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

• Published in: Taiwanese journal of mathematics Vol. 19; no. 4; pp. 1161 - 1182
• Main Authors: Djabi, Abdelmoumene, Merouani, Abdelbaki
• Format: Journal Article
• Language: English
• Published: Mathematical Society of the Republic of China 01.08.2015
• Subjects: Boundary conditions; Contact potentials; Election laws; Electric fields; Friction; Hilbert spaces; Inner products; Mathematical functions; Tensors; Variational inequalities
• ISSN: 1027-5487; 2224-6851
• DOI: 10.11650/tjm.19.2015.5453

We consider a mathematical problem for quasistatic contact between an electro 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. 2010Mathematics Subject Classification: 70F40, 74M10, 74M15, 49J40, 74M10, 74M15. Key words and phrases: Piezoelectric, Elastic-viscoplastic Fixed point, Friction contact, Variational inequality, Wear.