Modelling and Analysis of a Class of Metal--Forming Problems

Abstract

A class of steady-state metal-forming problems, with rigid-plastic, in- compressible, strain-rate dependent material model and nonlocal Coulomb's fric- tion, is considered. Primal, mixed and penalty variational formulations, containing variational inequalities with nonlinear and nondifferentiable terms, are derived and studied. Existence, uniqueness and convergence results are obtained and shortly presented. A priori finite element error estimates are derived and an algorithm, combining the finite element and secant-modulus methods, is utilized to solve an illustrative extrusion problem.