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Finite Element Modeling of Metal Forming Processes Using Updated Lagrangian Formulation

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Book cover Modeling of Metal Forming and Machining Processes

Part of the book series: Engineering Materials and Processes ((EMP))

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Abstract

In Chapter 5, we discussed the details of finite element method as well as the finite element modeling of metal forming processes using Eulerian formulation. In this chapter, we extend the finite element technique to the updated Lagrangian formulation. In Eulerian formulation, the domain is a fixed region in space (called control volume). However, in a Lagrangian formulation, the domain consists of a set of material particles that changes its shape continuously with the deformation. The updated Lagrangian formulation is an incremental method in which the domain is updated incrementally. Further, the measure of deformation used in Eulerian formulation is the rate of deformation tensor and the constitutive equation is expressed in terms of the stress and rate of deformation tensors. On the other hand, in updated Lagrangian formulation, the measure of deformation is an incremental strain tensor and the constitutive equation is expressed in terms of the incremental stress and incremental strain tensors. We shall discuss how finite element modeling needs to be modified in the light of these changes in the governing equations. Like that of the Eulerian formulation, the governing equations of the updated Lagrangian formulation also are non-linear and need an iterative scheme to obtain a solution. But the iterative scheme we adopt here is different from that of the previous chapter. However, like in the previous chapter, here also we adopt the Galerkin formulation for developing finite element equations.

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(2008). Finite Element Modeling of Metal Forming Processes Using Updated Lagrangian Formulation. In: Modeling of Metal Forming and Machining Processes. Engineering Materials and Processes. Springer, London. https://doi.org/10.1007/978-1-84800-189-3_6

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  • DOI: https://doi.org/10.1007/978-1-84800-189-3_6

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-188-6

  • Online ISBN: 978-1-84800-189-3

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