A quasistatic contact problem for viscoelastic materials with friction and damage

作者：Li, Yunxiang^*; Liu, Zhenhai

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(7): 2221-2229.

DOI：10.1016/j.na.2010.05.051

• Hemivariational inequality
• Viscoelastic
• Frictional contact
• Damage
• Stationary inclusion
• Weak solution

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is quasistatic, the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions. The mechanical damage of the material is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive the variational formulation of the problem, which is a coupled system of a hemivariational inequality and a parabolic equation. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract stationary inclusion and a fixed point theorem.

• 出版日期2010-10-1
• 单位湖南城市学院; 中南大学; 广西民族大学