Finite Element Continuation Analysis for Cnoidal Waves in Solids

Thomas Poulet; Roberto J. Cier; Sergio Rojas; Manolis Veveakis; Victor M. Calo

doi:10.1007/978-3-031-22213-9_3

Finite Element Continuation Analysis for Cnoidal Waves in Solids

Thomas Poulet, Roberto J. Cier, Sergio Rojas, Manolis Veveakis, Victor M. Calo

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

Under compression, rate-dependent solids subject to hydro-mechanical processes have been shown to accommodate singular cnoidal wave solutions [1], as a material instability at the stationary wave limit. Given the numerical complexity to solve the corresponding equation, we use a physical regularization approach [2] to cap the infinite stress growth with chemical pressurization of the material around the singularities. In this contribution, we show the results of a stability analysis of the underlying equation using a pseudo-arclength continuation algorithm with Finite Elements [3]. This allows to identify various solutions of the system with different numbers of peaks as a function of the problem parameters. We show the influence of the main material parameter, the existence of its critical values for different types of solutions, as well the evolution of peak spacing for the different admissible solutions. Finally, we investigate which initial conditions lead to solutions with stress peaks.

Original language	English
Title of host publication	Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials
Subtitle of host publication	Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics
Editors	Elena Pasternak, Arcady Dyskin
Place of Publication	Switzerland
Publisher	Springer
Pages	24-30
Number of pages	7
ISBN (Print)	9783031222122
DOIs	https://doi.org/10.1007/978-3-031-22213-9_3
Publication status	Published - 2023
Externally published	Yes
Event	International Workshop on Bifurcation and Degradation in Geomechanics, IWBDG 2022 - University of Western Australia, Perth, Australia Duration: 28 Nov 2022 → 1 Dec 2022 Conference number: 12th https://link.springer.com/book/10.1007/978-3-031-22213-9

Publication series

Name	Springer Series in Geomechanics and Geoengineering
ISSN (Print)	1866-8755
ISSN (Electronic)	1866-8763

Workshop

Workshop	International Workshop on Bifurcation and Degradation in Geomechanics, IWBDG 2022
Abbreviated title	IWBDG 2022
Country/Territory	Australia
City	Perth
Period	28/11/22 → 1/12/22
Internet address	https://link.springer.com/book/10.1007/978-3-031-22213-9

Keywords

Cnoidal waves
Compaction banding
Numerical continuation

Access to Document

10.1007/978-3-031-22213-9_3

Cite this

Poulet, T., Cier, R. J., Rojas, S., Veveakis, M., & Calo, V. M. (2023). Finite Element Continuation Analysis for Cnoidal Waves in Solids. In E. Pasternak, & A. Dyskin (Eds.), Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials: Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics (pp. 24-30). (Springer Series in Geomechanics and Geoengineering). Springer. https://doi.org/10.1007/978-3-031-22213-9_3

Poulet, Thomas ; Cier, Roberto J. ; Rojas, Sergio et al. / Finite Element Continuation Analysis for Cnoidal Waves in Solids. Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials: Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics. editor / Elena Pasternak ; Arcady Dyskin. Switzerland : Springer, 2023. pp. 24-30 (Springer Series in Geomechanics and Geoengineering).

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title = "Finite Element Continuation Analysis for Cnoidal Waves in Solids",

abstract = "Under compression, rate-dependent solids subject to hydro-mechanical processes have been shown to accommodate singular cnoidal wave solutions [1], as a material instability at the stationary wave limit. Given the numerical complexity to solve the corresponding equation, we use a physical regularization approach [2] to cap the infinite stress growth with chemical pressurization of the material around the singularities. In this contribution, we show the results of a stability analysis of the underlying equation using a pseudo-arclength continuation algorithm with Finite Elements [3]. This allows to identify various solutions of the system with different numbers of peaks as a function of the problem parameters. We show the influence of the main material parameter, the existence of its critical values for different types of solutions, as well the evolution of peak spacing for the different admissible solutions. Finally, we investigate which initial conditions lead to solutions with stress peaks.",

keywords = "Cnoidal waves, Compaction banding, Numerical continuation",

author = "Thomas Poulet and Cier, \{Roberto J.\} and Sergio Rojas and Manolis Veveakis and Calo, \{Victor M.\}",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; International Workshop on Bifurcation and Degradation in Geomechanics, IWBDG 2022, IWBDG 2022 ; Conference date: 28-11-2022 Through 01-12-2022",

