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.

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.

Prediction of Springback in Unconstrained Bending by a Model for Evolving Elastic and Plastic Anisotropy

2013 ◽  
Vol 554-557 ◽  
pp. 2330-2337
Author(s):  
Ivaylo N. Vladimirov ◽  
Stefanie Reese
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Elastic Anisotropy ◽  
Plastic Anisotropy ◽  
Material Model ◽  
Internal Variables ◽  
Time Step ◽  
Finite Element Software ◽  
Initial Anisotropy ◽  
Structure Tensors

Sheet metals exhibit anisotropic plastic behavior due to the large plastic deformations that occur during the rolling of the sheet and which induce texture and are responsible for the initial anisotropy. There exist various possibilities to introduce plastic anisotropy into the finite element modelling of sheet metal forming. The initial yield anisotropy can be incorporated either through an anisotropic yield surface or directly by means of a crystallographic texture model. Here, one basically differentiates between empirical and phenomenological anisotropic yield function equations, where the anisotropy coefficients can be obtained from mechanical tests, and texture-based models the coefficients of which are directly determined based on experimentally obtained orientation distributions. Another type of anisotropy that can be usually found in anisotropic materials is the elastic anisotropy. In metal plasticity one often considers the effect of elastic anisotropy significantly smaller than the effect of plastic anisotropy. Consequently, elastic isotropic expressions are often used for elastic stored energy functions with anisotropic yield criteria. However, the influence of elastic anisotropy in the elastoplastic behavior can be very important especially during elastic recovery processes during unloading after forming and springback. This research focuses, therefore, on the study of the influence of elastic anisotropy on the amount of springback in bending processes such as e.g. unconstrained bending. 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 applied to the simulation of springback of unconstrained bending.

Modelling Non-Quadratic Anisotropic Yield Criteria and Mixed Isotropic-Nonlinear Kinematic Hardening at Finite Strains

2014 ◽  
Vol 611-612 ◽  
pp. 19-26
Author(s):  
Tiago Jordao Grilo ◽  
Ivaylo Nikolov Vladimirov ◽  
Robertt Angelo Fontes Valente ◽  
Stefanie Reese
Keyword(s):  
Constitutive Model ◽  
Evolution Equations ◽  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Symmetric Tensor ◽  
Internal Variables ◽  
Exponential Map ◽  
Yield Criteria ◽  
User Subroutine ◽  
Algorithmic Strategy

A constitutive model that accounts for mixed isotropic-nonlinear kinematic hardening, suitable for any non-quadratic yield criteria, is proposed. The finite strain model is derived from a thermodynamically consistent framework and relies on the multiplicative split of the deformation gradient in the context of hyperelasticity. The nonlinear kinematic hardening approach is introduced in the constitutive model by means of the multiplicative split of the plastic deformation gradient. The constitutive equations are consistently derived by exploiting the dissipation inequality, and expressed by symmetric tensor-valued internal variables only. The exponential map algorithm was employed in the integration of the evolution equations. This algorithmic strategy has the advantage of preserving both the plastic incompressibility and the symmetry of the internal variables. The model was implemented into a material user-subroutine of a commercial finite element code (ABAQUS), and some numerical results are presented to assess the performance of the present model.

scholarly journals An alternative J2 material model with isotropic hardening for coupled thermal-structural finite-strain elastoplastic analyses

2018 ◽  
Vol 157 ◽  
pp. 06003 ◽  
Author(s):  
Ladislav Écsi ◽  
Pavel Élesztos ◽  
Roland Jančo
Keyword(s):  
Evolution Equations ◽  
Finite Strain ◽  
Material Model ◽  
The Body ◽  
Isotropic Hardening ◽  
Failure Mode Transition ◽  
Return Mapping ◽  
Elastoplastic Media ◽  
Strain Measures ◽  
Fully Coupled

In this paper an alternative J2 material model with isotropic hardening for finite-strain elastoplastic analyses is presented. The model is based on a new nonlinear continuum mechanical theory of finite deformations of elastoplastic media which allows us to describe the plastic flow in terms of various instances of the yield surface and corresponding stress measures in the initial and current configurations of the body. The approach also allows us to develop thermodynamically consistent material models in every respect. Consequently, the models not only do comply with the principles of material modelling, but also use constitutive equations, evolution equations and even ‘normality rules’ during return mapping which can be expressed in terms of power conjugate stress and strain measures or their objective rates. Therefore, such models and the results of the analyses employing them no longer depend on the description and the particularities of the material model formulation. Here we briefly present an improved version of our former material model capable of modelling ductile-to brittle failure mode transition and demonstrate the model in a numerical example using a fully coupled thermal-structural analysis.

Constitutive Modelling of Anisotropy, Hardening and Failure of Sheet Metals

2011 ◽  
Vol 473 ◽  
pp. 631-636 ◽  
Author(s):  
Ivaylo N. Vladimirov ◽  
Yalin Kiliclar ◽  
Vivian Tini ◽  
Stefanie Reese
Keyword(s):  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Forming Limit Diagram ◽  
Material Model ◽  
Constitutive Modelling ◽  
Forming Limit ◽  
Isotropic Hardening ◽  
Continuum Damage ◽  
Aluminium Sheets ◽  
Good Agreement

The paper discusses the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples investigate the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with test data for aluminium sheets display a good agreement between the finite element results and the experimental data.

An Extended 3D Finite Strain Constitutive Model for Shape Memory Alloys

2021 ◽  
pp. 1-37
Author(s):  
Mengqian Zhang ◽  
Theocharis Baxevanis
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Finite Strain ◽  
Volume Fraction ◽  
Internal Variables ◽  
Numerical Implementation ◽  
Deformation Response ◽  
Heat Effects

Abstract A 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for transformation volume contraction, smooth thermomechanical response, temperature dependence of the critical force required for (re)orientation, temperature and load dependence of the hysteresis width, asymmetry between forward and reverse phase transformation, and is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, that further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.

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.

Application and Analysis of Plane Woven C/SiC Composites Based on Continuum Damage Mechanics

2012 ◽  
Vol 490-495 ◽  
pp. 3916-3919 ◽  
Author(s):  
Yan Jun Chang ◽  
Ke Shi Zhang ◽  
Gui Qiong Jiao ◽  
Jian Yun Chen
Keyword(s):  
Constitutive Model ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Ceramic Matrix Composites ◽  
Shear Loading ◽  
Internal Variables ◽  
Anisotropic Damage ◽  
Initial Modulus ◽  
Sic Composites

The aim of this article was to propose a macroscopic damage model, which describes the nonlinear behavior observed on woven C/SiC ceramic matrix composites. The model was built within a thermodynamic framework with internal variables. The anisotropic damage evolution processes of the material were described by nonlinear damage isotropic and kinematic hardening functions in this model. The anisotropic damage and damage coupling were considered with a damage yield function including anisotropic coefficients. Using the principle of energy equivalence, the damage variables were defined by the unloading modulus and initial modulus. The damage variable and the irrecoverable strain induced by micro-crack propagation were deduced by thermodynamics. The constants of constitutive model were identified and the damage evolution processes under tensile and shear loading. Uniaxial tension and shear tests had been used to valid the constitutive model to C/SiC composites.

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