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Proximal Bundle Method for simplied unilateral adhesion contact problem of elasticity

Czepiel J.

Schedae Informaticae

2011

Vol. 20

115-136

We consider a mathematical model which describes the adhesive contact between a linearly elastic body and an obstacle. The process is static and frictionless. The normal contact is governed by two laws. The rst one is a Signorini law, representing the fact that there is no penetration between a body and an obstacle. The second one is a Winkler type law signifying that if there is no contact, the bonding force is proportional to the displacement below a given bonding threshold and equal to zero above the bonding threshold. The model leads to a variational-hemivariational inequality. We present the numerical results for solving a simple two-dimensional model problem with the Proximal Bundle Method (PBM). We analyze the method sensitivity and convergence speed with respect to its parameters.