Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction

• DOI: 10.1007/bf00541909
• Publication Date: 2022-02-17T11:51:13Z
• Authors: A. Klarbring
• Keywords: 0101 mathematics; 01 natural sciences

This work considers a contact problem with friction involving one contact point and two degrees-of-freedom. The contacting structure is linear elastic. Two different models of contact interaction are considered, the classical Signorini unilateral contact law and a normal compliance law. Coulomb's law of friction is used. All possible so-called rate problems are solved, from which one concludes that the quasistatic problem may possess non-uniqueness and non-existence of solutions. In the case of the normal compliance law this can be explained by a softening structural response. For Signorini's law softening explains only some of the possible situations where non-uniqueness can occur.