scholarly journals Eulerian elastoplasticity: Basic issues and recent results

2009 ◽  
Vol 36 (3) ◽  
pp. 167-205 ◽  
Author(s):  
O.T. Bruhns
Keyword(s):  
Constitutive Equations ◽  
Internal State ◽  
State Variables ◽  
Constitutive Function ◽  
Large Rotation ◽  
Internal State Variables ◽  
Material Frame Indifference ◽  
Eulerian Strain ◽  
Objective Rate ◽  
Plastic Parts

Traditional formulations of elastoplasticity in the presence of finite strain and large rotation are Eulerian type and widely used; they are based upon, among other things, the additive decomposition of the stretching or the Eulerian strain-rate into elastic and plastic parts. In such formulations, yield functions and objective rate constitutive equations are expressed in terms of objective Eulerian tensor quantities, including the stretching, the Kirchhoff stress, internal state variables, etc. Each of these quantities transforms in a corotational manner under a change of the observing frame. According to the principle of material frame-indifference or objectivity, each constitutive function should be invariant, whenever the observing frame is changed to another one by any given time-dependent rotation. In this work the general form of constitutive equations is discussed. Several frequently used objective rates are analyzed with respect to their serviceability to develop a self-consistent formulation, i.e. to be integrable to deliver an elastic in particular hyperelastic relation for vanishing plastic deformation. This would be of great importance, e.g., for so-called spring back calculations in metal forming.

Constitutive Equations With Internal State Variables for the Inelastic Behavior of Soft Rocks

1994 ◽  
Vol 47 (6S) ◽  
pp. S97-S101 ◽  
Author(s):  
M. Aubertin ◽  
D. E. Gill ◽  
B. Ladanyi
Keyword(s):  
Constitutive Equations ◽  
Internal State ◽  
Inelastic Behavior ◽  
State Variables ◽  
Physical Processes ◽  
Soft Rocks ◽  
Brittle Behavior ◽  
Internal State Variables ◽  
Compressive Stresses ◽  
Do So

The mechanical behavior of soft rocks is quite complex as it may involve a variety of deformation mechanisms. When loaded under compressive stresses at intermediate temperature, such rocks often show a semi-brittle response controlled by dislocations motion and microcracking. Because these two types of physical processes are acting simultaneously, the constitutive equations should involve a coupled approach. In this paper, the authors extend an existing unified model with internal state variables, developed for the ductile regime, to accommodate semi-brittle behavior of low porosity rocks. To do so, a damage variable Dv is introduced into the model. This requires a modification of the kinetic law and the addition of an evolution law for Dv. After presenting some of the main features of soft rocks behavior, the main equations are introduced together with a few attributes of this new model.

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.

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.

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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