Effect Of Incompressibility in The Analysis of Metal Forming Using Finite Element Method
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Date
2005-09
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Addis Ababa University
Abstract
Metal forming is one of the most common metal manufacturing processes used, which is noted for
its minimum waste and dimensional precision, and usually improves the mechanical properties of
the formed part. Metal forming process is a process that causes changes in the shape of solid metal
particles via plastic (permanent) deformations. Hence, knowledge of metallurgy and mechanics
combine to provide an insight to its behavior. Its applications are wide in the manufacturing of
machinery, automotive, aerospace and other hardware components.
The material is modeled as a hyperelastic, viscoplastic solid. A constitutive model with a single
scalar variable representing the isotropic resistance to the plastic flow is employed. Many finite
elements exhibit the so-called ‘volumetric locking’ in the analysis of incompressible or quasiincompressible
problems in metal forming. Nearly incompressible plasticity in metal forming
displays severe volume locking problems when low order standard nodal-based displacement
methods are used. This means that after deformation each small portion of the medium has the
volume as before the deformation.
In this thesis a finite element formulation for a frictionless large deformation contact problem in
metal forming is presented. It is based on the formulation which introduces the contact constraints
via Lagrange multipliers. The stabilized formulation which allows the use of low-order
interpolation functions for both displacement and the pressure field is applied to eliminate
volumetric locking effects and to circumvent numerical instabilities. Starting from the variational
formulation of the constitutive and the kinematic problems, the linearization of the principle of
virtual work relation, the contact potential energy, and finally the matrix formulation of the
method is derived. To improve the convergence property of the method an augmentation step was
included. Then the formulation is converted to a computer code written using Matlab. Finally the
program is used to solve a benchmark example.