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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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/

[1] S. A. Silling, “Reformulation of elasticity theory for discontinuities and long-range forces”, Journal of Mechanics and Physics of Solids, 48:1 (2000), 175–209 | DOI | MR

[2] Handbook of Peridynamic Modeling, ed. S. A. Siling, P. H. Geubelle, J. T. Foster, F. Bobaru, CRC Press by Taylor and Francis Group, LLC, New York, 2017, 586 pp. | MR

[3] E. Madenci, E. Oterkus, Peridynamic theory and its applications, Springer, New York, 2014, 289 pp.

[4] S. A. Siling, E. Askari, “A meshfree method based on the peridynamic model of solid mechanics”, Computers and Structures, 83 (2005), 1526–1535 | DOI

[5] D. Huang, C. Wang, G. Lu, P. Qiao, “An extended peridynamic approach for deformation and fracture analysis”, Engineering Fracture Mechanics, 141 (2015), 196–211 | DOI

[6] D. Huang, G. Lu, P. Qiao, “An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis”, International Journal of Mechanical Sciences, 8 (2015), 94–95

[7] S. A. Silling, M. Zimmermann, R. Abeyaratne, “Deformation of a peridynamic bar”, Journal of Elasticity, 17 (2003), 173–190 | DOI | MR

[8] F. Bobaru, M. Yabg, L. F. Alves, S. A. Siling, E. Askari, J. Xu, “Convergence, adaptive refinement, and scaling in 1D peridynamics”, International Journal for Numerical Methods in Engineering, 77 (2009), 852–877 | DOI

[9] S. A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari, “Peridynamic states and constitutive modeling”, Journal of Elasticity, 88 (2007), 151–184 | DOI | MR

[10] P. Seleson, D.J. Littlewood, “Convergence studies in meshfree peridynamic simulations”, Computers Mathematics with Applications, 71:11 (2016), 2432–2448 | DOI | MR

[11] P. Seleson, M. Parks, “On the role of the influence function in the peridynamic theory”, International Journal for Multiscale Computational Engineering, 9:6 (2011), 689–706 | DOI | MR

[12] P. Seleson, Connecting peridynamic models and coupling local and nonlocal systems, presentation at Mini-workshop: Mathematical Analysis for Peridynamics, 2011, 79 pp.

[13] M. L. Parks, P. Seleson, S. J. Plimpton, R. B. Lehoucq, S. A. Siling, Peridynamics with LAMMPS: A User Guide v0.2 Beta, New Mexico, 2008, 28 pp.

[14] Anisimov A.N., Grushin S.A., Voronin B.L., Kopkin S.V., Erofeev A.M., Demin D.A., Demina M.A., Zdorova M.V., Vetchinnikov M.V., Ericheva N.S., Kovalenko N.O., Kryuchkov I.A., Kechin A.G., Degtyarev V.A., Urm V.Ya., Kompleks programm molekulyarno-dinamicheskogo modelirovaniya (MoDyS), Svidetelstvo o gosudarstvennoi registratsii programmy dlya EVM No 2010614974, Sarov, 2010 (In Russ.)

[15] T. Qi, L. Shaofan, “Multiscale coupling of molecular dynamics and peridynamics”, Journal of the Mechanics and Physics of Solids, 95 (2016), 169–187 | DOI | MR

[16] M. L. Parks, R. B. Lehoucq, S. J. Plimpton, S.A. Silling, “Implementing peridynamics within a molecular dynamics code”, Computer Physics Communications, 179:11 (2008), 777–783 | DOI

[17] A. M. John, S. A. Silling, D. J. Littlewood, “A position-aware linear solid constitutive model for peridynamics”, Journal of Mechanics of Materials and Structures, 10:5 (2015), 539–557 | DOI | MR

[18] J.A. Mitchell, On the 'DSF' and the 'dreaded surface effect', presentation at Workshop on Nonlocal Damage and Failure, 2012, 18 pp.

[19] S. A. Silling, R. B. Lechoucq, “Convergence of peridynamics to classical elasticity theory”, Journal of Elasticity, 93 (2008), 13–37 | DOI | MR

[20] J.F. Kalthoff, S. Winkler, “Failure mode transition at high rates of shear loading”, International Conference on Impact Loading and Dynamic Behavior of Materials, 1987, 185–195