Elastic-Plastic Modeling of Kinematic Hardening Materials Based on F=FeFp Decomposition and the Logarithmic Strain Tensor

Volume 1 ◽  
2004 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Flow Rule ◽  
Deformation Gradient Tensor ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Corotational Rate ◽  
Stress Components ◽  
Shear Problem

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.

Elastic-Plastic Modeling of the Hardening Materials Based on an Eulerian Strain Tensor and a Proper Corotational Rate

2005 ◽  
Author(s):  
Reza Naghdabadi ◽  
Kamyar Ghavam
Keyword(s):  
Kinematic Hardening ◽  
Strain Tensor ◽  
Back Stress ◽  
Flow Rule ◽  
Governing Equations ◽  
Plastic Part ◽  
Elastic Plastic ◽  
Eulerian Strain ◽  
Corotational Rate ◽  
Conjugate Stress

In this paper a model for analyzing elastic-plastic kinematic hardening materials is introduced, based on the additive decomposition of the corotational rate of an Eulerian strain tensor In this model, the elastic constitutive equation as well as the flow rule and the hardening equation is expressed in terms of the elastic and plastic parts of the corotational rate of the mentioned Eulerian stain tensor and its conjugate stress tensor. In the flow rule, the plastic part of the corotational rate of the Eulerian strain tensor is related to the difference of the deviatoric part of the conjugate stress and the back stress tensors. A proportionality factor is used in this flow rule which must be obtained from a consistency condition based on the von Mises yield criterion. A Prager type kinematic hardening model is used which relates the corotational rate of the back stress tensor to the plastic part of the corotational rate of the Eulerian strain tensor. Also in this paper a proper corotational rate corresponding to the Eulerian strain tensor is introduced. Finally the governing equations for the analysis of elastic-plastic kinematic hardening materials are obtained. As an application, these governing equations are solved numerically for the simple shear problem and the stress and back stress components are plotted versus the shear displacement. The results are compared with those, which are available in the literature.

Elastic-Plastic Modeling of Hardening Materials Using a Corotational Rate Based on the Plastic Spin Tensor

2007 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Isotropic Hardening ◽  
Strain Rate Tensor ◽  
Spin Tensor ◽  
Plastic Spin ◽  
Elastic Plastic ◽  
Proposed Model ◽  
Corotational Rate ◽  
Shear Problem

In this paper based on the multiplicative decomposition of the deformation gradient, the plastic spin tensor and the plastic spin corotational rate are introduced. Using this rate (and also log-rate), an elastic-plastic constitutive model for hardening materials are proposed. In this model, the Armstrong-Frederick kinematic hardening and the isotropic hardening equations are used. The proposed model is solved for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the results of proposed theoretical model and the experimental data. As another example, the Prager kinematic hardening equation is used. In this case, the stress results are compared with those obtained by Bruhns et al. [2], in which they used the additive decomposition of the strain rate tensor.

Nonlinear Plastic Modeling of Materials Based on the Generalized Strain Rate Tensor

2008 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Strain Rate ◽  
Simple Shear ◽  
Large Deformations ◽  
Kinematic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Governing Equations ◽  
Elastic Plastic ◽  
Shear Problem ◽  
Plastic Hardening

In this paper, a method for modeling of elastic-plastic hardening materials under large deformations is proposed. In this model the generalized strain rate tensor is used. Such a tensor is obtained on the basis of the method which was introduced by the authors. Based on the generalized strain rate tensor, a flow rule, a Prager-type kinematic hardening equation and a kinematic decomposition is proposed and the governing equations for such materials are obtained. As an application, the governing equations for the simple shear problem are solved and some results are compared with those in the literature.

Corotational Analysis of Elastic-Plastic Hardening Materials Based on Different Kinematic Decompositions

2006 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Theoretical Models ◽  
Isotropic Hardening ◽  
Strain Rate Tensor ◽  
Elastic Plastic ◽  
Mixed Hardening ◽  
Hardening Models ◽  
Shear Problem ◽  
Plastic Hardening

In this paper, two corotational modeling for elastic-plastic, mixed hardening materials at finite deformations are introduced. In these models, the additive decomposition of the strain rate tensor as well as the multiplicative decomposition of the deformation gradient tensor is used. For this purpose, corotational constitutive equations are derived for elastic-plastic hardening materials with the non-linear Armstrong-Frederick kinematic hardening and isotropic hardening models. As an application of the proposed constitutive modeling, the governing equations are solved numerically for the simple shear problem with different corotational rates and the stress components are plotted versus the shear displacement. The results for stress, using the additive and the multiplicative decompositions are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the proposed theoretical models and the experimental data. As another example, the Prager kinematic hardening equation is used instead of the Armstrong-Frederick model. In this case the results for stress are compared with the theoretical results of Bruhns et al. [2].

