IJPAM: Volume 86, No. 1 (2013)
MATERIALS WITH DAMAGE
Department of Mathematics
University of Setif1
Abstract. We consider a dynamic frictionless contact problem between an elastic-viscoplastic body and a reactive foundation. The contact is modelled with normal compliance. The material is elastic-viscoplastic with two internal variables which may describe a temperature parameter and the damage of the system caused by plastic deformations. We derive a weak formulation of the system consisting of a motion equation, an energy equation, and an evolution damage inclusion. We prove existence and uniqueness of the solution, and the positivity of the temperature. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic type inequalities, differential equations and fixed-point arguments.
Received: April 29, 2013
AMS Subject Classification: 74H20, 74H25, 74M15, 74F05, 74R20
Key Words and Phrases: dynamic process, frictionless, contact damage field, subdi ferential, temperature, fixed point
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DOI: 10.12732/ijpam.v86i1.12 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395