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A Comparison of Micromechanical Models for the Homogenization of Microheterogeneous Elastic Composites

  • Anton MatzenmillerEmail author
  • Benjamin Kurnatowski
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 168)

Abstract

The structural analyses of stresses, strains and deformations by mathematical means and mechanical considerations demand for constitutive models, which set the mathematical mapping between the different physical fields. The constitutive properties of many materials like metals or plastics can be represented well by phenomenological models that do not explicitly concern about the underlying microscopical structure. Nevertheless, all solid matter shows a discrete texture if it is regarded on a sufficiently small lengthscale. In the vast field of composite materials solely phenomenological models need a sophisticated formulation and demand for elaborate experimental data in order to identify the rather high number of constituting parameters. Hence, micromechanical approaches have more and more moved into the focus of material modelling. Their central task is to deduce and obtain large scale properties from numerical analyses of the small scale structure followed by the application of averaging procedures to the computed small scale fields. Thereby, the level, on which the constitutive formulation is a purely phenomenological one, is pushed towards a lower scale. Since several years, the growth of computational power has lead to the propagation of micromechanically based constitutive approaches.

Keywords

Displacement Field Representative Volume Element Homogeneous Boundary Condition Fibre Shape Micromechanical Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The financial support of the DFG (Deutsche Forschungsgemeinschaft) under contract Ma 1186/4 is gratefully acknowledged for the second author.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mechanics, Department of Mechanical EngineeringUniversity of KasselKasselGermany

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