Application of Homogenization of Material Properties

  • Ming Dong
  • Siegfried Schmauder
Living reference work entry

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The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle-reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material with the mechanical behavior to be determined iteratively in a self-consistent manner. Good agreement has been obtained between experiment and calculation, and the embedded cell model is thus found to represent well metal matrix composites with randomly arranged inclusions.

Systematic studies of the mechanical behavior of fiber and particle-reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strengthening levels for regular inclusion arrangements from conventional unit cell models.

Based on the self-consistent embedded cell models, a self-consistent matricity model has been developed to simulate the mechanical behavior of composites with two randomly distributed phases of interpenetrating microstructures. The model is an extension of the self-consistent model for matrices with randomly distributed inclusions. In addition to the volume fraction of the phases, the matricity model allows a further parameter of the microstructure, the matricity M of each phase, to be included into the simulation of the mechanical behavior of composites with interpenetrating microstructures. Good agreement has been obtained between experiment and calculation with respect to the composites’ mechanical behavior, and the matricity model is thus found to represent well metal matrix composites with interpenetrating microstructures. The matricity model can be applied to describe the mechanical behavior of arbitrary microstructures as observed in two-phase functionally graded materials, where the volume fraction as well as the matricity of the phases varies between the extreme values of 0 and 1.


Composite materials Micromechanics Mechanical behavior Self-consistent embedded cell models Matricity 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Eberspächer Exhaust Technology GmbH & Co. KGEsslingenGermany
  2. 2.Institute for Materials Testing, Materials Science and Strength of Materials (IMWF)University of StuttgartStuttgartGermany

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