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Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When this feature is combined with strongly non‐linear, path‐dependent material behaviour, difficulties with convergence of the typically used iterative processes can be encountered. Demonstrates this by analysis of press‐fit connection, a typical problem in which both of those characteristics can be present. Offers an explanation as to the possible source of those difficulties. Suggests in support of this explanation, two simple modifications of the usual iterative schemes. In spite of their simplicity, they are found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.

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