Finite Element Simulations of Metal Forming Processes By Large Deformation Thermo-Elasto-Plastic Formulations with Grid Adaptive and Mesh Rezoning Methods.

Abstract

A concise survey of the literature related to the large deformation thermo-elasto-plasticity problems including unilateral contact and friction is presented. Starting from the principle of virtual work, the so-called total Lagrangian and updated Lagrangian formulations are derived based on some fundamental assumptions in linearizing nonlinear equations. Material behavior is described by the classical Pr and tl-Reuss equations generalized for large deformation analyses and nonisothermal problems. After a brief review of published explanations of friction, an incremental constitutive relation of friction contact is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and non-local effects are discussed. Finite element methods are applied to simulate several metal forming processes, such as necking in uniaxial tension, upsetting, indentation, direct extrusion, head forming, sheet metal forming, and backward extrusion. The emphasis is geared toward the numerical accuracy of the solutions. With this aim, the grid adaptive methods and a mesh rezoning technique are employed to improve the quality of finite element approximations.