Effect Of Incompressibility in The Analysis of Metal Forming Using Finite Element Method

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Addis Ababa University


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.