year = "2023",

doi = "10.1007/978-3-031-22213-9\_3",

language = "English",

isbn = "9783031222122",

series = "Springer Series in Geomechanics and Geoengineering",

publisher = "Springer",

pages = "24--30",

editor = "Elena Pasternak and Arcady Dyskin",

booktitle = "Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials",

address = "Switzerland",

url = "https://link.springer.com/book/10.1007/978-3-031-22213-9",

}

Poulet, T, Cier, RJ, Rojas, S, Veveakis, M & Calo, VM 2023, Finite Element Continuation Analysis for Cnoidal Waves in Solids. in E Pasternak & A Dyskin (eds), Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials: Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics. Springer Series in Geomechanics and Geoengineering, Springer, Switzerland, pp. 24-30, International Workshop on Bifurcation and Degradation in Geomechanics, IWBDG 2022, Perth, Western Australia, Australia, 28/11/22. https://doi.org/10.1007/978-3-031-22213-9_3

Finite Element Continuation Analysis for Cnoidal Waves in Solids. / Poulet, Thomas; Cier, Roberto J.; Rojas, Sergio et al.
Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials: Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics. ed. / Elena Pasternak; Arcady Dyskin. Switzerland: Springer, 2023. p. 24-30 (Springer Series in Geomechanics and Geoengineering).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Finite Element Continuation Analysis for Cnoidal Waves in Solids

AU - Poulet, Thomas

AU - Cier, Roberto J.

AU - Rojas, Sergio

AU - Veveakis, Manolis

AU - Calo, Victor M.

N1 - Conference code: 12th

PY - 2023

Y1 - 2023

N2 - Under compression, rate-dependent solids subject to hydro-mechanical processes have been shown to accommodate singular cnoidal wave solutions [1], as a material instability at the stationary wave limit. Given the numerical complexity to solve the corresponding equation, we use a physical regularization approach [2] to cap the infinite stress growth with chemical pressurization of the material around the singularities. In this contribution, we show the results of a stability analysis of the underlying equation using a pseudo-arclength continuation algorithm with Finite Elements [3]. This allows to identify various solutions of the system with different numbers of peaks as a function of the problem parameters. We show the influence of the main material parameter, the existence of its critical values for different types of solutions, as well the evolution of peak spacing for the different admissible solutions. Finally, we investigate which initial conditions lead to solutions with stress peaks.

AB - Under compression, rate-dependent solids subject to hydro-mechanical processes have been shown to accommodate singular cnoidal wave solutions [1], as a material instability at the stationary wave limit. Given the numerical complexity to solve the corresponding equation, we use a physical regularization approach [2] to cap the infinite stress growth with chemical pressurization of the material around the singularities. In this contribution, we show the results of a stability analysis of the underlying equation using a pseudo-arclength continuation algorithm with Finite Elements [3]. This allows to identify various solutions of the system with different numbers of peaks as a function of the problem parameters. We show the influence of the main material parameter, the existence of its critical values for different types of solutions, as well the evolution of peak spacing for the different admissible solutions. Finally, we investigate which initial conditions lead to solutions with stress peaks.

KW - Cnoidal waves

KW - Compaction banding

KW - Numerical continuation

UR - https://www.scopus.com/pages/publications/85144819819

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DO - 10.1007/978-3-031-22213-9_3

M3 - Conference Paper

AN - SCOPUS:85144819819

SN - 9783031222122

T3 - Springer Series in Geomechanics and Geoengineering

SP - 24

EP - 30

BT - Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials

A2 - Pasternak, Elena

A2 - Dyskin, Arcady

PB - Springer

CY - Switzerland

T2 - International Workshop on Bifurcation and Degradation in Geomechanics, IWBDG 2022

Y2 - 28 November 2022 through 1 December 2022

ER -

Poulet T, Cier RJ, Rojas S, Veveakis M, Calo VM. Finite Element Continuation Analysis for Cnoidal Waves in Solids. In Pasternak E, Dyskin A, editors, Multiscale Processes of Instability, Deformation and Fracturing in Geomaterials: Proceedings of 12th International Workshop on Bifurcation and Degradation in Geomechanics. Switzerland: Springer. 2023. p. 24-30. (Springer Series in Geomechanics and Geoengineering). doi: 10.1007/978-3-031-22213-9_3

Finite Element Continuation Analysis for Cnoidal Waves in Solids

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Keywords

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