scholarly journals Multi-Trigger Thermo-Electro-Mechanical Soft Actuators under Large Deformations

Polymers ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 489 ◽  
Author(s):  
Ebrahim Yarali ◽  
Reza Noroozi ◽  
Armin Yousefi ◽  
Mahdi Bodaghi ◽  
Mostafa Baghani
Keyword(s):  
Electric Field ◽  
Deformation Gradient ◽  
Free Energy Density ◽  
Radius Of Curvature ◽  
Thermal Stimulus ◽  
The Finite Element Method ◽  
Deformation Gradient Tensor ◽  
Runge Kutta Method ◽  
Stress Components ◽  
Soft Actuators

Dielectric actuators (DEAs), because of their exceptional properties, are well-suited for soft actuators (or robotics) applications. This article studies a multi-stimuli thermo-dielectric-based soft actuator under large bending conditions. In order to determine the stress components and induced moment (or stretches), a nominal Helmholtz free energy density function with two types of hyperelastic models are employed. Non-linear electro-elasticity theory is adopted to derive the governing equations of the actuator. Total deformation gradient tensor is multiplicatively decomposed into electro-mechanical and thermal parts. The problem is solved using the second-order Runge-Kutta method. Then, the numerical results under thermo-mechanical loadings are validated against the finite element method (FEM) outcomes by developing a user-defined subroutine, UHYPER in a commercial FEM software. The effect of electric field and thermal stimulus are investigated on the mean radius of curvature and stresses distribution of the actuator. Results reveal that in the presence of electric field, the required moment to actuate the actuator is smaller. Finally, due to simplicity and accuracy of the present boundary problem, the proposed thermally-electrically actuator is expected to be used in future studies and 4D printing of artificial thermo-dielectric-based beam muscles.

Descriptions of Reversed Yielding in Internally Pressurized Tubes

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Woncheol Jeong ◽  
Kwansoo Chung
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Kinematic Hardening ◽  
Material Model ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Law ◽  
Solving Equations ◽  
Associated Flow Rule ◽  
Reversed Deformation

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

The influence of non-dissipative quantities in kinematic hardening plasticity

2004 ◽  
Vol 218 (6) ◽  
pp. 615-622 ◽  
Author(s):  
M Wallin ◽  
M Ristinmaa ◽  
N S Ottosen
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Material Behaviour ◽  
Dissipative Part ◽  
Real Material ◽  
Shear Problem ◽  
Evolution Laws ◽  
Thin Walled ◽  
Plastic Parts ◽  
Walled Cylinder

A kinematic hardening plasticity model valid for finite strains is presented. The model is based on the well-known multiplicative split of the deformation gradient into elastic and plastic parts. The basic ingredient in the formulation is the introduction of a locally defined configuration—a centre configuration—which is associated with a deformation gradient that is used to characterize the kinematic hardening behaviour. The non-dissipative quantities allowed in the model are found when the plastic and kinematic hardening evolution laws are split into two parts: a dissipative part, which is restricted by the dissipation inequality, and a non-dissipative part, which can be chosen without any thermodynamic considerations. To investigate the predictive capabilities of the proposed kinematic hardening formulation, necking of a bar is considered. Moreover, to show the influence of the non-dissipative quantities, the simple shear problem and torsion of a thin-walled cylinder are considered. The numerical examples reveal that the non-dissipative quantities can affect the response to a large extent and are consequently valuable and important ingredients in the formulation when representing real material behaviour.

