Penalty method for unilateral contact problem with Coulomb's friction in time-fractional derivatives

Abstract

The purpose of this work is to study a mathematical model that describes a contact between a deformable body and a rigid foundation. A linear viscoelastic Kelvin-Voigt constitutive law with time-fractional derivatives describes the material’s behavior. The contact is modeled with Signorini’s condition coupled with Coulomb’s friction law. We derive a variational formulation of the model, and we prove the existence of a weak solution using the theory of monotone operators and Caputo derivative and the Rothe method. We also introduce the penalized problem and prove its solvability using the Galerkin method. Furthermore, we study the convergence of its solution to the solution of the original problem as the penalization parameter tends to zero.

Keywords

• fractional viscoelastic constitutive law
• caputo derivative
• contact with friction
• rothe method
• faedo-galerkin method
• compactness method
• penalty method
• 35r11
• 74m10
• 74m15
• 65n30
• 65m60
• 46b50