Anisotropic higher-order bounds and estimates based on crystallographic and morphological information

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14. 10. 2009

Česká společnost pro mechaniku – odborná skupina Počítačová mechanika a Ústav termomechaniky AV ČR, v.v.i. si Vás dovolují pozvat na přednášku

Anisotropic higher-order bounds and estimates based on crystallographic and morphological information

kterou prosloví T. Böhlke

Chair of Continuum Mechanics, University of Karlsruhe (TH), Kaiserstr. 10, 76131 Karlsruhe, Germany

Abstract
The elastic properties of uniform polycrystalline materials without defects depend on both the constitutive properties of the constituents and the microstructural characteristics like the distribution of grain orientations and grain shapes. For an overview concerning the homogenization of elastic properties see, e.g., [1]. The elementary bounds by Voigt and Reuss take into account only the volume fraction information of microstructure and hence are insensitive with respect to any morphological aspects of the grain structure.

In the presentation we discuss new anisotropic Hashin-Shtrikman bounds for aggregates of cubic and hexagonal crystals. In the case of anisotropic crystallographic symmetry and isotropic morphology, an explicit form is obtained which is nonlinear in the texture coefficients. For anisotropic morphology however, the result is obtained only numerically and shows a significant influence of two-point correlation function. Furthermore, we derive a new higher-order estimate of the effective elastic properties in terms of tensorial one-point and two-point correlation functions for the special case of uncorrelated grain shapes and grain orientations [2]. Based on the integral equation formulation, a series expansion for the effective elastic properties is used as starting point [3]. We especially consider the coupling terms that arise due to the interaction of the inhomogeneous distribution of crystal orientations and non-equiaxed grain geometry. The new bounds and estimates are used for prediciting the effective and apparent properties of metals and ceramics.

References
[1] Adams, B. and Olson, T.: The mesostructure-properties linkage in polycrystals, Progress in Materials Science, 43, 1–88, 1998. [2] Böhlke, T.: Texture simulation based on tensorial Fourier coefficients, Computers and Structures, 84, 1086–1094, 2006. [3] Torquato, S.: Effective Stiffness tensor of composite media – I. Exact series expansions, Journal of the Mechanics and Physics of Solids, 45, 1421–1448, 1997.

Přednáška bude přednesena ve středu 14. října 2009 v 10 hodin v Ústavu termomechaniky (posluchárna A), Dolejškova 5, Praha 8

Stručný životopis

10/1990-09/1991
Study of Mechanical Engineering at the Technical University, Berlin (TUB), Germany
10/1991-12/1995
Study of Applied Mechanics at the TUB with specialization in
1. strength of materials
2. fluid mechanics
12/1995
Diploma: 'cum laude'
01/1994-01/1995 and 04/1995-12/1995
Two research projects at the Institute of Mechanics of the Technical University, Berlin (Prof. Schoop), financed by the German Research Foundation (DFG), Germany
01/1996-11/2000
Scientific employee at the Institute of Mechanics, Otto-von-Guericke-University, Magdeburg (Prof. Bertram), Germany
05/1998-10/1998 and 08/1999
Visiting Scholar at the Polytechnic Institute (Troy, NY, USA), Mechanics of Materials Laboratory (Prof. Krempl)
11/2000
Graduation at the Otto-von-Guericke-University, Magdeburg, Title of the PhD thesis: Crystallographic Texture Evolution And Elastic Anisotropy: Simulation, Modeling, and Applications, Grade: 'summa cum laude' Referees: Prof. Bertram, Prof. Krempl
11/2001
Thesis Award in 2001 at the Otto-von-Guericke-University Magdeburg, Germany
12/2000-11/2002
Scientific assistant at the Institute of Mechanics, Otto-von-Guericke-University, Magdeburg (Prof. Bertram)
12/2002-09/2005
Junior Professor for Micro-Macro-Interaction in mechanics, Otto-von-Guericke-University, Magdeburg, Germany
10/2005-09/2006
Substitute Professor for Engineering Mechanics and Continuum Mechanics, University of Kassel, Germany
Since 10/2006
Professor at the Institute of Engineering Mechanics, Chair of Continuum Mechanics, University of Karlsruhe (TH), Germany
12/2007
Prize for"Excellent Teaching", University of Karlsruhe (TH), Germany

ČSM

Česká společnost pro mechaniku, z.s.

Odkazy

Anisotropic higher-order bounds and estimates based on crystallographic and morphological information