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Two mathematical models are developed within the theoretical framework oflarge strain elasticity for the determination of upper and lower bounds on thetotal strain energy of a finitely deformed hyperelastic body in unilateralcontact with a rigid surface or with an elastic substrate. The model problemstake the form of two continuous optimization problems with inequalityconstraints, the solutions of which are used to provide an enclosure on theuniform external load acting on the body's surface away from the contact zone.

Guaranteed upper and lower bounds on the uniform load of contact problems in elasticity