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.

scholarly journals An Alternative Material Model Using a Generalized J2 Finite-Strain Flow Plasticity Theory with Isotropic Hardening

2018 ◽  
Vol 23 (2) ◽  
pp. 339-353 ◽  
Author(s):  
L. Écsi ◽  
P. Élesztős
Keyword(s):  
Finite Strain ◽  
Biaxial Tension ◽  
Time Derivative ◽  
Continuum Theory ◽  
Material Model ◽  
Plasticity Theory ◽  
Isotropic Hardening ◽  
Return Mapping ◽  
Alternative Material ◽  
Nonlinear Continuum

Abstract In this paper an alternative material model using a generalized J2 finite-strain flow plasticity theory with isotropic hardening is presented. The model is based on a new nonlinear continuum mechanical theory of finite deformations of elasto-plastic media which allows for the development of objective and thermodynamically consistent material models. As a result, the constitutive equation, the evolution equation and even the ‘normality rule’, characterising the plastic flow in the material during return mapping, can be expressed in various forms, using several instances of the yield surface and corresponding pairs of stress measures and strain rates, respectively, which are conjugate with respect to the internal mechanical power and its arbitrary higher order time derivative. Therefore the results of the material model when used in numerical analyses are not affected by the description and particularities of the material model formulation. Here, we briefly outline the nonlinear continuum theory along with a detailed description of the material model and finally present the model in a numerical example using a cross-shaped specimen in biaxial tension.

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.

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.

Numerical Study of Material Degradation of a Silicone Cross-Shaped Specimen Using a Thermodynamically Consistent Mooney-Rivlin Material Model

2019 ◽  
Vol 952 ◽  
pp. 258-266 ◽  
Author(s):  
Róbert Jerábek ◽  
Ladislav Écsi
Keyword(s):  
Power Density ◽  
Finite Strain ◽  
Numerical Study ◽  
Deformation Gradient ◽  
Material Model ◽  
The Body ◽  
Model Description ◽  
Material Degradation ◽  
Material Models ◽  
Nonlinear Continuum

At present multiplicative plasticity theories are used to model material degradation of hyperelastic materials within the framework of finite-strain elastoplasticity. The theories assume that the intermediate configuration of the body is unstressed and that such multiaxially stretched bodies do not have compatible unstressed configurations. As a result, there does not exist a motion whose material gradient could define the plastic deformation gradient. The assumption is however not consistent with the theory of nonlinear continuum mechanics and the related theories are not continuum based. In this paper material degradation of a silicone cross-shaped specimen in biaxial tension is studied using a thermodynamically consistent Mooney-Rivlin material model. The material model is based on the first nonlinear continuum theory of finite deformations of elastoplastic media which allows for the development of objective and thermodynamically consistent material models within the framework of finite-strain elastoplasticity. Such material models are independent of the model description and the particularities of the model formulation and moreover they can relate the internal power density of the model to the internal power density of the specimen coming from the tensile test of the modelled material. In this paper a few analysis results are presented and briefly discussed.

scholarly journals A fully coupled two‐phase bone material model

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Mischa Blaszczyk ◽  
Klaus Hackl
Keyword(s):  
Material Model ◽  
Two Phase ◽  
Bone Material ◽  
Fully Coupled

Constitutive inequalities for isotropic elastic solids under finite strain

1970 ◽  
Vol 314 (1519) ◽  
pp. 457-472 ◽  
Keyword(s):  
Scalar Product ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Elastic Solids ◽  
Intrinsic Interest ◽  
Typical Member ◽  
Rates Of Change ◽  
Constitutive Inequalities ◽  
Strain Measures

Possible restrictions on isotropic constitutive laws for finitely deformed elastic solids are examined from the standpoint of Hill (1968). This introduced the notion of conjugate pairs of stress and strain measures, whereby families of contending inequalities can be generated. A typical member inequality stipulates that the scalar product of the rates of change of certain conjugate variables is positive in all circumstances. Interrelations between the various inequalities are explored, and some statical implications are established. The discussion depends on several ancillary theorems which are apparently new; these have, in addition, an intrinsic interest in the broad field of basic stress—strain analysis.

Finite Element Simulation Analysis on Residual Stress Relief of 7075 Aluminum Alloy Ring

2021 ◽  
Vol 1032 ◽  
pp. 135-140
Author(s):  
Shao Feng Wu ◽  
Xiang Sheng Gao ◽  
Xian Rang Zhang ◽  
Han Jun Gao
Keyword(s):  
Residual Stress ◽  
Aluminum Alloy ◽  
Simulation Analysis ◽  
Material Model ◽  
Stress Relief ◽  
Isotropic Hardening ◽  
7075 Aluminum Alloy ◽  
Vibration Stress ◽  
Structural Parts ◽  
Creep Constitutive Model

Vibration stress relief (VSR) and thermal stress relief (TSR) are important method to eliminate the residual stress of structural parts. The thermal vibratory stress relief (TVSR) is a new method to decrease and homogenize the residual stress. Based on the stress relaxation tests and the equivalent vibration equation of modal analysis, the creep constitutive model and the bilinear isotropic hardening plasticity material model (BISO) are combined to establish the numerical simulation model of TVSR of 7075 aluminum alloy ring part. The simulation results show that four different initial blank residual stress levels are obtained after quenching process, and the residual stress elimination and homogenization effect of TSR and TVSR is better than that of VSR. TVSR has a better effect on both residual stress elimination and homogenization, and the residual stress relief rate can reach more than 20%.

Nonlinear Material Model in Part Variation Simulations of Sheet Metals

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Soner Camuz ◽  
Samuel Lorin ◽  
Kristina Wärmefjord ◽  
Rikard Söderberg
Keyword(s):  
Material Model ◽  
Nonlinear Material ◽  
Isotropic Hardening ◽  
Elastoplastic Material ◽  
Processing Unit ◽  
Central Processing ◽  
Physical Experiments ◽  
Linear Relationships ◽  
Influence Coefficients ◽  
Variation Simulation

Current methodologies for variation simulation of compliant sheet metal assemblies and parts are simplified by assuming linear relationships. From the observed physical experiments, it is evident that plastic strains are a source of error that is not captured in the conventional variational simulation methods. This paper presents an adaptation toward an elastoplastic material model with isotropic hardening in the method of influence coefficients (MIC) methodology for variation simulations. The results are presented in two case studies using a benchmark case involving a two-dimensional (2D) quarter symmetric plate with a centered hole, subjected to both uniaxial and biaxial displacement. The adaptation shows a great reduction in central processing unit time with limited effect on the accuracy of the results compared to direct Monte Carlo simulations.

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