Modelling and Analysis of a Class of Metal-Forming Problems (Advances in Applied Mathematics and Mechanics, 2021)
A class of steady-state metal-forming problems, with rigid-plastic, incompressible,strain-rate dependent material model and nonlocal Coulomb's friction, is considered.Primal, mixed and penalty variational formulations, containing variational inequalitieswith nonlinear and nondifferentiable terms, are derived and studied. Existence, uniquenessand convergence results are obtained and shortly presented. A priori finite element errorestimates are derived and an algorithm, combining the finite element and secant-modulusmethods, is utilized to solve an illustrative extrusion problem.