Effective Properties of micro-heterogeneous Materials
Effective Properties of micro-heterogeneous Materials

• Analytische Homogenisierungsmodelle
• Numerische Homogenisierungsmethoden
• Abschätzung effektiver (makroskopischer) Materialparameter linearer Problemstellungen
• Vorstellung geeigneter numerischer Konzepte für geometrisch und physikalisch nichtlineare Aufgabenstellungen

Die Studierenden können zur effektiven Beschreibung von so genannten mikroheterogenen Materialien makroskopische Ersatzmodelle definieren. Sie können neben den klassischen analytischen Modellen auch numerische Homogenisierungsverfahren anwenden.

[1] Nemat-Nasser S. & Hori M. [1999]: Micromechanics: Overall properties of heterogeneous materials, Band 36 der Reihe North-Holland series in applied mathematics and mechanics. Elsevier Science Publisher B.V., 2. Auflage.
[2] Schröder J. [2000], Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen, Habilitationsschrift.
[3] Zhodi I. T. & Wriggers P. [2004]: Introduction to Computational Micromechanics, Lecture Notes in Applied and Computational Mechanics Vol. 20, Springer Verlag.

Introduction

– concept of micro-macro-transitions

– homogenization and localization

– representative volume elements

 Analytical methods

– Eshelbys approach

– Mean-Field-Theory of Tanaka and Mori

– Hashin-Shtrikman varitonal principles

 Discret numerical homogenization

– definition of macroscopic variables

– macroscopic and microscopic boundary value problems

– macro homogeneity condition (Hill-condition)

– derivation of different microscopic boundary condition

– numerical computation of effective material parameter

– material instabilities

In recent years multiphase steels have become a higher impactin many technical applications, because they allow to be designed with respect to thetechnical requirements. For a description of their effective material properties of thesemicro-heterogeneous materials macroscopic models has to be defined. The numerical ho-mogenization schemes are applied to an increasing number of problems to overcome therestrictions of the classical analytical approaches. The goal of this course is the teachingof the basic knowledge of this research topic.

[1] Nemat-Nasser S. & Hori M. [1999]: Micromechanics: Overall properties of heterogeneous materials, Band 36 der Reihe North-Holland series in applied mathematics and mechanics. Elsevier Science Publisher B.V., 2. Auflage.
[2] Schröder J. [2000], Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen, Habilitationsschrift.
[3] Zhodi I. T. & Wriggers P. [2004]: Introduction to Computational Micromechanics, Lecture Notes in Applied and Computational Mechanics Vol. 20, Springer Verlag.