Continuum Mechanics and Thermodynamics

, Volume 21, Issue 4, pp 297–315 | Cite as

Two-scale modelling of micromorphic continua

A numerical homogenization scheme
  • Ralf JänickeEmail author
  • Stefan Diebels
  • Hans-Georg Sehlhorst
  • Alexander Düster
Original Article


According to their peculiar mechanical properties, the description of cellular materials is of high interest. Modelling aspects to be considered are, e.g. pronounced size depending boundary layer effects as well as a deformation-driven evolution of anisotropy or porosity. In the present contribution, we pay special attention to the description of size-dependent microtopological effects on the one hand. On the other hand, we focus on the relevance of extended continuum theories describing the local deformation state of microstructured materials. We, therefore, introduce a homogenization scheme for two-scale problems replacing a heterogeneous Cauchy continuum on the microscale by a homogeneous effective micromorphic continuum on the macroscale. The transitions between both scales are obtained by appropriate projection and homogenization rules which have to be derived, on the one hand, by kinematic assumptions, i.e. the minimization of the macroscopic displacement field, and, on the other hand, by energetic considerations, i.e. the evaluation of an extended Hill–Mandel condition.


Multiscale materials Size effects Extended continua Homogenization Two-scale FEM 


46.05.+b 46.15.-x 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Ralf Jänicke
    • 1
    Email author
  • Stefan Diebels
    • 1
  • Hans-Georg Sehlhorst
    • 2
  • Alexander Düster
    • 2
  1. 1.Chair of Applied MechanicsSaarland UniversitySaarbrückenGermany
  2. 2.Numerische Strukturanalyse mit Anwendungen in der SchiffstechnikTechnische Universität Hamburg-HarburgHamburgGermany

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