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A comparison between the material point method and the finite element method in view of extrusion problems
Author(s) -
Schilling O.,
Reese S.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410166
Subject(s) - pointwise , finite element method , polygon mesh , material point method , basis (linear algebra) , point (geometry) , extrusion , numerical analysis , particle (ecology) , state variable , computer science , mathematics , algorithm , mathematical analysis , geometry , physics , materials science , structural engineering , engineering , composite material , oceanography , thermodynamics , geology
An appropriate method for the simulation of continuous forming processes is the material point method (MPM) [1],[2] which combines the viewpoints of fluid dynamics and solid mechanics. The MPM and related methods [3] are derived from the particle‐in‐cell methods [4]. Bodies are discretised by Lagragian particles with pointwise mass distributions. The differential equations in their weak form are solved on temporary meshes built of standard finite elements. At the end of each time step the particle positions are updated and the mesh is replaced by a new mesh with a regular shape. The state variables at the nodes of the new mesh are extracted from the state variables at the particles by a transfer algorithm. When particles pass element boundaries, numerical difficulties might be observed. These are eliminated by a smooth approximation of nodal data from material point data. The modified MPM has been implemented together with the FEM in one programme because the similarities of the methods outbalance the differences. On the basis of numerical examples the results of both methods are compared. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)