Micromechanics and Homogenization Principles

LecturerProf. Dipl.-Ing. Björn Kiefer, Ph.D.
AudienceDiploma and master course
Volume2/1/0 SWS (lecture/excercise/practical course)
InstructorsDipl.-Ing. Nils Lange

OPAL page:



1 Semester(s)


Successful participants of this course will be able to apply fundamental concepts of micromechanics to determine effective properties of multiphase elastic solids (composite materials, etc.). Participants will learn the theoretical foundations as well as the advantages and shortcomings of classical micromechanics techniques. The students will become familiar with advanced homogenization principles - both analytical and numerical in nature - that incorporate the influence of micro-defects (inclusions, cavities, cracks) and inelastic behavior. Participants will further acquire first experience with numerical implementation of these modeling concepts through programing examples.


The main ingredients are:

  • Micromechanics techniques for computing effective elastic properties of composite media
  • Fundamental Eshelby solutions, inclusions, inhomogeneities
  • Dilute distribution, Mori-Tanaka, and self-consistent approaches
  • Energetic bounds on effective properties
  • General averaging theorems, Hill-Mandel Principle, periodic homogenization, asymptotic expansions
  • Direct numerical homogenization schemes, including the FE2-method
  • Strength and failure, localization
  • Numerical examples (programing in Matlab /Mathematica/Python)


basic knowledge of Continuum Mechanics

Recommended Literature:

  • S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, Second Edition, North-Holland Series in Applied Mathematics and Mechanics, 1999
  • Christensen, Mechanics of Composite Materials, Dover Publications, 2005
  • D. Gross and T. Seelig, Bruchmechanik — mit einer Einführung in die Mikromechanik, Springer-Verlag Berlin Heidelberg, 2016

Requirements for Credit Points:

For the award of 4 credit points it is necessary to pass the module exam.