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 Reactive Inelasticity Theoretical Framework for Modeling Viscoelasticity, Plastic Deformation, and Damage in Fibrous Soft Tissue

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Babak N. Safa ◽  
Michael H. Santare ◽  
Dawn M. Elliott
Keyword(s):  
Plastic Deformation ◽  
Soft Tissues ◽  
Constitutive Relations ◽  
Deformation Gradient ◽  
Theoretical Framework ◽  
Extracellular Proteins ◽  
External Loading ◽  
High Water Content ◽  
State Variables ◽  
Mechanical Behaviors

Fibrous soft tissues are biopolymeric materials that are made of extracellular proteins, such as different types of collagen and proteoglycans, and have a high water content. These tissues have nonlinear, 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 tissue's fibrous matrix, 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 (ISV) and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as 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.

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.

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.

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.

Nonlinear Dynamic Response of Piezoelectric Plates Considering Damage Effects

2006 ◽  
Vol 324-325 ◽  
pp. 299-302 ◽  
Author(s):  
Yi Ming Fu ◽  
Xian Qiao Wang
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
State Variables ◽  
Nonlinear Dynamic Response ◽  
Internal State Variables ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Plates

Based on the Talreja’s tensor valued internal state variables damage model and the Helmhotlz free energy of piezoelectric material, the constitutive relations of the piezoelectric plates with damage are derived. Then, the nonlinear dynamic equations of the piezoelectric plates considering damage are established. By using the finite difference method and the Newmark scheme, these equations are solved and the effects of damage and electric loads on the nonlinear dynamic response of piezoelectric plates are discussed.

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.

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