scholarly journals Stress analysis of blood vessels by a viscoplastic constitutive model based on the internal variable theory.

1990 ◽  
Vol 56 (529) ◽  
pp. 2011-2015
Author(s):  
Eiichi TANAKA ◽  
Hiroshi YAMADA
Keyword(s):  
Constitutive Model ◽  
Stress Analysis ◽  
Blood Vessels ◽  
Internal Variable ◽  
Variable Theory ◽  
Model Based ◽  
Internal Variable Theory

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

An internal variable theory of adhesion

1998 ◽  
Vol 12 (8) ◽  
pp. 857-887 ◽  
Author(s):  
E. Bitterlin ◽  
J.F. Ganghoffer
Keyword(s):  
Internal Variable ◽  
Variable Theory ◽  
Internal Variable Theory

scholarly journals High Temperature Deformation Behavior of 8090 Al-Li Alloy

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Woo Young Jung ◽  
Tae Kwon Ha
Keyword(s):  
High Temperature ◽  
Deformation Behavior ◽  
Internal Variable ◽  
Grain Boundary Sliding ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Flow Curves ◽  
Variable Theory ◽  
Self Diffusion ◽  
Internal Variable Theory

High temperature deformation behavior, especially the superplasticity of an 8090 Al-Li alloy, was studied within the recent framework of the internal variable theory of structural superplasticity. In this study, a series of load relaxation tests were conducted at various temperatures ranging from 200°C to 530°C to obtain the flow curves of log ε˙versus log ε. The effect of grain size was also examined by varying the grain sizes through a proper thermomechanical treatment. The flow curves were found to be composite curves consisting of contributions from grain boundary sliding (GBS) and grain matrix deformation (GMD) at superplastic temperatures. The activation energy obtained for GMD was 124.9 kJ/mole in the temperature range from 470°C to 530°C, very similar to that for self-diffusion in pure Al.

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