The Study of Elastic-Plastic Fatigue Behavior of Nigerian-Rolled NST 37-2 Steel

2010 ◽  
Vol 3 ◽  
pp. 28-41
Author(s):  
B.O. Malomo ◽  
S.A. Ibitoye ◽  
L.O. Adekoya
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Fatigue Behavior ◽  
Numerical Results ◽  
Test Material ◽  
Flow Rule ◽  
Static Fatigue ◽  
Elastic Plastic

The NST 37-2 steel represents about 75% volume of Nigerian-produced steel which is yet to be fully characterized for its fatigue behavior. Thus, its suitability for many applications is questionable. This paper presents a framework based on the theory of elasto-plasticity in order to make appropriate recommendations in this regard. Experimentally, tensile tests were carried out on test specimens to establish the baseline material properties of the steel in annealed, as-rolled, normalized and hardened/tempered conditions. Fatigue tests were then conducted at 60% Su; 70% Su and 80% Su of the test material and fractographic examinations on the test specimens were subsequently carried out. The frequency harmonic fatigue analysis was implemented in the ANSYS software environment for the numerical study. The elastic-plastic material property was described by the von Mises yield criterion, the flow rule of Prandtl-Reuss, and the kinematic hardening rule of Prager. The numerical results indicate with respect to rate-dependence fatigue behavior that the annealed test specimen is most resilient under cyclic deformation as compared with the normalized, hardened/tempered and as-rolled specimens respectively. The experimental and numerical results were found to be in close agreement and based on the general performance, the steel material is recommended for use in low cycle, quasi-static fatigue applications.

A Viscoelastic-Elastoplastic Finite Strain Framework for Modeling Polymers

2014 ◽  
Author(s):  
Ireneusz Lapczyk ◽  
Juan A. Hurtado
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Finite Strain ◽  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Internal Variable ◽  
Creep Model ◽  
Internal Variables ◽  
Flow Rule ◽  
Finite Element Software

In this paper we present a new constitutive framework, the Parallel Rheological Framework (PRF), for modeling polymers that has been recently developed by the authors and implemented in the commercial finite element software Abaqus [1]. The framework is based on parallel finite-strain viscoelastic and elastoplastic networks. For each viscoelastic network a multiplicative split of the deformation gradient into elastic and viscous components is assumed. The evolution of the viscous component of the deformation gradient is governed by a flow rule obtained assuming the existence of a creep potential. The flow rule is expressed as a function of stress invariants and internal variables, and different evolution laws for the internal variables are allowed within the framework of the model. Similar to the viscoelastic networks, the deformation gradient in the elastoplastic network is decomposed into elastic and plastic components. The yield surface is defined assuming combined isotropic/kinematic hardening. The yield surface is a function of a scalar internal variable that describes isotropic hardening, and a tensorial internal variable (backstress) that describes the shift of the yield surface in the stress space. The evolution of the scalar variable is governed by associated flow rule, while the evolution of backstresses is determined by the Armstrong-Frederick law [2], which is extended to finite-strain deformations. Finally, stress softening is introduced into an elastoplastic network using a modified version of Ogden and Roxbourgh’s pseudo-elasticity model [3]. This paper presents an outline of the framework, including two recent enhancements: a new creep model (the power law model) and combined isotropic/kinematic hardening plasticity model. The framework is then applied to analyze numerically the uniaxial loading/unloading behaviors of filled natural rubber and an EPDM polymer. The results obtained using finite element simulations show very good correlation with experimental data.

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elastoplasticity

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Amin Eshraghi ◽  
Hamid Jahed ◽  
Katerina D. Papoulia
Keyword(s):  
Evolution Equations ◽  
Finite Strain ◽  
Kinematic Hardening ◽  
Nonlinear Evolution Equations ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Hardening Material ◽  
Jaumann Rate ◽  
Proposed Model ◽  
Nonlinear Hardening

An Eulerian rate formulation of finite strain elastoplasticity is developed based on a fully integrable rate form of hyperelasticity proposed in Part I of this work. A flow rule is proposed in the Eulerian framework, based on the principle of maximum plastic dissipation in six-dimensional stress space for the case of J2 isotropic plasticity. The proposed flow rule bypasses the need for additional evolution laws and/or simplifying assumptions for the skew-symmetric part of the plastic velocity gradient, known as the material plastic spin. Kinematic hardening is modeled with an evolution equation for the backstress tensor considering Prager’s yielding-stationarity criterion. Nonlinear evolution equations for the backstress and flow stress are proposed for an extension of the model to mixed nonlinear hardening. Furthermore, exact deviatoric/volumetric decoupled forms for kinematic and kinetic variables are obtained. The proposed model is implemented with the Zaremba–Jaumann rate and is used to solve the problem of rectilinear shear for a perfectly plastic and for a linear kinematic hardening material. Neither solution produces oscillatory stress or backstress components. The model is then used to predict the nonlinear hardening behavior of SUS 304 stainless steel under fixed-end finite torsion. Results obtained are in good agreement with reported experimental data. The Swift effect under finite torsion is well predicted by the proposed model.

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