PSI - Issue 23

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Available online at www.sciencedirect.com StructuralIntegrity Procedia 00 (2019) 000 – 000 StructuralIntegrity Procedia 00 (2019) 000 – 000

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Procedia Structural Integrity 23 (2019) 125–130

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICMSMF organizers © 201 9 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Continual models of solid media with a discrete set of slip planes (layered, block media) and with nonlinear viscous-plastic type lip conditions at the contac boundaries of structural elem nts are constructed. The resulting system of equations contai s a small viscosity parameter in the den m nator of nonlinear fr e terms. Fo a stable umerical solution f a system of differential equations, an explicit-implici method is pr posed with an explicit appro i ation of the qu tions of m tion and an implicit approxim tion of the constitutive r lations containing a small parameter. Examples of numerical solutions of dynamic problems on the scattering of waves o lay red cluster in an elastic medium, on the formation of slip and delamination zones at the boundaries of structural elements are given. © 201 9 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. 9th International Conference on Materials Structure and Micromechanics of Fracture Continual models of layered and block media with slippage and delamination Nikitin I.S. a, *, Burago N.G. b , Golubev V.I. c , Nikitin A.D. a a Institute of Computer Aided Design of RAS, 2-nd Brestskaya str., 19/18, Moscow, 123056, Russia b Ishlinsky Institute for Problems in Mechanics of RAS, Vernadskogo pr., 101-1, Moscow, 119526, Russia c Moscow Institute of Physics and Technology (National Research University), Institutskiy per., 9, Dolgoprudny, Moscow, 141701, Russia 9th International Conference on Materials Structure and Micromechanics of Fracture Continual models of layered and block media with slippage and delamination Nikitin I.S. a, *, Burago N.G. b , Golubev V.I. c , Nikitin A.D. a a I titute of Compute Aided Design of RAS, 2-nd Br stskaya str., 19/ 8, Mosc w, 123056, Russia b Ishlinsky Institute for Pr blems in Mechanics of RAS, Vernadskogo pr., 101-1, Moscow, 119526, Russia c Moscow Institute of Physics and Technology (National Research University), Institutskiy per., 9, Dolgoprudny, Moscow, 141701, Russia Abstract Abstract Continual models of solid media with a discrete set of slip planes (layered, block media) and with nonlinear viscous-plastic type slip conditions at the contact boundaries of structural elements are constructed. The resulting system of equations contains a small viscosity parameter in the denominator of nonlinear free terms. For a stable numerical solution of a system of differential equations, an explicit-implicit method is proposed with an explicit approximation of the equations of motion and an implicit approximation of the constitutive relations containing a small parameter. Examples of numerical solutions of dynamic problems on the scattering of waves on layered cluster in an elastic medium, on the formation of slip and delamination zones at the boundaries of structural elements are given. 1. Introduction Nowadays, more and more complex mathematical models are used to simulate different wave problems: seismic survey process (Golubev et al., 2017), seismic migration (Golubev et al., 2018a; Golubev et al., 2019), earthquake initiation (Golubev et al., 2018b).Continual models of deformable solid media with a discrete set of slip planes 1. Introduction Nowadays, more and more complex mathematical models are used to simulate differ nt w ve problems: seismic survey process (Golubev et al., 2017), seismic migration (Golubev et al., 2018 ; Golubev et al., 2019), earthquake initiation (Golubev et al., 2018b).Continual models of deformable solid media with a discrete set of slip planes Keywords: slip conditions; layered media; block media; delamination; explicit-implicit method; scattering of waves Keywords: slip conditions; layered media; block media; delamination; explicit-implicit method; scattering of waves

* Corresponding author. Tel.: +7-916-637-70-28. E-mail address: i_nikitin@list.ru * Correspon ing author. Tel.: +7-916-637-70-28. E-mail address: i_nikitin@list.ru

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICMSMF organizers 10.1016/j.prostr.2020.01.074