Bridging Length Scales Between Macroscopic Response and Microstructure Through Gradient Anisotropic Damage for MMC

2001 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Robert J. Dorgan ◽  
J. R. Dorroh
Keyword(s):  
Evolution Equations ◽  
Scale Effects ◽  
Internal State ◽  
Multiple Scale ◽  
Mathematical Approach ◽  
State Variables ◽  
Material Inhomogeneity ◽  
Internal State Variables ◽  
Gradient Approach ◽  
Systematic Framework

Abstract This work provides a consistent and systematic framework for the gradient approach in coupled damage-plasticity that enables one to better understand the effects of material inhomogeneity on the macroscopic behavior and the material instabilities. The idea of multiple scale effects is made more general and complete by introducing damage and plasticity internal state variables and the corresponding gradients at both the macro and mesoscale levels. The development of evolution equations for plasticity and damage is treated in a similar mathematical approach and formulation since both address defects such as dislocations for the former and cracks/voids for the later.

A Phenomenologically Based Constitutive Model for Rene´ 95

1992 ◽  
Vol 114 (4) ◽  
pp. 340-347 ◽  
Author(s):  
J. A. Sherwood ◽  
D. C. Stouffer
Keyword(s):  
Constitutive Model ◽  
Damage Accumulation ◽  
Evolution Equations ◽  
Internal State ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Flow Equation ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables

A unified constitutive model incorporating internal state variables based upon the deformation phenomena that are observed to occur at the microstructural level has been developed and applied to Rene´ 95. Material hardening is modeled using dragstress and back-stress state variables, while the reduction in the material’s load-carrying capability is described by using a damage-accumulation state variable. Application of the model to the tensile, cyclic, and creep loadings of Rene´ 95 at 650°C demonstrated that the model is capable of capturing cyclic hardening, damage accumulation, and tertiary creep by using one inelastic flow equation in concert with the state-variable-evolution equations.

scholarly journals Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140216 ◽  
Author(s):  
K. Haldar ◽  
D. C. Lagoudas
Keyword(s):  
Free Energy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Evolution Equations ◽  
Internal State ◽  
Polycrystalline Materials ◽  
State Variables ◽  
Magnetic Shape Memory ◽  
Magnetic Shape Memory Alloys ◽  
Internal State Variables

A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

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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