Titlebook: Computational Methods Based on Peridynamics and Nonlocal Operators; Theory and Applicati Timon Rabczuk,Huilong Ren,Xiaoying Zhuang Book 202

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Michel Rieutord,Francisco Espinosa LaraIn this chapter, the dual-support smoothed particle hydrodynamics are presented as a special case of the nonlocal operator method in Chap. 3. Several numerical examples in linear/nonlinear elasticity are presented.

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Dual-Support Smoothed Particle Hydrodynamics in Solid: Variational Principle and Implicit FormulatiIn this chapter, the dual-support smoothed particle hydrodynamics are presented as a special case of the nonlocal operator method in Chap. 3. Several numerical examples in linear/nonlinear elasticity are presented.

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https://doi.org/10.1007/978-3-031-20906-2Peridynamics; Nonlocal Operator Method, Modeling and Simulation; Computational Mechanics; Phase Field M

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978-3-031-20908-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Danuta Gabryś-Barker,Adam Wojtaszekthe horizon domain and the reaction force from the dual-horizon domain. We prove that the DH-PD satisfies the conservation of linear momentum and angular momentum. The DH-PD allows for an arbitrary horizon for each particle and the discretization can be nonuniform. Some numerical examples at the end

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Studying Situational Interactiononlocal operators, e.g. nonlocal gradient, nonlocal curl and nonlocal divergence. These nonlocal operators converge to the corresponding local ones when the support degenerates to one point. The operator matrices for these operators are derived explicitly. The residuals and tangent stiffness matrice