Geodesic
Peridynamics method for problems solve of solids destruction
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 4, pp. 452-468

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The article investigates the method of peridynamics, which is an alternative approach to solving destruction problems based on integral equations. It is assumed that particles in a continuum interact with each other at a finite distance, as in molecular dynamics. Damage is part of the theory at the level of two-particle interactions, so damage finding and destruction occurs when solving the equation of motion. During this work, bond-based and state-based peridynamics models of destruction used in the Sandia Laboratory were described and implemented within the framework of the MoDyS molecular dynamics software package. In the bond-based model, the defining relationship is the bond stiffness function, which corrects the force of particle-particle interaction and imposes a restriction on the use of the Poisson's ratio. The state-based model generalizes the bond-based approach and may be applied to materials with any Poisson's ratio. The relationship of both models is ascertained. Calculation convergence is demonstrated on the example of a one-dimensional elasticity problem. The possibility of using the implemented models for fracture problems is also shown.
Keywords: peridynamics, continuum mechanics, molecular dynamics, mesh-free method, fracture model, bond stiffness function.
Mots-clés : nonlocal interactions 
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     author = {D. A. Shishkanov and M. V. Vetchinnikov and Yu. N. Deryugin},
     title = {Peridynamics method for problems solve of solids destruction},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {452--468},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a3/}
}
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D. A. Shishkanov; M. V. Vetchinnikov; Yu. N. Deryugin. Peridynamics method for problems solve of solids destruction. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 4, pp. 452-468. http://geodesic.mathdoc.fr/item/SVMO_2022_24_4_a3/