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.

An Application of Incremental Plasticity Theory to Fatigue Life Prediction of Steels

1991 ◽  
Vol 113 (4) ◽  
pp. 404-410 ◽  
Author(s):  
W. R. Chen ◽  
L. M. Keer
Keyword(s):  
Fatigue Life ◽  
Life Prediction ◽  
Kinematic Hardening ◽  
Yield Condition ◽  
Strain Curve ◽  
Fatigue Life Prediction ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Stress Strain ◽  
Von Mises

An incremental plasticity model is proposed based on the von-Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and the uniaxial fatigue test results on smooth specimens. Experimental data of 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional loadings are given by this model

On the Modeling of Evolving Elastic and Plastic Anisotropy in the Finite Strain Regime – Application to Deep Drawing Processes

2012 ◽  
Vol 504-506 ◽  
pp. 679-684 ◽  
Author(s):  
Ivaylo N. Vladimirov ◽  
Michael P. Pietryga ◽  
Vivian Tini ◽  
Stefanie Reese
Keyword(s):  
Deep Drawing ◽  
Evolution Equations ◽  
Finite Strain ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Material Model ◽  
Internal Variables ◽  
Time Step ◽  
Finite Element Software ◽  
Structure Tensors

In this work, we discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been used for the simulation of the phenomenon of earing during cylindrical deep drawing.

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.

scholarly journals A New 3D Empirical Plastic and Damage Model for Simulating the Failure of Concrete Structure

2019 ◽  
Vol 13 (1) ◽  
Author(s):  
Yan-tao Jiao ◽  
Bo Wang ◽  
Zhen-zhong Shen
Keyword(s):  
Damage Mechanics ◽  
Evolution Equations ◽  
Influence Factor ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Nonlinear Behavior ◽  
Complex Stress State ◽  
Flow Rule ◽  
Wide Range

Abstract A new plastic–damage constitutive model based on the combination of damage mechanics and classical plastic theory was developed to simulate the failure of concrete. In order to explain different material behaviors of concrete under tensile and compressive loadings, the plastic yield criterion, the different kinematic hardening rule for tension and compressive and the isotropic flow rule were established in the effective stress space. Meanwhile, two different empirical damage evolution equations were adopted: one for compression and the other for tension. A multi-axial damage influence factor was also introduced to fully describe the anisotropic damage of concrete. Finally, the model response was compared with a wide range of experiment results. The results showed that the model could well describe the nonlinear behavior of concrete in a complex stress state.

Constitutive Description of Temperature-Dependent Nonproportional Cyclic Viscoplasticity

1997 ◽  
Vol 119 (1) ◽  
pp. 12-19 ◽  
Author(s):  
Xian Jie Yang
Keyword(s):  
Evolution Equations ◽  
Kinematic Hardening ◽  
Complex Loading ◽  
Deformation Resistance ◽  
Material Behavior ◽  
Temperature History ◽  
Loading History ◽  
Dependent Behavior ◽  
Proposed Model ◽  
Hardening Rules

This paper is concerned with the constitutive modeling of the temperature history dependent behavior of metallic materials under uniaxial and nonproportional cyclic loadings. In the study, a class of kinematic hardening rules characterized by a decomposition of the total kinematic hardening variable is discussed. A new nonproportionality is defined. In order to consider the influence of complex cyclic loading and temperature histories on materials behavior, an apparent isotropic deformation resistance parameter Qasm is proposed and the evolution equations of the isotropic deformation resistance Q are offered to correlate the memory effect of previous loading history on material behavior. The proposed model is applied to the description of complex cyclic deformation behavior of 1Cr18Ni9Ti stainless steel, and this model gives good results for the prediction of complex tests under complex loading history and at stepwise temperature changes.

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.

Finite Strain Constitutive Model of Evolving Elastic and Plastic Anisotropy by Means of Structure Tensors

2012 ◽  
Author(s):  
Ivaylo N. Vladimirov ◽  
Stefanie Reese
Keyword(s):  
Constitutive Model ◽  
Evolution Equations ◽  
Finite Strain ◽  
Elastic Anisotropy ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Material Model ◽  
Internal Variables ◽  
Time Step ◽  
Structure Tensors

In this paper, a finite strain constitutive model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening is presented. The evolution of elastic anisotropy is described by defining the Helmholtz free energy as an isotropic function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the Clausius-Duhem inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an implicit algorithm that automatically retains the symmetry of the internal variables in every time step. The material model is used as a user material subroutine UMAT infinite element package ABAQUS/Standard, by means of which the occurrence of earing during cylindrical deep drawing is simulated.

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.

scholarly journals A Cyclic Plasticity Model with Martensite Transformation for S30408 and Its Finite Element Implementation

2020 ◽  
Vol 10 (17) ◽  
pp. 6002
Author(s):  
Yanan Chen ◽  
Xiaohui Chen ◽  
Bingjun Gao ◽  
Xu Chen ◽  
Kai Zhang ◽  
...  
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Constitutive Model ◽  
Numerical Algorithm ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Flow Rule ◽  
Proposed Model ◽  
Metastable Austenitic Stainless Steel

The ability of the constitutive model to simulate the ratcheting behavior of metastable austenitic stainless steel S30408 is significant to ensure the safety of the liquefied natural gas (LNG) semi-trailer tanks in the lightweight process of the inner containers. This is because the lightweight inner vessels often encounter cyclic stresses due to the road inertia loads together with high mean stresses due to internal pressures. In this study, we performed cryogenic uniaxial tension experiments and a series of ratcheting experiments to investigate the cyclic plasticity behavior of the metastable austenitic stainless steel S30408. Based on the Ohno-Wang II model, we proposed a new cyclic plasticity constitutive model with martensitic transformation, which relates the content of deformation-induced martensite with isotropic hardening and kinematic hardening. The ratcheting behaviors of S30408 were first simulated by the proposed model with the incremental loading method using MATLAB. The results showed that the model could reasonably predict the ratcheting behavior of S30408, and the evolution law of martensite content could well predict the content of deformation-induced martensite. Under the assumption of the von Mises yield criterion and normal plasticity flow rule, we developed a numerical algorithm of plastic strain with the proposed model to implement the finite element calculation of the model. Internal iteration in the numerical algorithm was implemented with the Euler backward method, which calculated the trial strain for each equilibrium iteration using the consistent tangent matrix. With a user subroutine, the proposed model was programmed into ANSYS for a user - executable version. By simulating the uniaxial ratcheting of a S30408 round bar, we found that the calculated results were in good agreement with the experimental results, which promises further applications in the design of structures, such as LNG semi-trailer tanks.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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