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Keywords:
hemivariational inequality; Rothe method; Clarke subdifferential; Caputo derivative; fractional viscoelastic constitutive law; contact with friction; numerical scheme; finite element method; convergence analysis; error estimation
hemivariational inequality; Rothe method; Clarke subdifferential; Caputo derivative; fractional viscoelastic constitutive law; contact with friction; numerical scheme; finite element method; convergence analysis; error estimation
Summary:
We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here's a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation.
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