Stress formulation for frictionless contact of an elastic-perfectly-plastic body

Abstract

A mathematical model for frictionless contact of a deformable body with a rigid moving obstacle is analyzed. The Prandtl–Reuss elastic-perfectly-plastic constitutive law is used to describe the material's behavior, and contact is modeled with a unilateral condition imposed on the surface velocity. The problem is motivated by the process of the plowing of the ground. A variational formulation of the problem is derived in terms of the stresses and the existence of the unique weak solution is proven. The proof is based on arguments for differential inclusions obtained in A. Amassad, M. Shillor and M. Sofonea (2001). A quasistatic contact problem for an elastic perfectly plastic body with Tresca's friction. Nonlin. Anal., 35, 95–109. Finally, a study of the continuous dependence of the solution on the data is presented.

Keywords:

• Perfectly plastic material
• Qualistatic process
• Unilateral frictionless contact
• Weak solution
• Differential inclusion
• AMS Subject Classifications: 74C05
• 74M15
• 35R70

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Meir Shillor †

E-mail: [email protected]