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A two-dimensional homogenized model for a pile of thin elastic sheets with frictional contact

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Abstract

The present paper deals with the computational simulation of a pile of thin sheets. The sheets are not laminated or glued, but they interact by frictional contact. In general, it is not possible to perform a full-scale finite element contact computation for piles containing thousands of sheets; the problem size becomes too large, and numerical solution methods suffer from severe convergence problems due to the large number of strongly coupled contact conditions. In this paper, a macroscopic material model is presented for the two-dimensional case. The pile of sheets is homogenized by introducing an effective anisotropic constitutive law, which is motivated by formulations of the theory of elasto-plasticity. This macroscopic material law models the behavior of a pile of sheets, allowing for no tensile stresses in the direction normal to the sheets and obeying Coulomb’s law of friction in the tangential contact plane. Applying this macroscopic material model, an equivalent homogeneous body can be treated using much coarser discretizations. Computational results for the problems are provided, and a comparison with simplified contact computations is done.

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References

  1. Aigner, L., Sinwel, A., Gerstmayr, J., Irschik, H.: The constitutive modeling of homogenized contact and friction conditions in thin-sheet packages. In: Proceedings of the 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal (7–11 September 2009)

  2. Angelillo M.: Constitutive relations for no-tension materials. Meccanica 28, 195–202 (1993)

    Article  MATH  Google Scholar 

  3. Bufler H.: Planar elastic laminates and their homogenization. Acta Mech. 141, 1–36 (2000)

    Article  Google Scholar 

  4. Cherouat A., Radi B., Hami A.E.: The frictional contact of the composite fabric’s shaping. Acta Mech. 199, 29–41 (2008)

    Article  MATH  Google Scholar 

  5. FEA, A.U.: Dassault Systèmes (Simulia, 2008), http://www.simulia.com

  6. Greco F.: Homogenized mechanical behavior of composite micro-structures including micro-cracking and contact evolution. Eng. Fract. Mech. 76, 182–208 (2009)

    Article  Google Scholar 

  7. Heyman J.: The stone skeleton. Int. J. Solids Struct. 2, 249–279 (1966)

    Article  Google Scholar 

  8. Ladevéze P., Lubineau G., Marsal D.: Towards a bridge between the micro- and mesomechanics of delamination for laminated composites. Compos. Sci. Technol. 66, 698–712 (2006)

    Article  Google Scholar 

  9. Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, Third edition, International Series in Operations Research & Management Science, 116. Springer, New York (2008)

  10. Miehe C., Schröder J., Bayreuther C.: On the homogenization analysis of composite material based on discretized fluctuations on the micro-structure. Acta Mech. 155, 1–16 (2002)

    Article  MATH  Google Scholar 

  11. Milani G., Lourenço P., Tralli A.: Homogenised limit analysis of masonry walls, part i: failure surfaces. Comput. Struct. 84, 166–180 (2006)

    Article  Google Scholar 

  12. Milani G., Lourenço P., Tralli A.: Homogenised limit analysis of masonry walls, part ii: structural examples. Comput. Struct. 84, 181–195 (2006)

    Article  Google Scholar 

  13. Nemat-Nasser S., Hori M.: Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland Series in Applied Mathematics and Mechanics, vol. 37. North-Holland Publishing Co, Amsterdam (1993)

    Google Scholar 

  14. Omri A.E., Fennan A., Sidoroff F., Hihi A.: Elastic-plastic homogenization of layered composites. Eur. J. Mech. A/Solids 19, 585–601 (2000)

    Article  MATH  Google Scholar 

  15. Pasquale S.D.: New trends in the analysis of masonry structures. Meccanica 27, 173–184 (1992)

    Article  MATH  Google Scholar 

  16. Pellegrino C., Galvanetto U., Schrefler B.: Numerical homogenization of periodic composite materials with non-linear material components. Int. J. Numer. Methods Eng. 46, 1609–1637 (1999)

    Article  MATH  Google Scholar 

  17. Pfeiffer F., Glocker C.: Multibody Dynamics with Unilateral Contacts, Wiley Series in Nonlinear Science. Wiley, New York (1996)

    Book  Google Scholar 

  18. Simo J.C., Hughes T.J.R.: Computational Inelasticity, Interdisciplinary Applied Mathematics: Mechanics and Materials, vol. 7. Springer, New York (1998)

    Google Scholar 

  19. Vetyukov Y., Gerstmayr J., Irschik H.: Plastic multipliers as driving variables of numerical simulation in elastoplasticity. Mech. Res. Commun. 30, 421–430 (2003)

    Article  MATH  Google Scholar 

  20. Vorhauer L., Gerstmayr J.: Mechanically homogenized material model for a pack of sheets. PAMM 9, 423–424 (2009)

    Article  Google Scholar 

  21. Wriggers P.: Computational Contact Mechanics, 2nd edn. Springer, Berlin (2006)

    Book  MATH  Google Scholar 

  22. Ziegler F.: Mechanics of Solids and Fluids. Springer, Berlin (1995)

    Google Scholar 

  23. Zienkiewicz O.C., Taylor R.L.: The finite element method, vol. 1, 5th edn. Butterworth-Heinemann, Oxford (2000) The basis

    MATH  Google Scholar 

  24. Zienkiewicz O.C., Taylor R.L.: The finite element method, vol. 2, 5th edn. Butterworth-Heinemann, Oxford (2000) Solid mechanics

    Google Scholar 

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Authors and Affiliations

  1. Linz Center of Mechatronics GmbH, Altenberger Strasse 69, 4040, Linz, Austria

    Larissa G. Aigner, Johannes Gerstmayr & Astrid S. Pechstein

  2. Johannes Kepler University, Altenberger Strasse 69, 4040, Linz, Austria

    Astrid S. Pechstein

Authors
  1. Larissa G. Aigner
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  2. Johannes Gerstmayr
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  3. Astrid S. Pechstein
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Correspondence to Larissa G. Aigner.

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Aigner, L.G., Gerstmayr, J. & Pechstein, A.S. A two-dimensional homogenized model for a pile of thin elastic sheets with frictional contact. Acta Mech 218, 31–43 (2011). https://doi.org/10.1007/s00707-010-0399-1

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  • DOI: https://doi.org/10.1007/s00707-010-0399-1

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