## LSU Historical Dissertations and Theses

1989

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Abstract

A detailed formulation for finite element analysis of metal forming problems is carried out in this work. It incorporates every aspect of the analysis, including the iterative solution procedures for geometric and material non-linearities, implementation of the material model, and formulation of curved contact boundaries. The finite element formulation is based on a Total Lagrangian approach which by-passes the use of the Jaumann stress rate tensor commonly used in the Updated Lagrangian formulation. The yield model used is of the von Mises type with both kinematic and isotropic hardening and is formulated in the Eulerian space. This model is then transformed to the Lagrangian reference frame. In the evaluation of stresses, yielding is first detected through the use of an elastic-predictor stress; subsequently upon detection of yielding, the consistency condition is used to evaluate the actual stress and plastic strain tensors. This method is used in conjunction with subincrementation of the strain increment tensor. The curved kinematic boundaries are modeled using the Hermite parametric formulation although other formulations such as $\beta$-splines and Besier parametric curves may also be used with slight modifications. The above mentioned formulations are incorporated into the finite element program, UNIFES (UNIfied Finite Element Solver), which is developed by the author. This program may be used for analysis of 2-D and 3-D problems. A complete listing of this program along with the details of the formulations and a users guide is provided in this work. Applicability of the above formulations in solving metal extrusion problems is examined through several finite element analyses which are performed by using the UNIFES program. It is shown how the distance between the nodes on the die interface can lead to fluctuations in the extrusion pressure, and how the amplitude of these fluctuations may be reduced by mesh refinement, using multiple types of elements. The effect of changes in the die angle as well as changes in the reduction ratio, on the extrusion pressure is also investigated. A detailed account of the solution procedures is also provided.

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