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multiplicative-decomposition
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Elastic-plastic modeling of kinematic hardening materials based on F = FeFp decomposition and the logarithmic strain tensor
, Article Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis - 2004, Manchester, 19 July 2004 through 22 July 2004 ; Volume 1 , 2004 , Pages 337-342 ; 0791841731 (ISBN); 9780791841730 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
American Society of Mechanical Engineers
2004
Abstract
In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material
Hardening materials modeling in finite elastic-plastic deformations based on the stretch tensor decomposition
, Article Materials and Design ; Volume 29, Issue 1 , 2008 , Pages 161-172 ; 02613069 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
Elsevier Ltd
2008
Abstract
In this paper, finite elastic-plastic deformations of hardening materials are analyzed based on the modified multiplicative decomposition of the left stretch tensor. This decomposition is the modified form of the Metzger and Dubey's decomposition used in the frame work of the principal axes of the left stretch tensor. For this purpose, basis-free corotational constitutive equations are derived for elastic-plastic hardening materials with the Armstrong-Frederick kinematic hardening and isotropic hardening models. The proposed governing equations are solved with different corotational rates for the simple shear problem with the material properties of the stainless steel SUS 304. The results...
Thermo-Mechanical Behavior of Shape Memory Alloys Under Multiaxial Loadings: Constitutive Modeling and Numerical Implementation at Small and Finite Strains
, Ph.D. Dissertation Sharif University of Technology ; Naghdabadi, Reza (Supervisor) ; Sohrabpour, Saeed (Supervisor)
Abstract
Shape memory alloys (SMAs) are a type of smart materials which have unique features known as pseudo-elasticity, one-way and two-way shape memory eects. The interest in the mechanical behavior of SMAs is rapidly growing with the increasing number of potential industrial applications. The origin of SMA material features is a reversible thermo-elastic martensitic phase transformation between a high symmetry, austenitic phase and a low symmetry, martensitic phase. In most applications, SMAs experience general non-proportional thermo-mechanical loads. Thus, according to experimental observations, the so-called variant reorientation should be considered in the constitutive model development....
Constitutive Modeling & Numerical Implementation of Shape Memory Polymers Based on Continuum Thermodynamics
, Ph.D. Dissertation Sharif University of Technology ; Naghdabadi, Reza (Supervisor) ; Sohrabpour, Saeed (Supervisor) ; Arghavani, Jamal (Co-Advisor)
Abstract
Shape memory polymers (SMPs) are a class of multi-phase smart materials that have the ability to return from a deformed to their original shape . The origin of SMP material features is a reversible glassy-rubbery phase transformation between a high stiffness glassy phase and a low stiffness rubbery phase . Thus , according to experimental observations , the phase transformation must be considered in the constitutive model development . In most applications , SMPs experience arbitrary thermo-mechanical loadings . Moreover , SMP structures typically undergo large rotations and strains and the use of a finite deformation scheme is preferred. In this thesis , we study the SMP behavior under...
A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation
, Article Finite Elements in Analysis and Design ; Volume 62 , 2012 , Pages 18-27 ; 0168874X (ISSN) ; Baghani, M ; Arghavani, J ; Sharif University of Technology
2012
Abstract
In this paper, employing the logarithmic (or Hencky) strain as a more physical measure of strain, the time-dependent response of compressible viscoelastic materials is investigated. In this regard, we present a phenomenological finite strain viscoelastic constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The formulation is based on the multiplicative decomposition of the deformation gradient into elastic and viscoelastic parts, together with the use of the isotropic property of the Helmholtz strain energy function. Making use of a logarithmic mapping, we present an appropriate form of the proposed constitutive equations in the...
A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys
, Article International Journal of Plasticity ; Volume 27, Issue 6 , June , 2011 , Pages 940-961 ; 07496419 (ISSN) ; Auricchio, F ; Naghdabadi, R ; Sharif University of Technology
2011
Abstract
The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g.; the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We...
Kinematics and kinetics description of thermoelastic finite deformation from multiplicative decomposition of deformation gradient viewpoint
, Article Mechanics Research Communications ; Volume 37, Issue 6 , 2010 , Pages 515-519 ; 00936413 (ISSN) ; Kargarnovin, M. H ; Sharif University of Technology
Abstract
In this paper, using the multiplicative decomposition of the deformation gradient into mechanical and thermal parts, both kinematic and kinetic aspects of finite deformation thermoelasticity are considered. At first, the kinematics of the thermoelastic continua in the purely thermal process of nonisothermal deformation is investigated for finite deformation thermoelasticity. Also, a linear relation between the thermal expansion tensor and the rate of the thermal deformation tensor is presented. In order to model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the...
A Mechanobiological model for damage-induced growth in arterial tissue with application to in-stent restenosis
, Article Journal of the Mechanics and Physics of Solids ; Volume 101 , 2017 , Pages 311-327 ; 00225096 (ISSN) ; Naghdabadi, R ; Sohrabpour, S ; Holzapfel, G. A ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
In-stent restenosis (ISR) is one of the main drawbacks of stent implementation which limits the long-term success of the procedure. Morphological changes occurring within the arterial wall due to stent-induced mechanical injury are a major cause for activation of vascular smooth muscle cells (VSMCs), and the subsequent development of ISR. Considering the theory of volumetric mass growth and adopting a multiplicative decomposition of the deformation gradient into an elastic part and a growth part, we present a mechanobiological model for ISR. An evolution equation is developed for mass growth of the neointima, in which the activation of VSMCs due to stent-induced damage (injury) and the...
