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

Lecturer: Prof. Dr.-Ing. habil. Thomas Böhlke
Date: October 14, 2009 (Wednesday), 10.00
Location: Institute of Thermomechanics AS CR, v. v. i., Dolejškova 5, Prague, lecture room A

The Czech Society for Mechanics – the expert group for Computational mechanics and the Institute of Thermomechanics AS CR wish to invite you to a lecture by
Thomas Böhlke
Chair of Continuum Mechanics
University of Karlsruhe (TH)
Kaiserstr. 10, 76131 Karlsruhe, Germany

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.

[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.

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 in1. strength of materials2. fluid mechanics
12/1995 Diploma: 'cum laude'
01/1994-01/1995 and 04/1995-12/1995 Two research projects at the Institute of Mechanicsof 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 EvolutionAnd Elastic Anisotropy: Simulation, Modeling, andApplications,Grade: 'summa cum laude'Referees: Prof. Bertram, Prof. Krempl
11/2001 Thesis Award in 2001 at the Otto-von-Guericke-UniversityMagdeburg, 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 andContinuum 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

More information: Dr. Jiří Plešek

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