocal quantity unlike the infinitesimal deformation gradient. See [3] for detailed discussions.
- 3.
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Dai, Z., Bessa, M.A., Li, S., Liu, W.K. (2015). Particle Method Modeling of Nonlocal Multiresolution Continua. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VII. Lecture Notes in Computational Science and Engineering, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-06898-5_3
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