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.

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.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Modeling of Thermoplastic Materials for the Process-Simulation of Press-Fit Interconnections on Moulded Interconnected Devices

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Thomas Fellner ◽  
Elena Zukowski ◽  
Jürgen Wilde ◽  
H. Kück ◽  
H. Richter ◽  
...  
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Base Material ◽  
Creep Model ◽  
Assembly Process ◽  
Temperature Dependent ◽  
Reliability Modeling ◽  
Finite Element Software ◽  
Press Fit ◽  
Temperature Loads

This investigation is aimed at the modeling of both the fabrication process and the reliability of press-fit interconnections on moulded interconnect devices (MID). These are multifunctional three-dimensional substrates, produced by thermoplastic injection moulding for large-series applications. The assembly process and subsequently the durability of press-fit interconnections has been modeled and proved with a finite element software. Especially, a simulation tool for process optimizations was created and applied. In order to obtain realistic results, a creep model for the investigated base material, a liquid-crystal polymer (LCP), was generated and verified by experiments. Required friction coefficients between metal pin and base material were determined by adapting simulations and experiments. Retention forces of pins pressed into substrate holes during as well after the assembly process, and after temperature loads were predicted by simulations. Additionally, the decreasing extraction forces over time due to creep in the thermoplastic base material have been predicted for different storage temperatures as well with finite element analyses. Following, the numerical results of the process and reliability modeling were verified by experiments. It is concluded that the behavior of the mechanical contact of the pin-substrate system, can be suitably described time- and temperature-dependent.

Energy-Consistent Finite Element Modelling of Ferromagnetic Hysteresis

2012 ◽  
Author(s):  
Christophe Geuzaine ◽  
Laurent Stainier ◽  
Francois Henrotte
Keyword(s):  
Finite Element ◽  
Magnetic Energy ◽  
Kinematic Hardening ◽  
Hysteresis Loops ◽  
Macroscopic Model ◽  
Dissipated Energy ◽  
Internal Variables ◽  
Incremental Formulation ◽  
Ferromagnetic Hysteresis ◽  
Electromagnetic Models

In this article we propose a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. This variational approach is directly inspired from the kinematic hardening theory of plasticity, which opens the door for novel energy-consistent coupled mechanical/electromagnetic models.

scholarly journals Gradient Nonlocal Enhanced Microprestress-Solidification Theory and Its Finite Element Implementation

2021 ◽  
Vol 8 ◽  
Author(s):  
Teng Tong ◽  
Changqing Du ◽  
Xiaofan Liu ◽  
Siqi Yuan ◽  
Zhao Liu
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Deformation Gradient ◽  
Damage Model ◽  
Reinforced Concrete Beams ◽  
Chain Model ◽  
Finite Element Software ◽  
Order Deformation ◽  
Implicit Solver

Time-dependent responses of cracked concrete structures are complex, due to the intertwined effects between creep, shrinkage, and cracking. There still lacks an effective numerical model to accurately predict their nonlinear long-term deflections. To this end, a computational framework is constructed, of which the aforementioned intertwined effects are properly treated. The model inherits merits of gradient-enhanced damage (GED) model and microprestress-solidification (MPS) theory. By incorporating higher order deformation gradient, the proposed GED-MPS model circumvents damage localization and mesh-sensitive problems encountered in classical continuum damage theory. Moreover, the model reflects creep and shrinkage of concrete with respect to underlying moisture transport and heat transfer. Residing on the Kelvin chain model, rate-type creep formulation works fully compatible with the gradient nonlocal damage model. 1-D illustration of the model reveals that the model could regularize mesh-sensitivity of nonlinear concrete creep affected by cracking. Furthermore, the model depicts long-term deflections and cracking evolutions of simply-supported reinforced concrete beams in an agreed manner. It is noteworthy that the gradient nonlocal enhanced microprestress-solidification theory is implemented in the general finite element software Abaqus/Standard with the implicit solver, which renders the model suitable for large-scale creep-sensitive structures.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

scholarly journals Finite Element Analysis of RC Beams by the Discrete Model and CBIS Model Using LS-DYNA

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Seung H. Yang ◽  
Kwang S. Woo ◽  
Jeong J. Kim ◽  
Jae S. Ahn
Keyword(s):  
Finite Element ◽  
Discrete Model ◽  
Kinematic Hardening ◽  
Material Model ◽  
General Purpose ◽  
Solid Model ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Finite Element Software ◽  
Concrete Elements

There are several techniques to simulate rebar reinforced concrete, such as smeared model, discrete model, embedded model, CLIS (constrained Lagrange in solid) model, and CBIS (constrained beam in solid) model. In this study, however, the interaction between the concrete elements and the reinforcement beam elements is only simulated by the discrete model and CBIS (constrained beam in solid) model. The efficiency and accuracy comparisons are investigated with reference to the analysis results by both models provided by LS-DYNA explicit finite element software. The geometric models are created using LS-PrePost, general purpose preprocessing software for meshing. The meshed models are imported to LS-DYNA where the input files are then analyzed. Winfrith and CSCM concrete material options are employed to describe the concrete damage behavior. The reinforcement material model is capable of isotropic and kinematic hardening plasticity. The load versus midspan deflection curves of the finite element models correlate with those of the experiment. Under the conditions of the same level of accuracy, the CBIS model is evaluated to have the following advantages over the discrete model. First, it has the advantage of reducing the time required for FE modeling; second, saving computer CPU time due to a reduction in total number of nodes; and third, securing a good aspect ratio of concrete elements.

Application of Noninteraction Constitutive Models for Deformation of IN617 Under Combined Extreme Environments

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Bouchenot ◽  
Calvin Cole ◽  
Ali P. Gordon ◽  
Casey Holycross ◽  
Ravi C. Penmetsa
Keyword(s):  
Finite Element ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Extreme Environments ◽  
Constitutive Models ◽  
Original Data ◽  
Industrial Sector ◽  
Cycle Fatigue ◽  
Simple Method ◽  
Finite Element Software

Next-generation, reusable hypersonic aircraft will be subjected to extreme environments that produce complex fatigue loads at high temperatures, reminiscent of the life-limiting thermal and mechanical loads present in large gas-powered land-based turbines. In both of these applications, there is a need for greater fidelity in the constitutive material models employed in finite element simulations, resulting in the transition to nonlinear formulations. One such formulation is the nonlinear kinematic hardening (NLKH) model, which is a plasticity model quickly gaining popularity in the industrial sector, and can be found in commercial finite element software. The drawback to using models like the NLKH model is that the parameterization can be difficult, and the numerical fitting techniques commonly used for such tasks may result in constants devoid of physical meaning. This study presents a simple method to derive these constants by extrapolation of a reduced-order model, where the cyclic Ramberg–Osgood (CRO) formulation is used to obtain the parameters of a three-part NLKH model. This fitting scheme is used with basic literature-based data to fully characterize a constitutive model for Inconel 617 at temperatures between 20 °C and 1000 °C. This model is validated for low-cycle fatigue (LCF), creep-fatigue (CF), thermomechanical fatigue (TMF), and combined thermomechanical-high-cycle fatigue (HCF) using a mix of literature data and original data produced at the Air Force Research Laboratory (AFRL).

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.

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