Weak solvability of elliptic variational inequalities coupled with a nonlinear differential equation
In this paper, we prove the existence and uniqueness of elliptic variational inequalities coupled with a nonlinear ODE. Considering an elliptic equation in the domain allows us to include a fully nonlinear ODE on the contact surface which gives us new applications of frictional adhesion contact problems.
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New publication by Nadia Skoglund Taki.
Frictional adhesion contact problems are important in both industry and earth sciences. The adhesion process on the contact surface is modelled through a nonlinear ODE, which describes the active bonds. This process can be used to, for example, describe layered rocks. To include a fully nonlinear ODE for the adhesion process, we needed to simplify the strain tensor in the momentum balance equation. This setting is referred to as antiplane shear and captures many important physical phenomena. For example, normal faults and mode III cracks are categorized in the antiplane shear setting, where normal faults are used to, e.g., describe the early phase of earthquakes.