A rock damage constitutive model and damage energy dissipation rate analysis for characterising the crack closure effect

2017 ◽  
Vol 13 (1) ◽  
pp. 54-63 ◽  
Author(s):  
Tao Wen ◽  
Yourong Liu ◽  
Chenggang Yang ◽  
Xianlong Yi
Keyword(s):  
Energy Dissipation ◽  
Constitutive Model ◽  
Crack Closure ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Rock Damage ◽  
Rate Analysis ◽  
Damage Constitutive Model ◽  
Closure Effect

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

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