An adaptive method for history dependent materials

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Introduction: Finite element simulations of bulk forming processes, like extrusion or forging, can fail due to element distortion. Simulating a forming process requires either many re-meshing steps or an Eulerian formulation to avoid this problem. This re-meshing or usage of an Eulerian formulation, requires the mapping or convection of state variables. This causes inaccuracies for history dependent materials, for instance in hardening plasticity. In this research, a new method is examined which avoids the problems mentioned above. - Methods: The method will be divided in three main components and treated seperately below. The first component of the method is a linear triangular element formulation. It is cost effective and easy to generate on a cloud of nodes by means of Delaunay triangulation. For every increment of a forming process, the old triangulation is deleted and a new Delaunay triangulation is performed. Thereby, the nodal connectivity is changing in time during the process, hence avoiding the problem of mesh distortion. The method of alpha shapes is used to retrieve the boundary of the cloud of nodes. The second component is a nodal integration scheme of the weak form. Nodal integration avoids the problem of mapping state variables in case of triangulations. Furthermore the nodal integration scheme gives good results in incompressibility whereas ‘Gaussian’ integrated linear triangular elements will show locking behavior in the incompressible limit. The third componenent is an updated Lagrangian formulation. A Jaumann rate is used to account for stress rotation and a rate of deformation as a measure of strain was chosen. The formulation allows history dependent materials to be used in an adaptive strategy. - Results: To examine the performance of the method, two tests were performed. The first is the non-proportional loading of a piece of metal. The second test is the elasto-plastic deformation of a tapered bar. The tests show that indeed it is possible to use history dependent material models in an adaptive strategy without resorting to mapping or convection algorithms. Secondly the artefact of volumetric locking is absent and to conclude, the computation times for this method are found to be comparable to those of finite elements. Current point of research is resolving an oscillation related to the case of near incompressibility. Though volumetric locking was not found in the current research, the pressure was found to be oscillating spuriously in certain cases. Future research will focuss on resolving this pressure mode.
Original languageEnglish
Title of host publicationProceedings of the 9th World Congress on Computational Mechanics and 4th Asian PAcific Congress on Computational Mechanics
EditorsNasser Khalili, Somasundaram Valliappan, Qing Li, Adrian Russel
Place of PublicationSydney, Australia
PublisherCentre for Infrastructure Engineering and Safety
ISBN (Print)978-0-9808244-0-7
Publication statusPublished - 19 Jul 2010
EventWorld Congress on Computational Mechanics - The Hague
Duration: 1 Oct 20102 Oct 2010

Publication series

PublisherCentre for Infrastructure Engineering and Safety


ConferenceWorld Congress on Computational Mechanics
Other1-2 October 2010


  • IR-74974
  • Onderzoek van algemene industriele aardMechanical engineering and technology
  • METIS-270539


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