Computational Mechanics

, Volume 45, Issue 1, pp 45–59 | Cite as

Numerical investigations of foam-like materials by nested high-order finite element methods

  • H. -G. Sehlhorst
  • R. Jänicke
  • A. Düster
  • E. Rank
  • H. Steeb
  • S. Diebels
Open Access
Review Article


In this paper we present a multiscale framework suited for geometrically nonlinear computations of foam-like materials applying high-order finite elements (p-FEM). This framework is based on a nested finite element analysis (FEA) on two scales, one nonlinear boundary value problem on the macroscale and k independent nonlinear boundary value problems on the microscale allowing for distributed computing. The two scales are coupled by a numerical projection and homogenization procedure. On the microscale the foam-like structures are discretized by high-order continuum-based finite elements, which are known to be very efficient and robust with respect to locking effects. In our numerical examples we will discuss in detail three characteristic test cases (simple shear, tension and bending). Special emphasis is placed on the material’s deformation-induced anisotropy and the macroscopic load-displacement behavior.


Cellular foams Homogenization Large deformations 



The support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged (RA 624/16-1, DI 430/7-1). The authors wish to thank the reviewers for their helpful comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • H. -G. Sehlhorst
    • 1
  • R. Jänicke
    • 2
  • A. Düster
    • 1
  • E. Rank
    • 3
  • H. Steeb
    • 4
    • 5
  • S. Diebels
    • 2
  1. 1.Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik, Schwarzenbergstrasse 95 cTechnische Universität Hamburg-HarburgHamburgGermany
  2. 2.Lehrstuhl für Technische MechanikUniversität des SaarlandesSaarbrückenGermany
  3. 3.Lehrstuhl für Computation in EngineeringTechnische Universität MünchenMünchenGermany
  4. 4.Lehrstuhl für KontinuumsmechanikRuhr-Universität BochumBochumGermany
  5. 5.Multi Scale MechanicsTS, CTW, UTwenteEnschedeThe Netherlands

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