On anti-plane shear behavior of a Griffith permeable crack in piezoelectric materials by use of the non-local theory

2003 ◽  
Vol 19 (2) ◽  
pp. 181-188 ◽  
Author(s):  
Zhou Zhengong ◽  
Du Shanyi ◽  
Wang Biao
Keyword(s):  
Piezoelectric Materials ◽  
Shear Behavior ◽  
Local Theory ◽  
Permeable Crack ◽  
Plane Shear ◽  
Non Local

The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves

2007 ◽  
Vol 353-358 ◽  
pp. 258-262
Author(s):  
Zhen Gong Zhou ◽  
Lin Zhi Wu
Keyword(s):  
Shear Stress ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Stress Waves ◽  
Functionally Graded ◽  
Local Theory ◽  
Plane Shear ◽  
Functionally Graded Piezoelectric Materials ◽  
Non Local ◽  
Functionally Graded Piezoelectric

In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

A non-local rheology for dense granular flows

2009 ◽  
Vol 367 (1909) ◽  
pp. 5091-5107 ◽  
Author(s):  
Olivier Pouliquen ◽  
Yoel Forterre
Keyword(s):  
Granular Flows ◽  
Constitutive Law ◽  
Local Theory ◽  
Plane Shear ◽  
Static Regime ◽  
Entire Flow ◽  
Non Local ◽  
Inclined Planes ◽  
Inertial Regime ◽  
Dense Granular Flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

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