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.

Constitutive Modeling of Inelastic Solids for Plastic Flow Processes Under Cyclic Dynamic Loadings

1999 ◽  
Vol 121 (2) ◽  
pp. 210-220 ◽  
Author(s):  
W. Dornowski ◽  
P. Perzyna
Keyword(s):  
Plastic Deformation ◽  
Relaxation Time ◽  
Cyclic Loading ◽  
Internal State ◽  
Kinematic Hardening ◽  
State Variables ◽  
Wave Shape ◽  
Internal State Variables ◽  
Flow Processes ◽  
The Finite Difference Method

The main objective of the paper is the description of the behavior and fatigue damage of inelastic solids in plastic flow processes under dynamic cyclic loadings. Experimental motivations and physical foundations are given. Recent experimental observations for cycle fatigue damage mechanics at high temperature of metals suggest that the intrinsic microdamage process does very much depend on the strain rate effects as well as on the wave shape effects. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms; (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity. To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic-plastic response can be obtained. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is formulated and conditions under which this theory is valid are examined. Utilizing the finite difference method for regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented. Particular examples have been considered, namely, a dynamic, adiabatic and isothermal, cyclic loading processes for a thin steel plate with small rectangular hole located in the centre. Small two regions which undergo significant deformations and temperature rise have been determined. Their evolution until occurrence of final fracture has been simulated. The accumulation of damage and equivalent plastic deformation on each considered cycle has been obtained. It has been found that this accumulation distinctly depends on the wave shape of the assumed loading cycle.

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.

scholarly journals A Modeling Investigation of Thermal and Strain Induced Recovery and Nonlinear Hardening in Potential Based Viscoplasticity

1995 ◽  
Vol 117 (2) ◽  
pp. 157-167 ◽  
Author(s):  
S. M. Arnold ◽  
A. F. Saleeb ◽  
T. E. Wilt
Keyword(s):  
Internal State ◽  
Kinematic Hardening ◽  
Temperature Response ◽  
Dislocation Motion ◽  
Threshold Function ◽  
State Variables ◽  
Internal State Variables ◽  
Recovery Mechanisms ◽  
Modeling Stress ◽  
The Impact

Specific forms for both the Gibb’s and the complementary dissipation potentials were chosen such that a complete potential based multiaxial, isothermal, viscoplastic model was obtained. This model, in general, possesses three internal state variables (two scalars associated with dislocation density and one tensor associated with dislocation motion) both thermal and dynamic recovery mechanisms, and nonlinear kinematic hardening. This general model, although possessing associated flow and evolutionary laws, is shown to emulate three distinct classes of theories found in the literature, by modification of the driving threshold function F. A parametric study was performed on a specialized nondimensional multiaxial form containing only a single tensorial internal state variable (i.e., internal stress). The study was conducted with the idea of examining the impact of including a strain-induced recovery mechanism and the compliance operator, derived from the Gibb’s potential, on the uniaxial and multiaxial response. One important finding was that inclusion of strain-induced recovery provided the needed flexibility in modeling stress-strain and creep response of metals at low homologous temperatures, without adversely affecting the high temperature response. Furthermore, for nonproportional loading paths, the inclusion of the compliance operator had a significant influence on the multiaxial response, but had no influence on either uniaxial or proportional load histories.

A Micromechanical Basis for Constitutive Equations With Internal State Variables

1984 ◽  
Vol 106 (4) ◽  
pp. 322-325 ◽  
Author(s):  
E. W. Hart
Keyword(s):  
Internal Stress ◽  
Constitutive Equations ◽  
Inelastic Deformation ◽  
Internal State ◽  
Constitutive Relations ◽  
Micromechanical Model ◽  
Friction Stress ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables

A micromechanical model based on the glide and interaction of dislocations is developed to rationalize some of the phenomenological features of inelastic deformation. An origin for an internal stress is explicitly stated. The relation among the applied stress, the internal stress, and the glide friction stress is derived. The internal stress is shown to be linearly proportional to a stored anelastic strain. The micromechanical model is shown to provide a detailed basis for the state variable constitutive relations proposed by Hart.

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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