4 research outputs found
Analysis of electro-viscoelastic antiplane contact problem with total slip rate dependent friction
We consider a mathematical model which describes the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a total slip rate dependent friction law. The material is assumed to be electro-viscoelastic and the foundation is assumed to be electrically conductive. First, we describe the classical formulation for the antiplane problem and we give the corresponding variational formulation which is given by a system coupling an evolutionary variational equality for the displacement field and a time-dependent variational equation for the electric potential field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of variational inequalities and by using the Banach fixed-point Theorem
Empiri膷na analiza prisotnosti bid rigginga pri javnih razpisih za izgradnjo slovenskega avtocestnega omre啪ja
summary:We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field with a time-dependent variational equation for the potential field. Then we prove the existence of a unique weak solution to the model. Moreover, the proof is based on arguments of evolution equations and on the Banach fixed-point theorem