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2015 BILATERAL CONTACT PROBLEM WITH FRICTION AND WEAR FOR AN ELECTRO ELASTIC-VISCOPLASTIC MATERIALS WITH DAMAGE
Abdelmoumene Djabi, Abdelbaki Merouani
Taiwanese J. Math. 19(4): 1161-1182 (2015). DOI: 10.11650/tjm.19.2015.5453
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.

Copyright © 2015 The Mathematical Society of the Republic of China
Abdelmoumene Djabi and Abdelbaki Merouani "BILATERAL CONTACT PROBLEM WITH FRICTION AND WEAR FOR AN ELECTRO ELASTIC-VISCOPLASTIC MATERIALS WITH DAMAGE," Taiwanese Journal of Mathematics 19(4), 1161-1182, (2015). https://doi.org/10.11650/tjm.19.2015.5453
Published: 2015
Vol.19 • No. 4 • 2015
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