THE EVALUATION OF HYPERSINGULAR PERIDYNAMICS OPERATORS
DOI:
https://doi.org/10.37547/Keywords:
hypersingular operators, peridynamic, theoretical underpinnings, numerical evaluation methods, practical applications, peridynamic models.Abstract
This article provides a comprehensive overview of hypersingular operators in peridynamics, delving into their theoretical underpinnings, numerical evaluation methods, practical applications, and implications for advancing computational simulations in materials science and engineering. By examining the significance of hypersingular operators, we aim to enhance our understanding of peridynamic models and their capabilities in simulating intricate material responses.
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References
Abatangelo, N., Jarohs, S., & Saldaña, A. (2017). Positive powers of the Laplacian: from hypersingular integrals to boundary value problems. arXiv preprint arXiv:1709.00976.
Alimov, S., & Yuldasheva, A. (2021). Solvability of Singular Equations of Peridynamics on Two-Dimensional Periodic Structures. Journal of Peridynamics and Nonlocal Modeling, 1-19.
D’Elia, M., Du, Q., & Gunzburger, M. (2017). Recent progress in mathematical and computational aspects of peridynamics. Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1-26.
Li, Z., Yuan, S., Tang, H., Zhu, Y., & Sun, H. (2023). Quantifying nonlocal bedload transport: A regional-based nonlocal model for bedload transport from local to global scales. Advances in Water Resources, 177, 104444.
Šilhavý, M. (2017). Higher gradient expansion for linear isotropic peridynamic materials. Mathematics and Mechanics of Solids, 22(6), 1483-1493.
