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 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.

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.

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.

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.

Modeling and Simulation of Microstructure Evolution in Extruded Aluminum Profiles

2009 ◽  
Vol 424 ◽  
pp. 43-50
Author(s):  
Farhad Parvizian ◽  
T. Kayser ◽  
Bob Svendsen
Keyword(s):  
Plastic Deformation ◽  
Aluminum Alloys ◽  
Modeling And Simulation ◽  
Microstructure Evolution ◽  
Internal State ◽  
Extrusion Process ◽  
State Variables ◽  
Cooling Process ◽  
Microstructure Parameters ◽  
Simulation Results

The purpose of this work is to predict the microstructure evolution of aluminum alloys during hot metal forming processes using the Finite Element Method (FEM). Here, the focus will be on the extrusion process of aluminum alloys. Several micromechanical mechanisms such as diffusion, recovery, recrystallization and grain growth are involved in various subsequent stages of the extrusion and the cooling process afterward. The evolution of microstructure parameters is motivated by plastic deformation and temperature. A number of thermomechanical aspects such as plastic deformation, heat transfer between the material and the container, heat generated by friction, and cooling process after the extrusion are involved in the extrusion process and result in changes in temperature and microstructure parameters subsequently. Therefore a thermomechanically coupled modeling and simulation which includes all of these aspects is required for an accurate prediction of the microstructure evolution. A brief explanation of the isotropic thermoelastic viscoplastic material model including some of the simulation results of this model, which is implemented as a user material (UMAT) in the FEM software ABAQUS, will be given. The microstructure variables are thereby modeled as internal state variables. The simulation results are finally compared with some experimental results.

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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