ANALYSIS OF TWO QUASISTATIC HISTORY-DEPENDENT CONTACT MODELS

作者：Cheng, Xiaoliang^*; Migorski, Stanislaw; Ochal, Anna; Sofonea, Mircea

来源：Discrete and Continuous Dynamical Systems-Series B, 2014, 19(8): 2425-2445.

DOI：10.3934/dcdsb.2014.19.2425

• Viscoelastic material
• viscoplastic material
• normal compliance
• memory term
• frictional contact
• Clarke subdifferential
• history-dependent hemivariational inequality
• weak solution

We consider two mathematical models which describe the evolution of a viscoelastic and viscoplastic body, respectively, in contact with a piston or a device, the so-called obstacle or foundation. In both models the contact process is assumed to be quasistatic and the friction is described with a Clarke subdifferential boundary condition. The novelty of the models consists in the constitutive laws as well as in the contact conditions we use, which involve a memory term. We derive a variational formulation of the problems which is in the form of a system coupling a nonlinear integral equation with a history-dependent hemivariational inequality. Then, we prove the existence of a weak solution and, under additional assumptions, its uniqueness. The proof is based on a result on history-dependent hemivariational inequalities obtained in [18].

• 出版日期2014-10
• 单位浙江大学