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.

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 Modelling of single degree of freedom SMA oscillators by using rheological schemes

2018 ◽  
Vol 196 ◽  
pp. 01049
Author(s):  
Artur Zbiciak ◽  
Kacper Wasilewski
Keyword(s):  
Internal State ◽  
Constitutive Relations ◽  
Degree Of Freedom ◽  
State Variables ◽  
Numerical Application ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Internal State Variables ◽  
Load Removal ◽  
Modelling Approach

The article describes the approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Certain sets of rheological components are presented and their influence on the oscillator response is examined. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user's subroutines. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement.

scholarly journals The Granular Structure of Snow: An Internal-State Variable Approach

1986 ◽  
Vol 32 (112) ◽  
pp. 434-438 ◽  
Author(s):  
A. C. Hansen ◽  
R. L. Brown
Keyword(s):  
Internal State ◽  
Granular Structure ◽  
High Rate ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables ◽  
Variable Approach ◽  
Quantitative Stereology ◽  
The Mean ◽  
General Relations

AbstractA statistical model characterizing the granular structure of snow is developed using quantitative stereology. The model is based on specific parameters (e.g. bond radius, grain-size, etc.) which take the form of internal-state variables in a constitutive theory for high-rate deformation of snow. In addition to parameters developed by other authors in previous investigations, a new parameter characterizing the mean bond length is developed. More significantly, general relations are derived for the mean number of bonds per grain and mean number of grains per unit volume without making any assumptions regarding the shape or size of the ice grains, or their respective distributions.

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.

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 The Granular Structure of Snow: An Internal-State Variable Approach

1986 ◽  
Vol 32 (112) ◽  
pp. 434-438 ◽  
Author(s):  
A. C. Hansen ◽  
R. L. Brown
Keyword(s):  
Internal State ◽  
Granular Structure ◽  
High Rate ◽  
State Variables ◽  
State Variable ◽  
Internal State Variables ◽  
Variable Approach ◽  
Quantitative Stereology ◽  
The Mean ◽  
General Relations

AbstractA statistical model characterizing the granular structure of snow is developed using quantitative stereology. The model is based on specific parameters (e.g. bond radius, grain-size, etc.) which take the form of internal-state variables in a constitutive theory for high-rate deformation of snow. In addition to parameters developed by other authors in previous investigations, a new parameter characterizing the mean bond length is developed. More significantly, general relations are derived for the mean number of bonds per grain and mean number of grains per unit volume without making any assumptions regarding the shape or size of the ice grains, or their respective distributions.

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 Strain-Based Formulation for the Coupled Viscoelastic/Damage Behavior

2000 ◽  
Vol 68 (2) ◽  
pp. 304-311 ◽  
Author(s):  
K. Abdel-Tawab ◽  
Y. J. Weitsman
Keyword(s):  
Internal State ◽  
Internal State Variable ◽  
State Variables ◽  
Viscoelastic Creep ◽  
Damage Behavior ◽  
State Variable ◽  
Internal State Variables ◽  
Interfacial Cracks ◽  
Induced Changes ◽  
The Continuum

A strain-based thermodynamics framework is proposed for modeling the continuum damage behavior of viscoelastic materials. Damage is represented by an internal state variable in the form of a symmetric second rank tensor. The effect of damage on the constitutive behavior is introduced through direct coupling between the damage variable and the viscoelastic internal state variables. This approach accounts for time-dependent damage as well as damage-induced changes in material symmetry. Also, damage evolution is modeled by employing the concept of damage surfaces. This work is motivated by experimental observations of the response of swirl-mat and random chopped fiber mat polymeric composites where viscoelastic creep was accompanied by a multitude of fiber/matrix interfacial cracks.

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