Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics
In this paper, we develop a general framework for an evolutionary variational-hemivariational inequality coupled with a differential equation. The framework is adapted to a frictional contact problem with applications in earth sciences. In here we present an approximation of the so-called rate-and-state friction law and prove that the coupled system is well-posed.
Main content
Frictional contact problems are of high importance in both industry and geophysical applications. To describe a model in contact mechanics, you need a conservation law, a constitutive law, interface laws, boundary conditions, and initial conditions. These equations depend on the material in question. The interface laws describe the interaction between the bodies or a body and a foundation. An essential step in any mathematical model is to check if it is well-posed. In this paper, we present a new evolutionary frictional contact model and prove that it is well-posed.
Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics
DOI: 10.1177/10812865231209256
Nadia Skoglund Taki, Kundan Kumar