Two-dimensional finite element analysis of sheet-forming processes including bending effect

A two-dimensional formulation to include bending, inertia effects, and strain rate sensitivity is developed in this dissertation for the analysis of sheet forming processes. The aim of the work is to develop a computer model to predict the deformed part shape, principal strains, punch force and underscore the importance of including bending and rate sensitivity when required.;The bending model developed here uses an updated Lagrangian formulation based on incremental non-linear shell theory. Even for a very small sheet thickness to tool radius ratio, the shear deformation is found to be extremely small and is, therefore, neglected. The material is assumed to satisfy Hill's yield criterion and the associated flow rule with r and M as anisotropy parameters. A rigid-plastic method with initial elastic strain calculations and power law hardening in the plastic regime are used in the formulation. The governing equilibrium equations are derived from the principle of virtual work, using the symmetric second Piola-Kirchhoff stress and Green-Lagrange strain tensor. Modified Coulomb's law, with bilinear and hypertangent behaviour, is used to model the interfacial friction. The problem can be modelled as both quasi-static and dynamic with the Newmark scheme for the time integration of equilibrium equations. Due to its versatility in handling arbitrary boundary conditions and geometry with ease, the finite element methodology is used with Newton-Raphson solution algorithm and contact iterations. Hermite cubic elements are used for the in-plane and out-of-plane displacements, resulting in four degrees of freedom at each node.;Extensive comparisons for simple plane strain and axisymmetric geometries are made with experiments and other existing numerical solutions, showing very good agreement. Comparisons with exact analytical solutions and patch tests demonstrate the accuracy of the developed computer program. Parametric sensitivity studies are presented to investigate the influence of various numerical, material and process variables on the results.;Finally, the developed computer program is used to solve industry scale problems using tools with complex shapes and multiple curvatures. Comparisons with the experimental data and membrane results show an excellent agreement.