A quasistatic frictional contact problem with damage involving viscoelastic materials with short memory

作者：Li, Yunxiang; Migorski, Stanislaw^*; Han, Jiangfeng

来源：Mathematics and Mechanics of Solids, 2016, 21(10): 1167-1183.

DOI：10.1177/1081286514558657

• Hemivariational inequality
• viscoelastic
• quasistatic
• frictional contact
• damage
• evolutionary inclusion
• weak solution

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be quasistatic and the material behaviour is described by a viscoelastic constitutive law with damage. The friction and contact are modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the velocity and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of time-dependent stationary inclusions and a fixed point theorem.

• 出版日期2016-11
• 单位湖南城市学院