Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates

2004 ◽  
Vol 460 (2045) ◽  
pp. 1381-1405 ◽  
Author(s):  
R. A. Lebensohn ◽  
Y. Liu ◽  
P. Ponte Castañeda
Keyword(s):  
Power Law ◽  
Full Field ◽  
Self Consistent ◽  
Macroscopic Properties ◽  
Field Fluctuations

scholarly journals Collisional Evolution of Galaxy Clusters: Fokker–Planck and N-body models

2003 ◽  
Vol 208 ◽  
pp. 449-450
Author(s):  
Koji Takahashi ◽  
Tomohiro Sensui ◽  
Yoko Funato ◽  
Junichiro Makino
Keyword(s):  
Power Law ◽  
Dynamical Evolution ◽  
Cluster Center ◽  
Combined Effects ◽  
Clusters Of Galaxies ◽  
Relative Importance ◽  
Self Consistent ◽  
The Common ◽  
Good Agreement ◽  
Fokker Planck

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.

Improving the Self-Consistent Predictions of Texture Development of Polycrystals Incorporating Intragranular Field Fluctuations

2005 ◽  
Vol 495-497 ◽  
pp. 955-964 ◽  
Author(s):  
Ricardo A. Lebensohn ◽  
Carlos Tomé ◽  
Pedro Ponte Castañeda
Keyword(s):  
Basal Slip ◽  
Texture Evolution ◽  
Rate Sensitivity ◽  
Second Order ◽  
Homogenization Procedure ◽  
Compression Direction ◽  
Self Consistent ◽  
Field Fluctuations ◽  
Standard Linear ◽  
Derivatives Of

In this contribution we present how to implement the calculation of average field fluctuations inside the grains of a thermoelastic aggregate in terms of the derivatives of the stress potential given by the standard linear self-consistent (SC) model, and how this statistical information can be used to generate second-order estimates for the mechanical behavior of nonlinear viscoplastic polycrystals, by means of a rigorous non-linear homogenization procedure. To illustrate the differences between this second-order (SO) self-consistent approach and the classical first-order SC approximations, we compare them in terms of their predictions of the effective behavior of random fcc polycrystals as a function of their rate-sensitivity, and of the texture evolution in hcp ice polycrystals under uniaxial compression. In the latter case, the SO approximation is the only one able to predict a substantial accommodation of deformation by basal slip, even when the basal poles become strongly aligned with the compression direction and the basal slip systems became unfavorably oriented.

Evaluation of Two-Parameter Approaches to Describe Crack-Tip Fields in Engineering Structures

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Simon Kamel ◽  
Noel P. O’Dowd ◽  
Kamran M. Nikbin
Keyword(s):  
Power Law ◽  
Crack Tip ◽  
Tensile Behavior ◽  
Material Behavior ◽  
Stress Fields ◽  
Strain Hardening Exponent ◽  
Engineering Structures ◽  
New Approach ◽  
Full Field ◽  
Two Parameter

The application of two-parameter approaches to describe crack-tip stress fields has generally focused on Ramberg–Osgood (RO) power law material behavior, which limits the range of applicability of such approaches. In this work we consider the applicability of a J-Q or J-A2 approach (the latter is designated here as the J-A approach) to describe the stress fields for RO power law materials and for a material whose tensile behavior is not described by a RO model. The predictions of the two-parameter approaches are compared with full field finite-element predictions. Results are presented for shallow and deep-cracked tension and bend geometries, as these are expected to provide the expected range of constraint conditions in practice. A new approach for evaluating Q is proposed for a RO material, which, for a given geometry, makes Q dependent only on the strain hardening exponent.

The breaks and the hidden components in the power-law spectra of synchrotron radiation of the self-consistent current structures

2015 ◽  
Vol 22 (8) ◽  
pp. 083303 ◽  
Author(s):  
V. V. Kocharovsky ◽  
VI. V. Kocharovsky ◽  
V. Ju. Martyanov ◽  
S. V. Tarasov
Keyword(s):  
Synchrotron Radiation ◽  
Power Law ◽  
The Self ◽  
Self Consistent

The Stiffening Effect of Rigid Elliptical Inclusions on a Power-Law Material

1989 ◽  
Vol 111 (4) ◽  
pp. 368-371 ◽  
Author(s):  
J. M. Duva ◽  
Dirck Storm
Keyword(s):  
Plane Strain ◽  
Constitutive Relation ◽  
Power Law ◽  
Cross Sections ◽  
Particle Shape ◽  
Elliptical Cross ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
Single Inclusion ◽  
Stiffening Effect

An approximate constitutive relation is derived for plane strain deformation in a power-law viscous matrix reinforced with long rigid inclusions with elliptical cross sections. The analysis is based on the differential self-consistent scheme and numerical calculations estimating the influence of a single inclusion on the material surrounding it. In particular, the effects of particle shape and material nonlinearity are reported.

scholarly journals Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

2021 ◽  
Author(s):  
Semih Perdahcioglu ◽  
Shahrzad Mirhosseini ◽  
Ton van den Boogaard
Keyword(s):  
Crystal Plasticity ◽  
Yield Surface ◽  
Full Field ◽  
Macroscopic Models ◽  
Aggregate Behavior ◽  
Backward Euler ◽  
Self Consistent ◽  
Homogenization Scheme ◽  
The Difference ◽  
Homogenization Methods

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.

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