The Kachanov Method for a Rigid-Plastic Rolling Problem

Abstract

In this work, the method of successive linearization, proposed by L. M. Kachanov for solving nonlinear variational problems, arizing in the deformation theory of plasticity, is applied to a steady state, hot strip rolling problem. The material behaviour is described by a rigid-plastic, incompressible, strain rate dependent material model and for the roll-workpiece interface a constant friction law is used. The problem is stated in the form of a variational inequality with strongly nonlinear and nondifferentiable terms. The equivalent minimization problem is also given. Under certain restrictions on the material characteristics, existence and uniqueness results are obtained and the convergence of the method is proved.KeywordsVariational InequalityDeformation TheoryStrain Rate TensorDilatation StrainSuccessive LinearizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.