Analysis of plane strain rolling by the dynamic relaxation method

A numerical method for modelling plane strain rolling based on the use of dynamic relaxation (DR) is examined. This method is founded on Newton's second law of motion and quasi-static response is obtained by applying suitable damping. It differs from the conventional implicit finite element and finite difference methods in that a global stiffness matrix is not formed. Grid point displacements at the end of each time step are calculated explicitly from out-of-balance forces. The stresses are expressed as explicit functions of strains and related state variables and therefore this method offers the potential for modelling complex constitutive behaviour. Roll forces and flow patterns during the non-steady and steady stages of rolling are presented. Comparison with results reported in the literature which are based on experiments and on other numerical techniques show satisfactory agreement.