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Title: Dual-dual formulation for a contact problem with friction
Authors: Maischak, M
Stephan, EP
Keywords: Contact problems;Friction;Fenchel duality;Variational inequalities
Issue Date: 2015
Publisher: De Gruyter
Citation: Computational Methods in Applied Mathematics, 16(1): pp.1–16, (2015)
Abstract: A variational inequality formulation is derived for some frictional contact problems from linear elasticity. The formulation exhibits a two-fold saddle point structure and is of dual-dual type, involving the stress tensor as primary unknown as well as the friction force on the contact surface by means of a Lagrange multiplier. The approach starts with the minimization of the conjugate elastic potential. Applying Fenchel's duality theory to this dual minimization problem, the connection to the primal minimization problem and a dual saddle point problem is achieved. The saddle point problem possesses the displacement field and the rotation tensor as further unknowns. Introducing the friction force yields the dual-dual saddle point problem. The equivalence and unique solvability of both problems is shown with the help of the variational inequality formulations corresponding to the saddle point formulations, respectively.
ISSN: 1609-9389
Appears in Collections:Dept of Mathematics Research Papers

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