Well-posedness of evolutionary differential variational鈥揾emivariational 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听both听industry and geophysical applications.听To describe a model in contact mechanics,听you need a conservation law, a constitutive law, interface laws,听boundary conditions, and initial听conditions.听These equations depend on the material in question.听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.
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Well-posedness of evolutionary differential variational鈥揾emivariational inequalities and applications to frictional contact mechanics
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Nadia Skoglund Taki, Kundan Kumar