An Analytical study of quasistatic frictionless antiplane problem with adhesion

Abstract

In this thesis, we consider a mathematical model describing the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The adhesion between the contact surfaces, induced by a bonding agent, is explicitly accounted for. The material is assumed to be viscoelastic with long-term memory and nonhomogeneous properties, and the process is modeled as quasistatic. This work is devided into three chapters. First, we present preliminary results from functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem, incorporating adhesion effects, viscoelasticity with long-term memory, and matterial nonhomogeneity under quasistatic assumptions. Finally, the third chapter establishes a variational formulation of the coupled system, a volterra-type variational equality for the displacement field and an evolution equation for the bonding field..