Analysis of a sliding frictional contact problem with unilateral constraint

作者：Sofonea Mircea^*; Souleiman Yahyeh

来源：Mathematics and Mechanics of Solids, 2017, 22(3): 324-342.

DOI：10.1177/1081286515591304

• Elastic material
• frictional contact
• normal compliance
• unilateral constraint
• primal variational formulation
• dual variational formulation
• weak solution
• penalization method

We consider a mathematical model that describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraint, associated with a sliding version of Coulomb's law of dry friction. We present a description of the model, list the assumptions on the data and derive its primal variational formulation, in terms of displacement. Then we prove an existence and uniqueness result, Theorem 3.1. We proceed with a penalization method in the study of the contact problem for which we present a convergence result, Theorem 4.1. Finally, under additional hypotheses, we consider a variational formulation of the problem in terms of the stress, the so-called dual variational formulation, and prove an equivalence result, Theorem 5.3. The proofs of the theorems are based on arguments of monotonicity, compactness, convexity and lower semicontinuity.

• 出版日期2017-3