Analytical homogenization of linear elasticity based on the interface orientation distribution – A complement to the self-consistent approach

2015 ◽  
Vol 126 ◽  
pp. 398-416 ◽  
Author(s):  
Jan Kalisch ◽  
Rainer Glüge
Keyword(s):  
Linear Elasticity ◽  
Orientation Distribution ◽  
The Self ◽  
Self Consistent ◽  
Interface Orientation ◽  
Analytical Homogenization ◽  
Consistent Approach

Nonlinear Elastic Properties of Micro-Heterogeneous Media

1994 ◽  
Vol 116 (3) ◽  
pp. 325-330 ◽  
Author(s):  
E. Kro¨ner
Keyword(s):  
Statistical Methods ◽  
Elastic Constants ◽  
Linear Elasticity ◽  
Heterogeneous Media ◽  
Nonlinear Problems ◽  
The Self ◽  
Green Functions ◽  
First Approximation ◽  
Self Consistent ◽  
Nonlinear Elastic

Utilizing statistical methods known from linear elasticity it is shown how effective 3rd (and higher) order elastic constants (TOEC) of micro-heterogeneous media can be calculated. Emphasis is put on the self consistent scheme. The ensemble average of the fluctuating TOEC yields a 0th approximation to the rigorous selfconsistent moduli. A first approximation is also given in closed form. The insight that the well-established statistical methods of the linear theory, which uses Green functions, are applicable also to nonlinear problems is considered as the main result of this paper.

scholarly journals A self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Ross Angel ◽  
Mattia Mazzucchelli ◽  
Javier Gonzalez-Platas ◽  
Matteo Alvaro
Keyword(s):  
Cell Parameter ◽  
Equations Of State ◽  
Unit Cell ◽  
The Self ◽  
Polynomial Functions ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Self Consistent ◽  
Consistent Manner ◽  
Consistent Approach

A method for the self-consistent description of the large variations of unit-cell parameters of crystals with pressure and temperature is presented. It employs linearized versions of equations of state (EoSs) together with constraints to ensure internal consistency. The use of polynomial functions to describe the variation of the unit-cell angles in monoclinic and triclinic crystals is compared with the method of deriving them from linearized EoSs for d spacings. The methods have been implemented in the CrysFML Fortran subroutine library. The unit-cell parameters and the compressibility and thermal expansion tensors of crystals can be calculated from the linearized EoSs in an internally consistent manner in a new utility in the EosFit7c program, which is available as freeware at http://www.rossangel.net.

scholarly journals Hadron production in pp and AA collisions at mid-rapidity within self-similarity approach

2019 ◽  
Vol 204 ◽  
pp. 01022 ◽  
Author(s):  
Gennady Lykasov ◽  
Alexander Malakhov
Keyword(s):  
Experimental Data ◽  
Transverse Momentum ◽  
Hadron Production ◽  
The Self ◽  
Self Similarity ◽  
Satisfactory Description ◽  
Self Consistent ◽  
Consistent Approach ◽  
Aa Collisions

The self-consistent approach based on similarity of inclusive spectra of hadrons produced in pp and AA collisions is reviewed. We present its modification due to the quark-gluon dynamics to describe the inclusive spectra of hadrons produced in pp collision as a function of the transverse momentum pt at mid-rapidity. The extension of this approach to analyze the pion pt-spectra produced in AA collision at high and middle energies and mid-rapidity is given. A satisfactory description of experimental data on these spectra in pp and AA collisions within the offered approach is shown.

scholarly journals Influence of the Crystallographic and the Morphological Texture on the Elastic Properties of Fcc Crystal Aggregates

2010 ◽  
Vol 160 ◽  
pp. 83-86 ◽  
Author(s):  
K. Jöchen ◽  
Thomas Böhlke ◽  
F. Fritzen
Keyword(s):  
Grain Shape ◽  
Orientation Distribution ◽  
Homogenization Method ◽  
The Self ◽  
Elastic Response ◽  
Sheet Metals ◽  
Cubic Crystal ◽  
Crystalline Orientation ◽  
Full Field ◽  
Self Consistent

In this contribution, the prediction of the self-consistent homogenization method with regard to the effective material response of cubic crystal aggregates is analyzed and compared to results from full field simulations. The influence of the crystalline orientation distribution but also the effect of the grain shape on the macroscopic elastic response of sheet metals is especially emphasized.

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