An eulerian multiplicative constitutive model of finite elastoplasticity
, Article European Journal of Mechanics, A/Solids ; Volume 28, Issue 6 , 2009 , Pages 1088-1097 ; 09977538 (ISSN) ; Vafai, A ; Desai, C ; Sharif University of Technology
2009
Abstract
An Eulerian rate-independent constitutive model for isotropic materials undergoing finite elastoplastic deformation is formulated. Entirely fulfilling the multiplicative decomposition of the deformation gradient, a constitutive equation and the coupled elastoplastic spin of the objective corotational rate therein are explicitly derived. For the purely elastic deformation, the model degenerates into a hypoelastic-type equation with the Green-Naghdi rate. For the small elastic- and rigid-plastic deformations, the model converges to the widely-used additive model where the Jaumann rate is used. Finally, as an illustration, using a combined exponential isotropic-nonlinear kinematic hardening...
A thermodynamically consistent electro-chemo-mechanical theory for modeling axonal swelling
, Article Journal of the Mechanics and Physics of Solids ; Volume 145 , 2020 ; Naghdabadi, R ; Sohrabpour, S ; Li, Y ; Hu, Y ; Sharif University of Technology
Elsevier Ltd
2020
Abstract
In the present study, for the first time, a thermodynamically consistent large deformation theory is developed to model the multi physics problem of axonal swelling which is the hallmark of most of the brain diseases. To this end, the relevant axonal compartments are first explained and the corresponding model parts are introduced. Next, the problem is formulated as an open thermodynamic system and the corresponding constitutive and evolution equations are extracted utilizing the balance laws. Here, a multiplicative decomposition of the deformation gradient is used to capture the active behavior of the axonal actin cortex. Specific free energy functions are given for the model parts to...
Kinematic and Constitutive Modeling of Elastic and Thermoelastic Continua with Finite Deformation using Multiplicative Decomposition of Deformation Gradient
, Ph.D. Dissertation Sharif University of Technology ; Naghdabadi, Reza (Supervisor) ; Kargarnovin, Mohammad Hassan (Supervisor)
Abstract
In this thesis, a deformation measure is introduced which leads to a class of strain measures in the Lagrangian and Eulerian descriptions. In order to develop a constitutive equation, a second-order constitutive relation based on these strain measures is considered for modeling the mechanical behavior of solids at finite deformation. For this purpose and performance evaluation of the proposed strains, a Hookean-type constitutive equation is considered and the uniaxial loading as well as simple shear and pure shear tests are examined and the results are compared with the test data. Also, in order to characterize the mechanical behavior of elastic continua, constitutive equations through a...
A finite deformation constitutive model for shape memory polymers based on Hencky strain
, Article Mechanics of Materials ; Vol. 73 , 2014 , pp. 1-10 ; ISSN: 01676636 ; Arghavani, J ; Naghdabadi, R ; Sharif University of Technology
Abstract
In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic...
Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation
, Article International Journal of Plasticity ; Volume 27, Issue 9 , 2011 , Pages 1445-1455 ; 07496419 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
Abstract
In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good...
Development of a mathematical methodology to investigate biohydrogen production from regional and national agricultural crop residues: A case study of Iran
, Article International Journal of Hydrogen Energy ; Volume 42, Issue 4 , 2017 , Pages 1989-2007 ; 03603199 (ISSN) ; Karimi Alavijeh, M ; Zilouei, H ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
This study aims to construct a quantitative framework to assess biological production of hydrogen from agricultural residues in a country or region. The presented model is able to determine proper crops for biohydrogen production, its possible applications and use as well as environmental aspects. A multiplicative decomposition method was designed to forecast future production and Monte Carlo simulation was employed in the model to evaluate the risk of estimations. From 2013 to 2050, the hydrogen production capacity could increase from 53.59 to 164.41 kilotonnes (kt) in Iran. The highest contribution to biohydrogen production (52.1% in 2013 and 73.3% in 2050) belongs to cereal crops...
Modeling of rate dependent finite deformation viscoelastic behavior of foams
, Article 2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008, Boston, MA, 31 October 2008 through 6 November 2008 ; Volume 12 , 2009 , Pages 435-442 ; 9780791848739 (ISBN) ; Asghari, M ; Naghdabadi, R ; Sharif University of Technology
2009
Abstract
The behavior of foams is typically rate-dependent and viscoelastic. In this paper, multiplicative decomposition of the deformation gradient and the second law of thermodynamics are employed to develop the differential constitutive equations for isotropic viscoelastic foams experiencing finite deformations, from a phenomenological point of view, i.e. without referring to micro-structural viewpoint. A model containing an equilibrium hyperelastic spring which is parallel to a Maxwell model has been utilized for introducing constitutive formulation. The deformation gradient tensor is decomposed into two parts: elastic deformation gradient tensor and viscoelastic deformation gradient tensor. A...