A Domain Evolution Model for the Ferroelastic Hysteresis of Piezoceramic Materials

Aerospace ◽  
2003 ◽  
Author(s):  
V. Narayanan ◽  
X. Lu ◽  
S. Hanagud
Keyword(s):  
Distribution Function ◽  
Mechanical Loading ◽  
Domain Switching ◽  
Internal State ◽  
Mechanical Strain ◽  
Inelastic Strain ◽  
State Variables ◽  
Domain Evolution ◽  
Internal State Variables ◽  
Piezoelectric Strain

In this paper, we model the thermo-ferroelastic hysteresis phenomena under large mechanical loading by using internal state variables that are associated with a statistical description of microstructural domain characterization. This work is to extend our previous work [1, 2] to include the ferroelastic effects. Under large mechanical loading, the total bulk strain includes the mechanical strain and the bulk piezoelectric strain. The piezoelectric strain is the accompanying strain with the evolution of the domain network, which is described by a domain orientation distribution function. In ferroelastic hysteresis, the domain evolution, which is mainly contributed by 90° domain switching, is delineated by the evolution of the associated domain distribution function and further simplified by the evolution of the associated internal state variables that are the parameters of the domain distribution function. For the mechanical field, the mechanical strain is divided into two parts- the elastic strain and the inelastic strain. The inelastic strain is the corresponding internal variable to describe the inelastic behavior under large mechanical loading. Therefore, the remnant strain contains two parts: the remnant piezoelectric strain and remnant inelastic strain. The dissipation and the associated temperature increase per unit cycle in the ferroelastic hysteresis are studied.

A constitutive model for anisotropic, kinematic hardening materials

1997 ◽  
Vol 32 (3) ◽  
pp. 175-181
Author(s):  
W Deng ◽  
A Asundi ◽  
C W Woo
Keyword(s):  
Inelastic Deformation ◽  
Internal State ◽  
Kinematic Hardening ◽  
Small Deformation ◽  
Inelastic Strain ◽  
State Variables ◽  
Internal State Variables ◽  
Deformation Plasticity ◽  
Independent Variable ◽  
Evolution Laws

Based on previous work by the authors, a model for anisotropic, kinematic hardening materials is constructed to describe constitutive equations and evolution laws in rate-independent, small deformation plasticity on the basis of thermodynamics. Unlike other theories developed earlier wherein only internal state variables are chosen to describe inelastic deformation, the present paper also considers inelastic strain as an independent variable. This can be shown to reduce to the well-known plastic strain in the case of rate-independent plasticity.

Elastoviscoplastic Models with Relaxed Configurations and Internal State Variables

1990 ◽  
Vol 43 (7) ◽  
pp. 131-151 ◽  
Author(s):  
Sanda Cleja T¸igoiu ◽  
Eugen Soo´s
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Internal State ◽  
State Variables ◽  
Internal State Variables ◽  
Local Current

We present the microstructural basis, the initial macroscopical formulations, and a possible axiomatic reconstruction of the elastoviscoplastic model for metals based on the use of the local, current, relaxed configurations. Structural analysis and experimental data show that using these configurations offers advantages for the formulation of the material laws when the deformations are small or moderately large. Our review aims to be a concise, historical, and critical exposition of the main stages, contributions and results, which led, during the late sixties and the beginning of seventies, to the formulation of the fundamental ideas lying at the basis of the model. We delineate the role played by Lee, Liu, Teodosiu, Sidoroff, Mandel, and Kratochvil in the first formulation of the theory between 1966 and 1972, as well as the contributions of Dafalias and Loret to the development of the model between 1983 and 1985. Finally, we discuss some results obtained between 1985 and 1988 with models based on local current relaxed configurations.

The steady two-dimensional reflexion of an oblique partly dispersed shock wave from a plane wall

1973 ◽  
Vol 61 (1) ◽  
pp. 159-172 ◽  
Author(s):  
H. Buggisch
Keyword(s):  
Shock Wave ◽  
Internal State ◽  
Plane Wall ◽  
Plane Shock ◽  
Two Dimensional ◽  
State Variables ◽  
Reflected Shock ◽  
Internal State Variables ◽  
Specific Entropy ◽  
Instantaneous Values

The steady two-dimensional problem of reflexion of an oblique partly dispersed plane shock wave from a plane wall is studied analytically. Viscosity, diffusion and heat conduction are neglected. The thermodynamic state of the gas is assumed to be determined by the instantaneous values of the specific entropy s, pressure p and a finite number of internal state variables. Results for the flow field behind the reflected shock are obtained by a perturbation method which is based on the assumption that the influence of relaxation is relatively weak.

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