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dc.contributor.authorMaischak, M-
dc.contributor.authorStephan, EP-
dc.identifier.citationComputational Methods in Applied Mathematics, 16(1): pp.1–16, (2015)en_US
dc.description.abstractA 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.en_US
dc.description.sponsorshipThis work is supported by the German Research Foundation within the priority program 1180 Prediction and Manipulation of Interactions between Structure and Process.en_US
dc.publisherDe Gruyteren_US
dc.subjectContact problemsen_US
dc.subjectFenchel dualityen_US
dc.subjectVariational inequalitiesen_US
dc.titleDual-dual formulation for a contact problem with frictionen_US
dc.relation.isPartOfComputational Methods in Applied Mathematics-
Appears in Collections:Dept of Mathematics Research Papers

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