Taiwanese Journal of Mathematics

BILATERAL CONTACT PROBLEM WITH FRICTION AND WEAR FOR AN ELECTRO ELASTIC-VISCOPLASTIC MATERIALS WITH DAMAGE

Abdelmoumene Djabi and Abdelbaki Merouani

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Abstract

We consider a mathematical problem for quasistatic contact between anelectro elastic-viscoplastic body and an obstacle. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. We employ the electro elastic-viscoplastic with damage constitutive law for the material. The evolution of the damage is described by an inclusion of parabolic type. The problem is formulated as a system of an elliptic variational inequality for the displacement, a parabolic variational inequality for the damage and a variational equality for the electric stress. We establish a variational formulation for the model and we give the wear conditions for the existence of a unique weak solution to the problem. The proofs are based on classical results for elliptic variational inequalities, parabolic inequalities and fixed point arguments.

Article information

Source
Taiwanese J. Math., Volume 19, Number 4 (2015), 1161-1182.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133694

Digital Object Identifier
doi:10.11650/tjm.19.2015.5453

Mathematical Reviews number (MathSciNet)
MR3384684

Zentralblatt MATH identifier
1357.74038

Subjects
Primary: 70F40: Problems with friction 74M10: Friction 74M15: Contact 49J40: Variational methods including variational inequalities [See also 47J20] 74M10: Friction 74M15: Contact

Keywords
piezoelectric elastic-viscoplastic Fixed point friction contact variational inequality wear

Citation

Djabi, Abdelmoumene; Merouani, Abdelbaki. BILATERAL CONTACT PROBLEM WITH FRICTION AND WEAR FOR AN ELECTRO ELASTIC-VISCOPLASTIC MATERIALS WITH DAMAGE. Taiwanese J. Math. 19 (2015), no. 4, 1161--1182. doi:10.11650/tjm.19.2015.5453. https://projecteuclid.org/euclid.twjm/1499133694


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