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Micro Cold Forming - Subproject B2: Distribution-based Simulation

Working Group:WG Numerics of PDEs
Leadership: Prof. Dr. Alfred Schmidt ((0421) 218-63851, E-Mail: alfred.schmidt@uni-bremen.de )
Processor: Dr.-Ing. Jonathan Montalvo Urquizo
Funding: DFG
Project partner: IWT, Stiftung Institut für Werkstofftechnik
Institut für Statistik, Universität Bremen
Time period: 02.01.2007 - 31.12.2014
Bild des Projekts Mikrokaltumformen - Teilprojekt B2: Verteilungsbasierte Simulation

Methods for the direct incorporation of the statistical distribution of material properties into FEM-simulation of micro forming processes

For microcomponents, the small dimensions and consequent small amount of material grains cause large statistical variations in the mechanical material properties. This variations can strongly influence the effect of forces applied on the microcomponents and, finally, during a cold forming process can lead to construction parts with short durability.

Some microcomponents of interest for the micro forming process have very small thickness (in the order of 10 µm), while the other two dimensions can belong to the sub-millimetre or the millimetre range. Experimentally can be observed how the small dimensions of material and/or size of the components cause a strong dependence of the material parameters on these small dimensions. An example of this might be a decrease of the elastic limit or the tensile strength by miniaturization of the components.

Aluminiumfolie Aluminium Foil
Drei-Skalen Ansatz für die BerechnungenThree scales scheme for the numerical simulations
For this reasons, a simulation of a micro forming process needs to consider the statistical variations of the material parameters. A clasical FEM-Simulation for a complex structured microcomponent would need a large number of elements. Furthermore, the multiple computation of the mechanical forming process with different material properties would drastically increase the computation time and would not guarantee the correct capture of the local variations. The scientific challenge is to develop a new modeling strategy for the distribution-based differential equations and the corresponding finite element simulation in which the variations of the material properties are coupled info the FEM-Solver in form of statistical distributions.

This project aims at deriving, implementing, and testing a new and universal method to model mechanical laws that follow a local distribution and at their direct incorporation into the simulation of micro forming processes for semi-finished parts and construction parts. The results of the microcomponent simulations should be the corresponding statistical distributions of the material properties and/or responses. In the long term, it is expected that the method deliver important statements, as e.g. the probability that a simulated component would present failures or completely break.

Sonderforschungsbereich 747 - MikrokaltumformenCollaborative Research Centre 747 - Micro cold forming
Kleine Platte und Verteilungen der Spannungskomponenten an drei verschiedenen StellenSmall plate and distributions of the stress components at three different locations
Through the connection of the new models based on statistics and a macroscopic FE-Method, the final product will be a simulation tool where the distributed material properties are considered. The coupled systems of partial differential equations, extended by the new equations and parameters from the statistic models will be discretized and solved. The necessary FEM-Simulations will be implemented in the academic FEM-Toolbox ALBERTA.

 More Information: SFB747


Publications

  1. J. Montalvo Urquizo, M. Ungermann.
    Size Selection for Representative Volume Elements on Texturized Thin Metallic Sheets under Elastic Loads.
    PAMM, 2013 1:265-266, WILEY-VCH, 2013.

    DOI: DOI: 10.1002/pamm.201310128
    online at: http://onlinelibrary.wiley.com/doi/10.1002/pamm.201310128/abstract

  2. J. Montalvo Urquizo, A. Schmidt.
    Simulation Technologies: FEM-Simulation.
    Micro Metal Forming, F. Vollertsen (Eds.), Production & Process Engineering, pp. 347-359, Springer Verlag, 2013.

    online at: Springer-Verlag Website

  3. J. Montalvo Urquizo, P. Bobrov, W. Brannath.
    Simulation Technologies: Hybrid Simulation.
    Micro Metal Forming, F. Vollertsen (Eds.), Production & Process Engineering, pp. 359-368, Springer Verlag, 2013.

    online at: Springer-Verlag Website

  4. J. Montalvo Urquizo.
    Material libraries for texturized thin metal sheets in elastic range.
    PAMM, 12(1):235-236, WILEY-VCH, 2012.
  5. P. Bobrov, J. Montalvo Urquizo.
    Calculation of effective elastic constants for texturized steel through numerical experiments (in Russian).
    7th Russian Conference on Science and Tehnology: Mechanics of micro materials and damage, 23.04.-27.04.12, Ekaterinburg, Russia.
  6. J. Montalvo Urquizo, P. Bobrov, W. Wosniok, A. Schmidt.
    Elastic responses of texturized microscale materials using FEM simulations and stochastic material properties.
    Mechanics of Materials, 47:1-10, Elsevier, 2012.

    DOI: 10.1016/j.mechmat.2011.11.008

  7. J. Montalvo Urquizo.
    Mechanic-stochastic model for the simulation of elastic material response in thin metallic polycrystals.
    7th GRACM International Congress on Computational Mechanics, 29.06.-02.07.2011, Athens, Greece.
    Conference Proceedings, 2011.
  8. J. Montalvo Urquizo, P. Bobrov, W. Brannath, W. Wosniok, A. Schmidt, M. Hunkel, J. Lütjens.
    Stochastic model for textured polycrystals.
    5th International Conference CHEBYSHEV, 14.05.2011-18.05.2011.
  9. P. Bobrov, J. Montalvo Urquizo, J. Lütjens, W. Brannath, W. Wosniok, A. Schmidt, M. Hunkel.
    Ein stochastisches Modell zur Rekonstruktion elastischer Eigenschaften für texturierte Metalle.
    Kolloquium Mikroproduktion und Abschlusskolloquium SFB 499, 11.10.-12.10.2011, Karlsruhe, Germany.

    online at: Proceedings Fulltext as PDF

  10. P. Bobrov, J. Montalvo Urquizo, A. Schmidt, W. Wosniok.
    Mechanic-Stochastic Model for the Simulation of Polycrystals.
    PAMM, Vol. 10(1):279-280, WILEY-VCH, 2010.

    DOI: 10.1002/pamm.201010132

  11. P. Bobrov, J. Lütjens, J. Montalvo Urquizo, W. Wosniok, M. Hunkel, A. Schmidt, J. Timm.
    Zur verteilungsbasierten Modellierung von Mikrowerkstoffen.
    4. Kolloquium Mikroproduktion, 28.-29.10.2009, Bremen, Germany.