Numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage

Weimin Han; Michal Jureczka; Anna Ochal

doi:10.1016/j.cam.2020.112886

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Numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage

Journal article

Peer reviewed

Numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage

Weimin Han, Michal Jureczka and Anna Ochal

Journal of computational and applied mathematics, Vol.377, p.112886

10/15/2020

DOI: 10.1016/j.cam.2020.112886

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https://ruj.uj.edu.pl/xmlui/handle/item/271784View

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Abstract

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic differential inclusion for the damage function. A solution existence and uniqueness result is commented. A fully discrete scheme is introduced with the time derivative of the damage function approximated by the backward finite difference and the spatial derivatives approximated by finite elements. An optimal order error estimate is derived for the fully discrete scheme when linear elements are used for the velocity and displacement variables, and piecewise constants are used for the damage function. Simulation results on numerical examples are reported illustrating the performance of the fully discrete scheme and the theoretically predicted convergence orders.

Convergence

Damage

Fully discrete scheme

Hemivariational inequality

Optimal order error estimate

Quasistatic contact

Details

Title: Subtitle: Numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage
Creators: Weimin Han - University of Iowa
Michal Jureczka - Jagiellonian University
Anna Ochal - Jagiellonian University
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.377, p.112886
DOI: 10.1016/j.cam.2020.112886
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V
Grant note: DOI: 10.13039/501100004569, name: Ministerstwo Edukacji i Nauki, award: 4004/GGPJII/H2020/2018/0, 440328/PnH2/2019; DOI: 10.13039/501100007601, name: Horizon 2020; DOI: 10.13039/100010661, name: Horizon 2020 Framework Programme; DOI: 10.13039/100010665, name: H2020 Marie Skłodowska-Curie Actions, award: 823731
Language: English
Date published: 10/15/2020
Academic Unit: Mathematics
Record Identifier: 9984240772902771

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