Finite Deformation Elastoplasticity for Rate and Temperature Dependent Polycrystalline Metals

2011 ◽  
Author(s):  
Richard A. Regueiro ◽  
Douglas J. Bammann ◽  
Esteban B. Marin ◽  
George C. Johnson
Keyword(s):  
Internal State ◽  
Lattice Structure ◽  
Deformation Gradient ◽  
State Variables ◽  
Temperature Dependent ◽  
Multiplicative Decomposition ◽  
Strain Rate Effects ◽  
Internal State Variables ◽  
Polycrystalline Metals ◽  
Rate Effects

An elastoplasticity model is formulated and demonstrated in one-dimension (1D) for modeling finite deformations in poly-crystalline metals. Quasi-static to high strain rate effects as well as temperature sensitivity are included. A multiplicative decomposition of the deformation gradient into elastic, plastic, and thermal parts, that includes a volumetric/isochoric split of the elastic stretching tensor is assumed. The kinematics and thermodynamic formulation lead to constitutive equations, stresses, and constraints on the evolution of the internal state variables. The model accounts for (i) dislocation drag effects on flow stress, and (ii) generation (hardening) and annihilation (recovery) of statistically-stored dislocations (SSDs). The resulting model is normalized to dimensionless form to allow dimensionless material parameters fit for one metal to approximate the behavior of another metal of similar lattice structure, if data are limited. One dimensional material parameter fitting is demonstrated for two refractory metals, body centered cubic (bcc) Tantalum and Tungsten.

scholarly journals A Reactive Inelasticity Theoretical Framework for modeling Viscoelasticity, Plastic Deformation, and damage in Soft Tissue

2018 ◽  
Author(s):  
Babak N. Safa ◽  
Michael H. Santare ◽  
Dawn M. Elliott
Keyword(s):  
Plastic Deformation ◽  
Soft Tissue ◽  
Internal State ◽  
Constitutive Relations ◽  
Deformation Gradient ◽  
Theoretical Framework ◽  
External Loading ◽  
State Variables ◽  
Mechanical Behaviors ◽  
Internal State Variables

AbstractSoft tissues are biopolymeric materials, primarily made of collagen and water. These tissues have non-linear, anisotropic, and inelastic mechanical behaviors that are often categorized into viscoelastic behavior, plastic deformation, and damage. While tissue’s elastic and viscoelastic mechanical properties have been measured for decades, there is no comprehensive theoretical framework for modeling inelastic behaviors of these tissues that is based on their structure. To model the three major inelastic mechanical behaviors of soft tissue we formulated a structurally inspired continuum mechanics framework based on the energy of molecular bonds that break and reform in response to external loading (reactive bonds). In this framework, we employed the theory of internal state variables and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as internal state variables that allowed for consistent modeling of all three of the inelastic behaviors of tissue by using the same sets of constitutive relations. Several numerical examples are provided that address practical problems in tissue mechanics, including the difference between plastic deformation and damage. This model can be used to identify relationships between tissue’s mechanical response to external loading and its biopolymeric structure.

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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